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Response:

Calculated Shard: 152 (from laksa168)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa152.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://en.wikipedia.org/wiki/String_theory_landscape\')), getAhrefsUnparsedNoserviceFromURL(\'https://en.wikipedia.org/wiki/String_theory_landscape\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape","crawl_time":1774063985,"first_indexed_time":1378522689,"http_code":200,"src_unparsed":"org,wikipedia!en,\/wiki\/String_theory_landscape s443","src_root_hash":"17790707453426894952","history_drop_reason":null,"meta_title":"String theory landscape - Wikipedia","meta_descriptions":[],"attrs_boilerpipe_text":"From Wikipedia, the free encyclopedia\nIn\nstring theory\n, the\nstring theory landscape\n(or\nlandscape of vacua\n) is the collection of possible\nfalse vacua\n,\n[\n1\n]\ntogether comprising a collective \"landscape\" of choices of parameters governing\ncompactifications\n.\nThe term \"landscape\" comes from the notion of a\nfitness landscape\nin\nevolutionary biology\n.\n[\n2\n]\nIt was first applied to cosmology by\nLee Smolin\nin his book\nThe Life of the Cosmos\n(1997), and was first used in the context of string theory by\nLeonard Susskind\n.\n[\n3\n]\nCompactified Calabi–Yau manifolds\n[\nedit\n]\nIn string theory, the estimated count of distinct flux vacua is commonly stated as having a lower bound of\n,\n[\n4\n]\nbut more recently this has been revised to\n,\n[\n5\n]\nand the true number may still be far higher. The large number of possibilities arises from choices of\nCalabi–Yau manifolds\nand choices of generalized\nmagnetic fluxes\nover various\nhomology\ncycles, found in\nF-theory\n.\nIf there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is\nNP complete\n.\n[\n6\n]\nThis is a version of the\nsubset sum problem\n.\nA possible mechanism of string theory vacuum stabilization, now known as the\nKKLT mechanism\n, was proposed in 2003 by\nShamit Kachru\n,\nRenata Kallosh\n,\nAndrei Linde\n, and\nSandip Trivedi\n.\n[\n7\n]\nFine-tuning by the anthropic principle\n[\nedit\n]\nFine-tuning\nof constants like the\ncosmological constant\nor the\nHiggs boson\nmass is usually assumed to occur for precise physical reasons as opposed to taking their particular values at random. That is, these values should be uniquely consistent with underlying physical laws.\nThe number of theoretically allowed configurations has prompted suggestions\n[\naccording to whom?\n]\nthat this is not the case, and that many different vacua are physically realized.\n[\n8\n]\nThe\nanthropic principle\nproposes that fundamental constants may have the values they have because such values are necessary for life (and therefore intelligent observers to measure the constants). The\nanthropic landscape\nthus refers to the collection of those portions of the landscape that are suitable for supporting intelligent life.\nIn 1987,\nSteven Weinberg\nproposed that the observed value of the\ncosmological constant\nwas so small because it is impossible for life to occur in a universe with a much larger cosmological constant.\n[\n9\n]\nWeinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts\n[\nwhich?\n]\nhave been made to apply similar reasoning to models of particle physics.\n[\n10\n]\nSuch attempts are based in the general ideas of\nBayesian probability\n; interpreting probability in a context where it is only possible to draw one\nsample\nfrom a\ndistribution\nis problematic in\nfrequentist probability\nbut not in Bayesian probability, which is not defined in terms of the frequency of repeated events.\nIn such a framework, the probability\nof observing some fundamental parameters\nis given by,\nwhere\nis the prior probability, from fundamental theory, of the parameters\nand\nis the \"anthropic selection function\", determined by the number of \"observers\" that would occur in the universe with parameters\n.\n[\ncitation needed\n]\nThese probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:\n[\ncitation needed\n]\n[\nyear needed\n]\nThe  function\nis completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way.\nThe function\nis completely unknown, since so little is known about the origin of life. Simplified criteria (such as the number of galaxies) must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable universe.\nSimplified approaches\n[\nedit\n]\nTegmark\net al.\nhave recently considered these objections and proposed a simplified anthropic scenario for\naxion\ndark matter\nin which they argue that the first two of these problems do not apply.\n[\n11\n]\nVilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.\n[\n12\n]\nA problem with many of the simplified approaches people\n[\nwho?\n]\nhave tried is that they \"predict\" a cosmological constant that is too large by a factor of 10–1000 orders of magnitude (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed.\n[\n13\n]\n[\n14\n]\n[\n15\n]\nFew dispute the large number of metastable vacua.\n[\ncitation needed\n]\nThe existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial.\n[\nfurther explanation needed\n]\nCosmological constant problem\n[\nedit\n]\nAndrei Linde\n,\nSir Martin Rees\nand\nLeonard Susskind\nadvocate it as a solution to the\ncosmological constant problem\n.\n[\ncitation needed\n]\nWeak scale supersymmetry from the landscape\n[\nedit\n]\nThe string landscape ideas can be applied to the notion of weak scale supersymmetry and the Little Hierarchy problem.\nFor string vacua which include the MSSM (Minimal Supersymmetric Standard Model)  as the low energy effective field theory, all values of SUSY breaking fields\nare expected to be equally likely on the landscape. This led Douglas\n[\n16\n]\nand others to propose that the SUSY breaking scale is distributed as a power\nlaw in the landscape\nwhere\nis the number of F-breaking fields \n(distributed as complex numbers) and\nis the number of D-breaking fields (distributed as real numbers).\nNext, one may impose the Agrawal, Barr, Donoghue, Seckel (ABDS) anthropic requirement\n[\n17\n]\nthat the derived weak scale lie within a factor of a few\nof our measured value (lest nuclei as needed for life as we know it become unstable (the atomic principle)). \nCombining these effects with a mild power-law draw to large soft SUSY breaking terms, \none may calculate the Higgs boson and superparticle masses expected from the landscape.\n[\n18\n]\nThe Higgs mass probability distribution peaks around 125 GeV while sparticles (with the exception of light higgsinos) tend to \nlie well beyond current LHC search limits. This approach is an example of the application of stringy naturalness.\nScientific relevance\n[\nedit\n]\nDavid Gross\nsuggests\n[\ncitation needed\n]\nthat the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the\nSmolin–Susskind debate\non the merits of the landscape.\nThere are several popular books about the anthropic principle in cosmology.\n[\n19\n]\nThe authors of two physics blogs,\nLubos Motl\nand\nPeter Woit\n, are opposed to this use of the anthropic principle.\n[\nwhy?\n]\n[\n20\n]\nSwampland\nExtra dimensions\nM-theory\n^\nThe number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10\n500\n. See\nM. Douglas\n, \"The statistics of string \/ M theory vacua\",\nJHEP\n0305\n, 46 (2003).\narXiv\n:\nhep-th\/0303194\n; S. Ashok and M. Douglas, \"Counting flux vacua\",\nJHEP\n0401\n, 060 (2004).\n^\nBaggott, Jim (2018).\nQuantum Space Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe\n. Oxford University Press. p. 288.\nISBN\n \n978-0-19-253681-5\n.\n^\nL. Smolin, \"Did the universe evolve?\",\nClassical and Quantum Gravity\n9\n, 173–191 (1992). L. Smolin,\nThe Life of the Cosmos\n(Oxford, 1997)\n^\nRead, James; Le Bihan, Baptiste (2021).\n\"The landscape and the multiverse: What's the problem?\"\n.\nSynthese\n.\n199\n(\n3–\n4):\n7749–\n7771.\ndoi\n:\n10.1007\/s11229-021-03137-0\n.\nS2CID\n \n234815857\n.\n^\nTaylor, Washington; Wang, Yi-Nan (2015). \"The F-theory geometry with most flux vacua\".\nJournal of High Energy Physics\n.\n2015\n(12): 164.\narXiv\n:\n1511.03209\n.\nBibcode\n:\n2015JHEP...12..164T\n.\ndoi\n:\n10.1007\/JHEP12(2015)164\n.\nS2CID\n \n41149049\n.\n^\nFrederik Denef; Douglas, Michael R. (2007). \"Computational complexity of the landscape\".\nAnnals of Physics\n.\n322\n(5):\n1096–\n1142.\narXiv\n:\nhep-th\/0602072\n.\nBibcode\n:\n2007AnPhy.322.1096D\n.\ndoi\n:\n10.1016\/j.aop.2006.07.013\n.\nS2CID\n \n281586\n.\n^\nKachru, Shamit; Kallosh, Renata; Linde, Andrei; Trivedi, Sandip P. (2003). \"de Sitter Vacua in String Theory\".\nPhysical Review D\n.\n68\n(4) 046005.\narXiv\n:\nhep-th\/0301240\n.\nBibcode\n:\n2003PhRvD..68d6005K\n.\ndoi\n:\n10.1103\/PhysRevD.68.046005\n.\nS2CID\n \n119482182\n.\n^\nL. Susskind, \"The anthropic landscape of string theory\",\narXiv\n:\nhep-th\/0302219\n.\n^\nS. Weinberg, \"Anthropic bound on the cosmological constant\",\nPhys. Rev. Lett.\n59\n, 2607 (1987).\n^\nS. M. Carroll, \"Is our universe natural?\" (2005)\narXiv\n:\nhep-th\/0512148\nreviews a number of proposals in preprints dated 2004\/5.\n^\nM. Tegmark, A. Aguirre, M. Rees and F. Wilczek, \"Dimensionless constants, cosmology and other dark matters\",\narXiv\n:\nastro-ph\/0511774\n. F. Wilczek, \"Enlightenment, knowledge, ignorance, temptation\",\narXiv\n:\nhep-ph\/0512187\n. See also the discussion at\n[1]\n.\n^\nSee,\ne.g.\nAlexander Vilenkin (2007). \"A measure of the multiverse\".\nJournal of Physics A: Mathematical and Theoretical\n.\n40\n(25):\n6777–\n6785.\narXiv\n:\nhep-th\/0609193\n.\nBibcode\n:\n2007JPhA...40.6777V\n.\ndoi\n:\n10.1088\/1751-8113\/40\/25\/S22\n.\nS2CID\n \n119390736\n.\n^\nAbraham Loeb (2006). \"An observational test for the anthropic origin of the cosmological constant\".\nJournal of Cosmology and Astroparticle Physics\n.\n0605\n(5): 009.\narXiv\n:\nastro-ph\/0604242\n.\nBibcode\n:\n2006JCAP...05..009L\n.\ndoi\n:\n10.1088\/1475-7516\/2006\/05\/009\n.\nS2CID\n \n39340203\n.\n^\nJaume Garriga & Alexander Vilenkin (2006). \"Anthropic prediction for Lambda and the Q catastrophe\".\nProg. Theor. Phys. Suppl\n.\n163\n:\n245–\n57.\narXiv\n:\nhep-th\/0508005\n.\nBibcode\n:\n2006PThPS.163..245G\n.\ndoi\n:\n10.1143\/PTPS.163.245\n.\nS2CID\n \n118936307\n.\n^\nDelia Schwartz-Perlov & Alexander Vilenkin (2006). \"Probabilities in the Bousso-Polchinski multiverse\".\nJournal of Cosmology and Astroparticle Physics\n.\n0606\n(6): 010.\narXiv\n:\nhep-th\/0601162\n.\nBibcode\n:\n2006JCAP...06..010S\n.\ndoi\n:\n10.1088\/1475-7516\/2006\/06\/010\n.\nS2CID\n \n119337679\n.\n^\nM. R. Douglas, \"Statistical analysis of the supersymmetry breaking scale\",\narXiv\n:\nhep-th\/0405279\n.\n^\nV. Agrawal, S. M. Barr, J. F. Donoghue and \nD. Seckel, \"Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking\",\nPhys. Rev. Lett.\n80\n, 1822 (1998).\narXiv\n:\nhep-ph\/9801253\n^\nH. Baer, V. Barger, H. Serce and K. Sinha, \"Higgs and superparticle mass predictions from the landscape\",\nJHEP\n03\n, 002 (2018),\narXiv\n:\n1712.01399\n.\n^\nL. Susskind,\nThe cosmic landscape: string theory and the illusion of intelligent design\n(Little, Brown, 2005). M. J. Rees,\nJust six numbers: the deep forces that shape the universe\n(Basic Books, 2001). R. Bousso and J. Polchinski, \"The string theory landscape\",\nSci. Am.\n291\n, 60–69 (2004).\n^\nMotl's blog criticized the anthropic principle and Woit's\nblog\nfrequently attacks the anthropic string landscape.\nString landscape; moduli stabilization; flux vacua; flux compactification\non\narxiv.org\n.\nCvetič, Mirjam\n; García-Etxebarria, Iñaki; Halverson, James (March 2011). \"On the computation of non-perturbative effective potentials in the string theory landscape\".\nFortschritte der Physik\n.\n59\n(\n3–\n4):\n243–\n283.\narXiv\n:\n1009.5386\n.\nBibcode\n:\n2011ForPh..59..243C\n.\ndoi\n:\n10.1002\/prop.201000093\n.\nS2CID\n \n46634583\n.","attrs_markdown":"[Jump to content](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#bodyContent)\n\nMain menu\n\nMain menu\n\nmove to sidebar\n\nhide\n\nNavigation\n\n- [Main page](https:\/\/en.wikipedia.org\/wiki\/Main_Page \"Visit the main page [z]\")\n- [Contents](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Contents \"Guides to browsing Wikipedia\")\n- [Current events](https:\/\/en.wikipedia.org\/wiki\/Portal:Current_events \"Articles related to current events\")\n- [Random article](https:\/\/en.wikipedia.org\/wiki\/Special:Random \"Visit a randomly selected article [x]\")\n- [About Wikipedia](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:About \"Learn about Wikipedia and how it works\")\n- [Contact us](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Contact_us \"How to contact Wikipedia\")\n\nContribute\n\n- [Help](https:\/\/en.wikipedia.org\/wiki\/Help:Contents \"Guidance on how to use and edit Wikipedia\")\n- [Learn to edit](https:\/\/en.wikipedia.org\/wiki\/Help:Introduction \"Learn how to edit Wikipedia\")\n- [Community portal](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Community_portal \"The hub for editors\")\n- [Recent changes](https:\/\/en.wikipedia.org\/wiki\/Special:RecentChanges \"A list of recent changes to Wikipedia [r]\")\n- [Upload file](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:File_upload_wizard \"Add images or other media for use on Wikipedia\")\n- [Special pages](https:\/\/en.wikipedia.org\/wiki\/Special:SpecialPages \"A list of all special pages [q]\")\n\n[![](https:\/\/en.wikipedia.org\/static\/images\/icons\/enwiki-25.svg) ![Wikipedia](https:\/\/en.wikipedia.org\/static\/images\/mobile\/copyright\/wikipedia-wordmark-en-25.svg) ![The Free Encyclopedia](https:\/\/en.wikipedia.org\/static\/images\/mobile\/copyright\/wikipedia-tagline-en-25.svg)](https:\/\/en.wikipedia.org\/wiki\/Main_Page)\n\n[Search](https:\/\/en.wikipedia.org\/wiki\/Special:Search \"Search Wikipedia [f]\")\n\nAppearance\n\n- [Donate](https:\/\/donate.wikimedia.org\/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en)\n- [Create account](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:CreateAccount&returnto=String+theory+landscape \"You are encouraged to create an account and log in; however, it is not mandatory\")\n- [Log in](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:UserLogin&returnto=String+theory+landscape \"You're encouraged to log in; however, it's not mandatory. [o]\")\n\nPersonal tools\n\n- [Donate](https:\/\/donate.wikimedia.org\/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en)\n- [Create account](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:CreateAccount&returnto=String+theory+landscape \"You are encouraged to create an account and log in; however, it is not mandatory\")\n- [Log in](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:UserLogin&returnto=String+theory+landscape \"You're encouraged to log in; however, it's not mandatory. [o]\")\n\n## Contents\nmove to sidebar\n\nhide\n\n- [(Top)](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape)\n- [1 Compactified Calabi–Yau manifolds](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#Compactified_Calabi%E2%80%93Yau_manifolds)\n- [2 Fine-tuning by the anthropic principle](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#Fine-tuning_by_the_anthropic_principle)\n  Toggle Fine-tuning by the anthropic principle subsection\n  - [2\\.1 Weinberg model](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#Weinberg_model)\n  - [2\\.2 Simplified approaches](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#Simplified_approaches)\n  - [2\\.3 Interpretation](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#Interpretation)\n    - [2\\.3.1 Cosmological constant problem](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#Cosmological_constant_problem)\n  - [2\\.4 Weak scale supersymmetry from the landscape](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#Weak_scale_supersymmetry_from_the_landscape)\n    - [2\\.4.1 Scientific relevance](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#Scientific_relevance)\n    - [2\\.4.2 Popular reception](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#Popular_reception)\n- [3 See also](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#See_also)\n- [4 References](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#References)\n- [5 External links](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#External_links)\n\nToggle the table of contents\n\n# String theory landscape\n7 languages\n\n- [Беларуская](https:\/\/be.wikipedia.org\/wiki\/%D0%9B%D0%B0%D0%BD%D0%B4%D1%88%D0%B0%D1%84%D1%82_%D1%82%D1%8D%D0%BE%D1%80%D1%8B%D1%96_%D1%81%D1%82%D1%80%D1%83%D0%BD \"Ландшафт тэорыі струн – Belarusian\")\n- [Deutsch](https:\/\/de.wikipedia.org\/wiki\/Stringlandschaft \"Stringlandschaft – German\")\n- 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[Printable version](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&printable=yes \"Printable version of this page [p]\")\n\nIn other projects\n\n- [Wikidata item](https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/Q4253887 \"Structured data on this page hosted by Wikidata [g]\")\n\nAppearance\n\nmove to sidebar\n\nhide\n\nFrom Wikipedia, the free encyclopedia\n\nCollection of possible string theory vacua\n\n| [String theory](https:\/\/en.wikipedia.org\/wiki\/String_theory \"String theory\") |\n|---|\n| [![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/8\/8c\/Calabi_yau_formatted.svg\/120px-Calabi_yau_formatted.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:Calabi_yau_formatted.svg) |\n| Fundamental objects |\n| [String](https:\/\/en.wikipedia.org\/wiki\/String_\\(physics\\) \"String (physics)\") [Cosmic string](https:\/\/en.wikipedia.org\/wiki\/Cosmic_string \"Cosmic string\") [Brane](https:\/\/en.wikipedia.org\/wiki\/Brane \"Brane\") [D-brane](https:\/\/en.wikipedia.org\/wiki\/D-brane \"D-brane\") |\n| Perturbative theory |\n| [Bosonic](https:\/\/en.wikipedia.org\/wiki\/Bosonic_string_theory \"Bosonic string theory\") [Superstring](https:\/\/en.wikipedia.org\/wiki\/Superstring_theory \"Superstring theory\") ([Type I](https:\/\/en.wikipedia.org\/wiki\/Type_I_string_theory \"Type I string theory\"), [Type II](https:\/\/en.wikipedia.org\/wiki\/Type_II_string_theory \"Type II string theory\"), [Heterotic](https:\/\/en.wikipedia.org\/wiki\/Heterotic_string_theory \"Heterotic string theory\")) |\n| Non-perturbative results |\n| [S-duality](https:\/\/en.wikipedia.org\/wiki\/S-duality \"S-duality\") [T-duality](https:\/\/en.wikipedia.org\/wiki\/T-duality \"T-duality\") [U-duality](https:\/\/en.wikipedia.org\/wiki\/U-duality \"U-duality\") [M-theory](https:\/\/en.wikipedia.org\/wiki\/M-theory \"M-theory\") [F-theory](https:\/\/en.wikipedia.org\/wiki\/F-theory \"F-theory\") [AdS\/CFT correspondence](https:\/\/en.wikipedia.org\/wiki\/AdS\/CFT_correspondence \"AdS\/CFT correspondence\") |\n| Phenomenology |\n| [Phenomenology](https:\/\/en.wikipedia.org\/wiki\/String_phenomenology \"String phenomenology\") [Cosmology](https:\/\/en.wikipedia.org\/wiki\/String_cosmology \"String cosmology\") [Brane cosmology](https:\/\/en.wikipedia.org\/wiki\/Brane_cosmology \"Brane cosmology\") [Landscape]() |\n| Mathematics |\n| [Geometric Langlands correspondence](https:\/\/en.wikipedia.org\/wiki\/Geometric_Langlands_correspondence \"Geometric Langlands correspondence\") [Mirror symmetry](https:\/\/en.wikipedia.org\/wiki\/Mirror_symmetry_\\(string_theory\\) \"Mirror symmetry (string theory)\") [Monstrous moonshine](https:\/\/en.wikipedia.org\/wiki\/Monstrous_moonshine \"Monstrous moonshine\") [Vertex algebra](https:\/\/en.wikipedia.org\/wiki\/Vertex_algebra \"Vertex algebra\") [K-theory](https:\/\/en.wikipedia.org\/wiki\/K-theory_\\(physics\\) \"K-theory (physics)\") |\n| Related concepts [Theory of everything](https:\/\/en.wikipedia.org\/wiki\/Theory_of_everything \"Theory of everything\") [Conformal field theory](https:\/\/en.wikipedia.org\/wiki\/Conformal_field_theory \"Conformal field theory\") [Quantum gravity](https:\/\/en.wikipedia.org\/wiki\/Quantum_gravity \"Quantum gravity\") [Supersymmetry](https:\/\/en.wikipedia.org\/wiki\/Supersymmetry \"Supersymmetry\") [Supergravity](https:\/\/en.wikipedia.org\/wiki\/Supergravity \"Supergravity\") [Twistor string theory](https:\/\/en.wikipedia.org\/wiki\/Twistor_string_theory \"Twistor string theory\") [*N* = 4 supersymmetric Yang–Mills theory](https:\/\/en.wikipedia.org\/wiki\/N_%3D_4_supersymmetric_Yang%E2%80%93Mills_theory \"N = 4 supersymmetric Yang–Mills theory\") [Kaluza–Klein theory](https:\/\/en.wikipedia.org\/wiki\/Kaluza%E2%80%93Klein_theory \"Kaluza–Klein theory\") [Multiverse](https:\/\/en.wikipedia.org\/wiki\/Multiverse \"Multiverse\") [Holographic principle](https:\/\/en.wikipedia.org\/wiki\/Holographic_principle \"Holographic principle\") |\n| Theorists [Aganagić](https:\/\/en.wikipedia.org\/wiki\/Mina_Aganagi%C4%87 \"Mina Aganagić\") [Arkani-Hamed](https:\/\/en.wikipedia.org\/wiki\/Nima_Arkani-Hamed \"Nima Arkani-Hamed\") [Atiyah](https:\/\/en.wikipedia.org\/wiki\/Michael_Atiyah \"Michael Atiyah\") [Banks](https:\/\/en.wikipedia.org\/wiki\/Tom_Banks_\\(physicist\\) \"Tom Banks (physicist)\") [Berenstein](https:\/\/en.wikipedia.org\/wiki\/David_Berenstein \"David Berenstein\") [Bousso](https:\/\/en.wikipedia.org\/wiki\/Raphael_Bousso \"Raphael Bousso\") [Costello](https:\/\/en.wikipedia.org\/wiki\/Kevin_Costello \"Kevin Costello\") [Curtright](https:\/\/en.wikipedia.org\/wiki\/Thomas_Curtright \"Thomas Curtright\") [Dijkgraaf](https:\/\/en.wikipedia.org\/wiki\/Robbert_Dijkgraaf \"Robbert Dijkgraaf\") [Distler](https:\/\/en.wikipedia.org\/wiki\/Jacques_Distler \"Jacques Distler\") [Douglas](https:\/\/en.wikipedia.org\/wiki\/Michael_R._Douglas \"Michael R. Douglas\") [Duff](https:\/\/en.wikipedia.org\/wiki\/Michael_Duff_\\(physicist\\) \"Michael Duff (physicist)\") [Dvali](https:\/\/en.wikipedia.org\/wiki\/Gia_Dvali \"Gia Dvali\") [Ferrara](https:\/\/en.wikipedia.org\/wiki\/Sergio_Ferrara \"Sergio Ferrara\") [Fischler](https:\/\/en.wikipedia.org\/wiki\/Willy_Fischler \"Willy Fischler\") [Friedan](https:\/\/en.wikipedia.org\/wiki\/Daniel_Friedan \"Daniel Friedan\") [Gates](https:\/\/en.wikipedia.org\/wiki\/Sylvester_James_Gates \"Sylvester James Gates\") [Gliozzi](https:\/\/en.wikipedia.org\/wiki\/Ferdinando_Gliozzi \"Ferdinando Gliozzi\") [Gopakumar](https:\/\/en.wikipedia.org\/wiki\/Rajesh_Gopakumar \"Rajesh Gopakumar\") [Green](https:\/\/en.wikipedia.org\/wiki\/Michael_Green_\\(physicist\\) \"Michael Green (physicist)\") [Greene](https:\/\/en.wikipedia.org\/wiki\/Brian_Greene \"Brian Greene\") [Gross](https:\/\/en.wikipedia.org\/wiki\/David_Gross \"David Gross\") [Gubser](https:\/\/en.wikipedia.org\/wiki\/Steven_Gubser \"Steven Gubser\") [Gukov](https:\/\/en.wikipedia.org\/wiki\/Sergei_Gukov \"Sergei Gukov\") [Guth](https:\/\/en.wikipedia.org\/wiki\/Alan_Guth \"Alan Guth\") [Hanson](https:\/\/en.wikipedia.org\/wiki\/Andrew_J._Hanson \"Andrew J. Hanson\") [Harvey](https:\/\/en.wikipedia.org\/wiki\/Jeffrey_A._Harvey \"Jeffrey A. Harvey\") [Hořava](https:\/\/en.wikipedia.org\/wiki\/Petr_Ho%C5%99ava_\\(theorist\\) \"Petr Hořava (theorist)\") [Horowitz](https:\/\/en.wikipedia.org\/wiki\/Gary_Horowitz \"Gary Horowitz\") [Gibbons](https:\/\/en.wikipedia.org\/wiki\/Gary_Gibbons \"Gary Gibbons\") [Kachru](https:\/\/en.wikipedia.org\/wiki\/Shamit_Kachru \"Shamit Kachru\") [Kaku](https:\/\/en.wikipedia.org\/wiki\/Michio_Kaku \"Michio Kaku\") [Kallosh](https:\/\/en.wikipedia.org\/wiki\/Renata_Kallosh \"Renata Kallosh\") [Kaluza](https:\/\/en.wikipedia.org\/wiki\/Theodor_Kaluza \"Theodor Kaluza\") [Kapustin](https:\/\/en.wikipedia.org\/wiki\/Anton_Kapustin \"Anton Kapustin\") [Klebanov](https:\/\/en.wikipedia.org\/wiki\/Igor_Klebanov \"Igor Klebanov\") [Knizhnik](https:\/\/en.wikipedia.org\/wiki\/Vadim_Knizhnik \"Vadim Knizhnik\") [Kontsevich](https:\/\/en.wikipedia.org\/wiki\/Maxim_Kontsevich \"Maxim Kontsevich\") [Klein](https:\/\/en.wikipedia.org\/wiki\/Oskar_Klein \"Oskar Klein\") [Linde](https:\/\/en.wikipedia.org\/wiki\/Andrei_Linde \"Andrei Linde\") [Maldacena](https:\/\/en.wikipedia.org\/wiki\/Juan_Mart%C3%ADn_Maldacena \"Juan Martín Maldacena\") [Mandelstam](https:\/\/en.wikipedia.org\/wiki\/Stanley_Mandelstam \"Stanley Mandelstam\") [Marolf](https:\/\/en.wikipedia.org\/wiki\/Donald_Marolf \"Donald Marolf\") [Martinec](https:\/\/en.wikipedia.org\/wiki\/Emil_Martinec \"Emil Martinec\") [Minwalla](https:\/\/en.wikipedia.org\/wiki\/Shiraz_Minwalla \"Shiraz Minwalla\") [Moore](https:\/\/en.wikipedia.org\/wiki\/Greg_Moore_\\(physicist\\) \"Greg Moore (physicist)\") [Motl](https:\/\/en.wikipedia.org\/wiki\/Lubo%C5%A1_Motl \"Luboš Motl\") [Mukhi](https:\/\/en.wikipedia.org\/wiki\/Sunil_Mukhi \"Sunil Mukhi\") [Myers](https:\/\/en.wikipedia.org\/wiki\/Robert_Myers_\\(physicist\\) \"Robert Myers (physicist)\") [Nanopoulos](https:\/\/en.wikipedia.org\/wiki\/Dimitri_Nanopoulos \"Dimitri Nanopoulos\") [Năstase](https:\/\/en.wikipedia.org\/wiki\/Hora%C8%9Biu_N%C4%83stase \"Horațiu Năstase\") [Nekrasov](https:\/\/en.wikipedia.org\/wiki\/Nikita_Nekrasov \"Nikita Nekrasov\") [Neveu](https:\/\/en.wikipedia.org\/wiki\/Andr%C3%A9_Neveu \"André Neveu\") [Nielsen](https:\/\/en.wikipedia.org\/wiki\/Holger_Bech_Nielsen \"Holger Bech Nielsen\") [van Nieuwenhuizen](https:\/\/en.wikipedia.org\/wiki\/Peter_van_Nieuwenhuizen \"Peter van Nieuwenhuizen\") [Novikov](https:\/\/en.wikipedia.org\/wiki\/Sergei_Novikov_\\(mathematician\\) \"Sergei Novikov (mathematician)\") [Olive](https:\/\/en.wikipedia.org\/wiki\/David_Olive \"David Olive\") [Ooguri](https:\/\/en.wikipedia.org\/wiki\/Hirosi_Ooguri \"Hirosi Ooguri\") [Ovrut](https:\/\/en.wikipedia.org\/wiki\/Burt_Ovrut \"Burt Ovrut\") [Polchinski](https:\/\/en.wikipedia.org\/wiki\/Joseph_Polchinski \"Joseph Polchinski\") [Polyakov](https:\/\/en.wikipedia.org\/wiki\/Alexander_Markovich_Polyakov \"Alexander Markovich Polyakov\") [Rajaraman](https:\/\/en.wikipedia.org\/wiki\/Arvind_Rajaraman \"Arvind Rajaraman\") [Ramond](https:\/\/en.wikipedia.org\/wiki\/Pierre_Ramond \"Pierre Ramond\") [Randall](https:\/\/en.wikipedia.org\/wiki\/Lisa_Randall \"Lisa Randall\") [Randjbar-Daemi](https:\/\/en.wikipedia.org\/wiki\/Seifallah_Randjbar-Daemi \"Seifallah Randjbar-Daemi\") [Roček](https:\/\/en.wikipedia.org\/wiki\/Martin_Ro%C4%8Dek \"Martin Roček\") [Rohm](https:\/\/en.wikipedia.org\/wiki\/Ryan_Rohm \"Ryan Rohm\") [Sagnotti](https:\/\/en.wikipedia.org\/wiki\/Augusto_Sagnotti \"Augusto Sagnotti\") [Scherk](https:\/\/en.wikipedia.org\/wiki\/Jo%C3%ABl_Scherk \"Joël Scherk\") [Schwarz](https:\/\/en.wikipedia.org\/wiki\/John_Henry_Schwarz \"John Henry Schwarz\") [Seiberg](https:\/\/en.wikipedia.org\/wiki\/Nathan_Seiberg \"Nathan Seiberg\") [Sen](https:\/\/en.wikipedia.org\/wiki\/Ashoke_Sen \"Ashoke Sen\") [Shenker](https:\/\/en.wikipedia.org\/wiki\/Stephen_Shenker \"Stephen Shenker\") [Siegel](https:\/\/en.wikipedia.org\/wiki\/Warren_Siegel \"Warren Siegel\") [Silverstein](https:\/\/en.wikipedia.org\/wiki\/Eva_Silverstein \"Eva Silverstein\") [Sơn](https:\/\/en.wikipedia.org\/wiki\/%C4%90%C3%A0m_Thanh_S%C6%A1n \"Đàm Thanh Sơn\") [Staudacher](https:\/\/en.wikipedia.org\/wiki\/Matthias_Staudacher \"Matthias Staudacher\") [Steinhardt](https:\/\/en.wikipedia.org\/wiki\/Paul_Steinhardt \"Paul Steinhardt\") [Strominger](https:\/\/en.wikipedia.org\/wiki\/Andrew_Strominger \"Andrew Strominger\") [Sundrum](https:\/\/en.wikipedia.org\/wiki\/Raman_Sundrum \"Raman Sundrum\") [Susskind](https:\/\/en.wikipedia.org\/wiki\/Leonard_Susskind \"Leonard Susskind\") ['t Hooft](https:\/\/en.wikipedia.org\/wiki\/Gerard_%27t_Hooft \"Gerard 't Hooft\") [Townsend](https:\/\/en.wikipedia.org\/wiki\/Paul_Townsend \"Paul Townsend\") [Trivedi](https:\/\/en.wikipedia.org\/wiki\/Sandip_Trivedi \"Sandip Trivedi\") [Turok](https:\/\/en.wikipedia.org\/wiki\/Neil_Turok \"Neil Turok\") [Vafa](https:\/\/en.wikipedia.org\/wiki\/Cumrun_Vafa \"Cumrun Vafa\") [Veneziano](https:\/\/en.wikipedia.org\/wiki\/Gabriele_Veneziano \"Gabriele Veneziano\") [Verlinde](https:\/\/en.wikipedia.org\/wiki\/Erik_Verlinde \"Erik Verlinde\") [Verlinde](https:\/\/en.wikipedia.org\/wiki\/Herman_Verlinde \"Herman Verlinde\") [Wess](https:\/\/en.wikipedia.org\/wiki\/Julius_Wess \"Julius Wess\") [Witten](https:\/\/en.wikipedia.org\/wiki\/Edward_Witten \"Edward Witten\") [Yau](https:\/\/en.wikipedia.org\/wiki\/Shing-Tung_Yau \"Shing-Tung Yau\") [Yoneya](https:\/\/en.wikipedia.org\/wiki\/Tamiaki_Yoneya \"Tamiaki Yoneya\") [Zamolodchikov](https:\/\/en.wikipedia.org\/wiki\/Alexander_Zamolodchikov \"Alexander Zamolodchikov\") [Zamolodchikov](https:\/\/en.wikipedia.org\/wiki\/Alexei_Zamolodchikov \"Alexei Zamolodchikov\") [Zaslow](https:\/\/en.wikipedia.org\/wiki\/Eric_Zaslow \"Eric Zaslow\") [Zumino](https:\/\/en.wikipedia.org\/wiki\/Bruno_Zumino \"Bruno Zumino\") [Zwiebach](https:\/\/en.wikipedia.org\/wiki\/Barton_Zwiebach \"Barton Zwiebach\") |\n| [History](https:\/\/en.wikipedia.org\/wiki\/History_of_string_theory \"History of string theory\") [Glossary](https:\/\/en.wikipedia.org\/wiki\/Glossary_of_string_theory \"Glossary of string theory\") |\n| [v](https:\/\/en.wikipedia.org\/wiki\/Template:String_theory \"Template:String theory\") [t](https:\/\/en.wikipedia.org\/wiki\/Template_talk:String_theory \"Template talk:String theory\") [e](https:\/\/en.wikipedia.org\/wiki\/Special:EditPage\/Template:String_theory \"Special:EditPage\/Template:String theory\") |\n\nIn [string theory](https:\/\/en.wikipedia.org\/wiki\/String_theory \"String theory\"), the **string theory landscape** (or **landscape of vacua**) is the collection of possible [false vacua](https:\/\/en.wikipedia.org\/wiki\/False_vacuum \"False vacuum\"),[\\[1\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-Ashok-1) together comprising a collective \"landscape\" of choices of parameters governing [compactifications](https:\/\/en.wikipedia.org\/wiki\/Compactification_\\(physics\\) \"Compactification (physics)\").\n\nThe term \"landscape\" comes from the notion of a [fitness landscape](https:\/\/en.wikipedia.org\/wiki\/Fitness_landscape \"Fitness landscape\") in [evolutionary biology](https:\/\/en.wikipedia.org\/wiki\/Evolutionary_biology \"Evolutionary biology\").[\\[2\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-2) It was first applied to cosmology by [Lee Smolin](https:\/\/en.wikipedia.org\/wiki\/Lee_Smolin \"Lee Smolin\") in his book *[The Life of the Cosmos](https:\/\/en.wikipedia.org\/wiki\/The_Life_of_the_Cosmos \"The Life of the Cosmos\")* (1997), and was first used in the context of string theory by [Leonard Susskind](https:\/\/en.wikipedia.org\/wiki\/Leonard_Susskind \"Leonard Susskind\").[\\[3\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-3)\n\n## Compactified Calabi–Yau manifolds\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=1 \"Edit section: Compactified Calabi–Yau manifolds\")\\]\n\nMain article: [Compactification (physics)](https:\/\/en.wikipedia.org\/wiki\/Compactification_\\(physics\\) \"Compactification (physics)\")\n\nIn string theory, the estimated count of distinct flux vacua is commonly stated as having a lower bound of 10 500 {\\\\displaystyle 10^{500}} ![{\\\\displaystyle 10^{500}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/9fc79f91eb42fdee58d7e3e2d441013ad2488959),[\\[4\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-4) but more recently this has been revised to 10 272 , 000 {\\\\displaystyle 10^{272,000}} ![{\\\\displaystyle 10^{272,000}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c7ea2462969aa025b37c43ee26b6a3e026316b53),[\\[5\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-5) and the true number may still be far higher. The large number of possibilities arises from choices of [Calabi–Yau manifolds](https:\/\/en.wikipedia.org\/wiki\/Calabi%E2%80%93Yau_manifold \"Calabi–Yau manifold\") and choices of generalized [magnetic fluxes](https:\/\/en.wikipedia.org\/wiki\/Magnetic_flux \"Magnetic flux\") over various [homology](https:\/\/en.wikipedia.org\/wiki\/Homology_\\(mathematics\\) \"Homology (mathematics)\") cycles, found in [F-theory](https:\/\/en.wikipedia.org\/wiki\/F-theory \"F-theory\").\n\nIf there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is [NP complete](https:\/\/en.wikipedia.org\/wiki\/NP_complete \"NP complete\").[\\[6\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-6) This is a version of the [subset sum problem](https:\/\/en.wikipedia.org\/wiki\/Subset_sum_problem \"Subset sum problem\").\n\nA possible mechanism of string theory vacuum stabilization, now known as the **KKLT mechanism**, was proposed in 2003 by [Shamit Kachru](https:\/\/en.wikipedia.org\/wiki\/Shamit_Kachru \"Shamit Kachru\"), [Renata Kallosh](https:\/\/en.wikipedia.org\/wiki\/Renata_Kallosh \"Renata Kallosh\"), [Andrei Linde](https:\/\/en.wikipedia.org\/wiki\/Andrei_Linde \"Andrei Linde\"), and [Sandip Trivedi](https:\/\/en.wikipedia.org\/wiki\/Sandip_Trivedi \"Sandip Trivedi\").[\\[7\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-7)\n\n## Fine-tuning by the anthropic principle\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=2 \"Edit section: Fine-tuning by the anthropic principle\")\\]\n\nMain articles: [Fine-tuning (physics)](https:\/\/en.wikipedia.org\/wiki\/Fine-tuning_\\(physics\\) \"Fine-tuning (physics)\") and [Anthropic principle](https:\/\/en.wikipedia.org\/wiki\/Anthropic_principle \"Anthropic principle\")\n\n[Fine-tuning](https:\/\/en.wikipedia.org\/wiki\/Fine-tuning_\\(physics\\) \"Fine-tuning (physics)\") of constants like the [cosmological constant](https:\/\/en.wikipedia.org\/wiki\/Cosmological_constant \"Cosmological constant\") or the [Higgs boson](https:\/\/en.wikipedia.org\/wiki\/Higgs_boson \"Higgs boson\") mass is usually assumed to occur for precise physical reasons as opposed to taking their particular values at random. That is, these values should be uniquely consistent with underlying physical laws.\n\nThe number of theoretically allowed configurations has prompted suggestions\\[*[according to whom?](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Manual_of_Style\/Words_to_watch#Unsupported_attributions \"Wikipedia:Manual of Style\/Words to watch\")*\\] that this is not the case, and that many different vacua are physically realized.[\\[8\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-8) The [anthropic principle](https:\/\/en.wikipedia.org\/wiki\/Anthropic_principle \"Anthropic principle\") proposes that fundamental constants may have the values they have because such values are necessary for life (and therefore intelligent observers to measure the constants). The *anthropic landscape* thus refers to the collection of those portions of the landscape that are suitable for supporting intelligent life.\n\n### Weinberg model\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=3 \"Edit section: Weinberg model\")\\]\n\nIn 1987, [Steven Weinberg](https:\/\/en.wikipedia.org\/wiki\/Steven_Weinberg \"Steven Weinberg\") proposed that the observed value of the [cosmological constant](https:\/\/en.wikipedia.org\/wiki\/Cosmological_constant \"Cosmological constant\") was so small because it is impossible for life to occur in a universe with a much larger cosmological constant.[\\[9\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-9)\n\nWeinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts\\[*[which?](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Avoid_weasel_words \"Wikipedia:Avoid weasel words\")*\\] have been made to apply similar reasoning to models of particle physics.[\\[10\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-10)\n\nSuch attempts are based in the general ideas of [Bayesian probability](https:\/\/en.wikipedia.org\/wiki\/Bayesian_probability \"Bayesian probability\"); interpreting probability in a context where it is only possible to draw one [sample](https:\/\/en.wikipedia.org\/wiki\/Sample_size \"Sample size\") from a [distribution](https:\/\/en.wikipedia.org\/wiki\/Probability_distribution \"Probability distribution\") is problematic in [frequentist probability](https:\/\/en.wikipedia.org\/wiki\/Frequentist_probability \"Frequentist probability\") but not in Bayesian probability, which is not defined in terms of the frequency of repeated events.\n\nIn such a framework, the probability P ( x ) {\\\\displaystyle P(x)} ![{\\\\displaystyle P(x)}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/89833156eff2c51bfb8750db3306a0544ce34e14) of observing some fundamental parameters x {\\\\displaystyle x} ![{\\\\displaystyle x}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/87f9e315fd7e2ba406057a97300593c4802b53e4) is given by,\n\nP\n\n(\n\nx\n\n)\n\n\\=\n\nP\n\np\n\nr\n\ni\n\no\n\nr\n\n(\n\nx\n\n)\n\n×\n\nP\n\ns\n\ne\n\nl\n\ne\n\nc\n\nt\n\ni\n\no\n\nn\n\n(\n\nx\n\n)\n\n,\n\n{\\\\displaystyle P(x)=P\\_{\\\\mathrm {prior} }(x)\\\\times P\\_{\\\\mathrm {selection} }(x),}\n\n![{\\\\displaystyle P(x)=P\\_{\\\\mathrm {prior} }(x)\\\\times P\\_{\\\\mathrm {selection} }(x),}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/cd5c5e9caa69d16bda58b1d40e39d5f19308f211)\n\nwhere P p r i o r {\\\\displaystyle P\\_{\\\\mathrm {prior} }} ![{\\\\displaystyle P\\_{\\\\mathrm {prior} }}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/8b9334b97d41d76b64c846d2c73f5e8009acde1e) is the prior probability, from fundamental theory, of the parameters x {\\\\displaystyle x} ![{\\\\displaystyle x}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/87f9e315fd7e2ba406057a97300593c4802b53e4) and P s e l e c t i o n {\\\\displaystyle P\\_{\\\\mathrm {selection} }} ![{\\\\displaystyle P\\_{\\\\mathrm {selection} }}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f83c7cd3c00307571cd5af18a6f4029cf1252faa) is the \"anthropic selection function\", determined by the number of \"observers\" that would occur in the universe with parameters x {\\\\displaystyle x} ![{\\\\displaystyle x}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/87f9e315fd7e2ba406057a97300593c4802b53e4).\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\nThese probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\\[*[year needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Manual_of_Style\/Dates_and_numbers \"Wikipedia:Manual of Style\/Dates and numbers\")*\\]\n\n- The function\n  P\n  \n  p\n  \n  r\n  \n  i\n  \n  o\n  \n  r\n  \n  {\\\\displaystyle P\\_{\\\\mathrm {prior} }}\n  \n  ![{\\\\displaystyle P\\_{\\\\mathrm {prior} }}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/8b9334b97d41d76b64c846d2c73f5e8009acde1e)\n  is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way.\n- The function\n  P\n  \n  s\n  \n  e\n  \n  l\n  \n  e\n  \n  c\n  \n  t\n  \n  i\n  \n  o\n  \n  n\n  \n  {\\\\displaystyle P\\_{\\\\mathrm {selection} }}\n  \n  ![{\\\\displaystyle P\\_{\\\\mathrm {selection} }}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f83c7cd3c00307571cd5af18a6f4029cf1252faa)\n  is completely unknown, since so little is known about the origin of life. Simplified criteria (such as the number of galaxies) must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable universe.\n\n### Simplified approaches\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=4 \"Edit section: Simplified approaches\")\\]\n\n[Tegmark](https:\/\/en.wikipedia.org\/wiki\/Max_Tegmark \"Max Tegmark\") *et al.* have recently considered these objections and proposed a simplified anthropic scenario for [axion](https:\/\/en.wikipedia.org\/wiki\/Axion \"Axion\") [dark matter](https:\/\/en.wikipedia.org\/wiki\/Dark_matter \"Dark matter\") in which they argue that the first two of these problems do not apply.[\\[11\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-11)\n\nVilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.[\\[12\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-12)\n\nA problem with many of the simplified approaches people\\[*[who?](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Manual_of_Style\/Words_to_watch#Unsupported_attributions \"Wikipedia:Manual of Style\/Words to watch\")*\\] have tried is that they \"predict\" a cosmological constant that is too large by a factor of 10–1000 orders of magnitude (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed.[\\[13\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-13)[\\[14\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-14)[\\[15\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-15)\n\n### Interpretation\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=5 \"Edit section: Interpretation\")\\]\n\nFew dispute the large number of metastable vacua.\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\] The existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial.\\[*[further explanation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Please_clarify \"Wikipedia:Please clarify\")*\\]\n\n#### Cosmological constant problem\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=6 \"Edit section: Cosmological constant problem\")\\]\n\n[Andrei Linde](https:\/\/en.wikipedia.org\/wiki\/Andrei_Linde \"Andrei Linde\"), [Sir Martin Rees](https:\/\/en.wikipedia.org\/wiki\/Sir_Martin_Rees \"Sir Martin Rees\") and [Leonard Susskind](https:\/\/en.wikipedia.org\/wiki\/Leonard_Susskind \"Leonard Susskind\") advocate it as a solution to the [cosmological constant problem](https:\/\/en.wikipedia.org\/wiki\/Cosmological_constant_problem \"Cosmological constant problem\").\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\n### Weak scale supersymmetry from the landscape\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=7 \"Edit section: Weak scale supersymmetry from the landscape\")\\]\n\nThe string landscape ideas can be applied to the notion of weak scale supersymmetry and the Little Hierarchy problem. For string vacua which include the MSSM (Minimal Supersymmetric Standard Model) as the low energy effective field theory, all values of SUSY breaking fields are expected to be equally likely on the landscape. This led Douglas[\\[16\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-16) and others to propose that the SUSY breaking scale is distributed as a power law in the landscape P p r i o r ∼ m s o f t 2 n F \\+ n D − 1 {\\\\displaystyle P\\_{prior}\\\\sim m\\_{soft}^{2n\\_{F}+n\\_{D}-1}} ![{\\\\displaystyle P\\_{prior}\\\\sim m\\_{soft}^{2n\\_{F}+n\\_{D}-1}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f84426fcffb7b6d00faa610a5ab08a8680d127a5) where n F {\\\\displaystyle n\\_{F}} ![{\\\\displaystyle n\\_{F}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/ccc36cc9554ca4e1cf9ece1b4bba77c31dba3389) is the number of F-breaking fields (distributed as complex numbers) and n D {\\\\displaystyle n\\_{D}} ![{\\\\displaystyle n\\_{D}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/b21e96ed85525311a68773d60c9abc849ad8cb50) is the number of D-breaking fields (distributed as real numbers). Next, one may impose the Agrawal, Barr, Donoghue, Seckel (ABDS) anthropic requirement[\\[17\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-17) that the derived weak scale lie within a factor of a few of our measured value (lest nuclei as needed for life as we know it become unstable (the atomic principle)). Combining these effects with a mild power-law draw to large soft SUSY breaking terms, one may calculate the Higgs boson and superparticle masses expected from the landscape.[\\[18\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-18) The Higgs mass probability distribution peaks around 125 GeV while sparticles (with the exception of light higgsinos) tend to lie well beyond current LHC search limits. This approach is an example of the application of stringy naturalness.\n\n#### Scientific relevance\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=8 \"Edit section: Scientific relevance\")\\]\n\n[David Gross](https:\/\/en.wikipedia.org\/wiki\/David_Gross \"David Gross\") suggests\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\] that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the [Smolin–Susskind debate](https:\/\/en.wikipedia.org\/wiki\/Smolin%E2%80%93Susskind_debate \"Smolin–Susskind debate\") on the merits of the landscape.\n\n#### Popular reception\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=9 \"Edit section: Popular reception\")\\]\n\nThere are several popular books about the anthropic principle in cosmology.[\\[19\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-19) The authors of two physics blogs, [Lubos Motl](https:\/\/en.wikipedia.org\/wiki\/Lubos_Motl \"Lubos Motl\") and [Peter Woit](https:\/\/en.wikipedia.org\/wiki\/Peter_Woit \"Peter Woit\"), are opposed to this use of the anthropic principle.\\[*[why?](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Please_clarify \"Wikipedia:Please clarify\")*\\][\\[20\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-20)\n\n## See also\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=10 \"Edit section: See also\")\\]\n\n- [![icon](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/6f\/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg\/40px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg)[Physics portal](https:\/\/en.wikipedia.org\/wiki\/Portal:Physics \"Portal:Physics\")\n\n- [Swampland](https:\/\/en.wikipedia.org\/wiki\/Swampland_\\(physics\\) \"Swampland (physics)\")\n- [Extra dimensions](https:\/\/en.wikipedia.org\/wiki\/String_theory#Extra_dimensions \"String theory\")\n- [M-theory](https:\/\/en.wikipedia.org\/wiki\/M-theory \"M-theory\")\n\n## References\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=11 \"Edit section: References\")\\]\n\n1. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-Ashok_1-0)** The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See [M. Douglas](https:\/\/en.wikipedia.org\/wiki\/Michael_R._Douglas \"Michael R. Douglas\"), \"The statistics of string \/ M theory vacua\", *JHEP* **0305**, 46 (2003). [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0303194](https:\/\/arxiv.org\/abs\/hep-th\/0303194); S. Ashok and M. Douglas, \"Counting flux vacua\", *JHEP* **0401**, 060 (2004).\n2. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-2)**\n   Baggott, Jim (2018). [*Quantum Space Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe*](https:\/\/books.google.com\/books?id=HwN6DwAAQBAJ&pg=PA288). Oxford University Press. p. 288. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n   \n   [978-0-19-253681-5](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-0-19-253681-5 \"Special:BookSources\/978-0-19-253681-5\")\n   \n   .\n3. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-3)** L. Smolin, \"Did the universe evolve?\", *Classical and Quantum Gravity* **9**, 173–191 (1992). L. Smolin, *[The Life of the Cosmos](https:\/\/en.wikipedia.org\/wiki\/The_Life_of_the_Cosmos \"The Life of the Cosmos\")* (Oxford, 1997)\n4. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-4)**\n   Read, James; Le Bihan, Baptiste (2021). [\"The landscape and the multiverse: What's the problem?\"](https:\/\/doi.org\/10.1007%2Fs11229-021-03137-0). *Synthese*. **199** (3–4\\): 7749–7771\\. [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1007\/s11229-021-03137-0](https:\/\/doi.org\/10.1007%2Fs11229-021-03137-0). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [234815857](https:\/\/api.semanticscholar.org\/CorpusID:234815857).\n5. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-5)**\n   Taylor, Washington; Wang, Yi-Nan (2015). \"The F-theory geometry with most flux vacua\". *Journal of High Energy Physics*. **2015** (12): 164. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1511\\.03209](https:\/\/arxiv.org\/abs\/1511.03209). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2015JHEP...12..164T](https:\/\/ui.adsabs.harvard.edu\/abs\/2015JHEP...12..164T). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1007\/JHEP12(2015)164](https:\/\/doi.org\/10.1007%2FJHEP12%282015%29164). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [41149049](https:\/\/api.semanticscholar.org\/CorpusID:41149049).\n6. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-6)**\n   Frederik Denef; Douglas, Michael R. (2007). \"Computational complexity of the landscape\". *Annals of Physics*. **322** (5): 1096–1142\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0602072](https:\/\/arxiv.org\/abs\/hep-th\/0602072). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2007AnPhy.322.1096D](https:\/\/ui.adsabs.harvard.edu\/abs\/2007AnPhy.322.1096D). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/j.aop.2006.07.013](https:\/\/doi.org\/10.1016%2Fj.aop.2006.07.013). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [281586](https:\/\/api.semanticscholar.org\/CorpusID:281586).\n7. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-7)**\n   Kachru, Shamit; Kallosh, Renata; Linde, Andrei; Trivedi, Sandip P. (2003). \"de Sitter Vacua in String Theory\". *Physical Review D*. **68** (4) 046005. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0301240](https:\/\/arxiv.org\/abs\/hep-th\/0301240). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2003PhRvD..68d6005K](https:\/\/ui.adsabs.harvard.edu\/abs\/2003PhRvD..68d6005K). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1103\/PhysRevD.68.046005](https:\/\/doi.org\/10.1103%2FPhysRevD.68.046005). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [119482182](https:\/\/api.semanticscholar.org\/CorpusID:119482182).\n8. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-8)**\n   L. Susskind, \"The anthropic landscape of string theory\",\n   \n   [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0302219](https:\/\/arxiv.org\/abs\/hep-th\/0302219).\n9. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-9)** S. Weinberg, \"Anthropic bound on the cosmological constant\", *Phys. Rev. Lett.* **59**, 2607 (1987).\n10. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-10)**\n    S. M. Carroll, \"Is our universe natural?\" (2005)\n    \n    [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0512148](https:\/\/arxiv.org\/abs\/hep-th\/0512148) reviews a number of proposals in preprints dated 2004\/5.\n11. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-11)**\n    M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, \"Dimensionless constants, cosmology and other dark matters\",\n    \n    [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[astro-ph\/0511774](https:\/\/arxiv.org\/abs\/astro-ph\/0511774). F. Wilczek, \"Enlightenment, knowledge, ignorance, temptation\",\n    \n    [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-ph\/0512187](https:\/\/arxiv.org\/abs\/hep-ph\/0512187). See also the discussion at [\\[1\\]](http:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=310).\n12. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-12)**\n    See, *e.g.*\n    \n    Alexander Vilenkin (2007). \"A measure of the multiverse\". *Journal of Physics A: Mathematical and Theoretical*. **40** (25): 6777–6785\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0609193](https:\/\/arxiv.org\/abs\/hep-th\/0609193). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2007JPhA...40.6777V](https:\/\/ui.adsabs.harvard.edu\/abs\/2007JPhA...40.6777V). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1088\/1751-8113\/40\/25\/S22](https:\/\/doi.org\/10.1088%2F1751-8113%2F40%2F25%2FS22). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [119390736](https:\/\/api.semanticscholar.org\/CorpusID:119390736).\n13. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-13)**\n    Abraham Loeb (2006). \"An observational test for the anthropic origin of the cosmological constant\". *Journal of Cosmology and Astroparticle Physics*. **0605** (5): 009. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[astro-ph\/0604242](https:\/\/arxiv.org\/abs\/astro-ph\/0604242). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2006JCAP...05..009L](https:\/\/ui.adsabs.harvard.edu\/abs\/2006JCAP...05..009L). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1088\/1475-7516\/2006\/05\/009](https:\/\/doi.org\/10.1088%2F1475-7516%2F2006%2F05%2F009). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [39340203](https:\/\/api.semanticscholar.org\/CorpusID:39340203).\n14. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-14)**\n    Jaume Garriga & Alexander Vilenkin (2006). \"Anthropic prediction for Lambda and the Q catastrophe\". *Prog. Theor. Phys. Suppl*. **163**: 245–57\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0508005](https:\/\/arxiv.org\/abs\/hep-th\/0508005). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2006PThPS.163..245G](https:\/\/ui.adsabs.harvard.edu\/abs\/2006PThPS.163..245G). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1143\/PTPS.163.245](https:\/\/doi.org\/10.1143%2FPTPS.163.245). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [118936307](https:\/\/api.semanticscholar.org\/CorpusID:118936307).\n15. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-15)**\n    Delia Schwartz-Perlov & Alexander Vilenkin (2006). \"Probabilities in the Bousso-Polchinski multiverse\". *Journal of Cosmology and Astroparticle Physics*. **0606** (6): 010. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0601162](https:\/\/arxiv.org\/abs\/hep-th\/0601162). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2006JCAP...06..010S](https:\/\/ui.adsabs.harvard.edu\/abs\/2006JCAP...06..010S). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1088\/1475-7516\/2006\/06\/010](https:\/\/doi.org\/10.1088%2F1475-7516%2F2006%2F06%2F010). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [119337679](https:\/\/api.semanticscholar.org\/CorpusID:119337679).\n16. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-16)**\n    M. R. Douglas, \"Statistical analysis of the supersymmetry breaking scale\",\n    \n    [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0405279](https:\/\/arxiv.org\/abs\/hep-th\/0405279).\n17. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-17)**\n    V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel, \"Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking\", *Phys. Rev. Lett.* **80**, 1822 (1998).\n    \n    [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-ph\/9801253](https:\/\/arxiv.org\/abs\/hep-ph\/9801253)\n18. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-18)**\n    H. Baer, V. Barger, H. Serce and K. Sinha, \"Higgs and superparticle mass predictions from the landscape\", *JHEP* **03**, 002 (2018),\n    \n    [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1712\\.01399](https:\/\/arxiv.org\/abs\/1712.01399) .\n19. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-19)** L. Susskind, *The cosmic landscape: string theory and the illusion of intelligent design* (Little, Brown, 2005). M. J. Rees, *Just six numbers: the deep forces that shape the universe* (Basic Books, 2001). R. Bousso and J. Polchinski, \"The string theory landscape\", *Sci. Am.* **291**, 60–69 (2004).\n20. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-20)** Motl's blog criticized the anthropic principle and Woit's [blog](http:\/\/www.math.columbia.edu\/~woit\/blog\/) frequently attacks the anthropic string landscape.\n\n## External links\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=12 \"Edit section: External links\")\\]\n\n- [String landscape; moduli stabilization; flux vacua; flux compactification](http:\/\/xstructure.inr.ac.ru\/x-bin\/theme2.py?arxiv=hep-th&level=1&index1=5460697) on [arxiv.org](https:\/\/en.wikipedia.org\/wiki\/Arxiv.org \"Arxiv.org\").\n- [Cvetič, Mirjam](https:\/\/en.wikipedia.org\/wiki\/Mirjam_Cveti%C4%8D \"Mirjam Cvetič\"); García-Etxebarria, Iñaki; Halverson, James (March 2011). \"On the computation of non-perturbative effective potentials in the string theory landscape\". *Fortschritte der Physik*. **59** (3–4\\): 243–283\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1009\\.5386](https:\/\/arxiv.org\/abs\/1009.5386). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2011ForPh..59..243C](https:\/\/ui.adsabs.harvard.edu\/abs\/2011ForPh..59..243C). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1002\/prop.201000093](https:\/\/doi.org\/10.1002%2Fprop.201000093). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [46634583](https:\/\/api.semanticscholar.org\/CorpusID:46634583).\n\n| [v](https:\/\/en.wikipedia.org\/wiki\/Template:String_theory_topics \"Template:String theory topics\") [t](https:\/\/en.wikipedia.org\/wiki\/Template_talk:String_theory_topics \"Template talk:String theory topics\") [e](https:\/\/en.wikipedia.org\/wiki\/Special:EditPage\/Template:String_theory_topics \"Special:EditPage\/Template:String theory topics\")[String theory](https:\/\/en.wikipedia.org\/wiki\/String_theory \"String theory\") |   |\n|---|---|\n| Background | [Strings](https:\/\/en.wikipedia.org\/wiki\/String_\\(physics\\) \"String (physics)\") [Cosmic strings](https:\/\/en.wikipedia.org\/wiki\/Cosmic_string \"Cosmic string\") [History of string theory](https:\/\/en.wikipedia.org\/wiki\/History_of_string_theory \"History of string theory\") [First superstring revolution](https:\/\/en.wikipedia.org\/wiki\/First_superstring_revolution \"First superstring revolution\") [Second superstring revolution](https:\/\/en.wikipedia.org\/wiki\/Second_superstring_revolution \"Second superstring revolution\") [String theory landscape]() |\n| Theory | [Nambu–Goto action](https:\/\/en.wikipedia.org\/wiki\/Nambu%E2%80%93Goto_action \"Nambu–Goto action\") [Polyakov action](https:\/\/en.wikipedia.org\/wiki\/Polyakov_action \"Polyakov action\") [Bosonic string theory](https:\/\/en.wikipedia.org\/wiki\/Bosonic_string_theory \"Bosonic string theory\") [Superstring theory](https:\/\/en.wikipedia.org\/wiki\/Superstring_theory \"Superstring theory\") [Type I string](https:\/\/en.wikipedia.org\/wiki\/Type_I_string_theory \"Type I string theory\") [Type II string](https:\/\/en.wikipedia.org\/wiki\/Type_II_string_theory \"Type II string theory\") [Type IIA string](https:\/\/en.wikipedia.org\/wiki\/Type_II_string_theory \"Type II string theory\") [Type IIB string](https:\/\/en.wikipedia.org\/wiki\/Type_II_string_theory \"Type II string theory\") [Heterotic string](https:\/\/en.wikipedia.org\/wiki\/Heterotic_string_theory \"Heterotic string theory\") [N=2 superstring](https:\/\/en.wikipedia.org\/wiki\/N%3D2_superstring \"N=2 superstring\") [F-theory](https:\/\/en.wikipedia.org\/wiki\/F-theory \"F-theory\") [String field theory](https:\/\/en.wikipedia.org\/wiki\/String_field_theory \"String field theory\") [Matrix string theory](https:\/\/en.wikipedia.org\/wiki\/Matrix_string_theory \"Matrix string theory\") [Non-critical string theory](https:\/\/en.wikipedia.org\/wiki\/Non-critical_string_theory \"Non-critical string theory\") [Non-linear sigma model](https:\/\/en.wikipedia.org\/wiki\/Non-linear_sigma_model \"Non-linear sigma model\") [Tachyon condensation](https:\/\/en.wikipedia.org\/wiki\/Tachyon_condensation \"Tachyon condensation\") [RNS formalism](https:\/\/en.wikipedia.org\/wiki\/RNS_formalism \"RNS formalism\") [GS formalism](https:\/\/en.wikipedia.org\/wiki\/GS_formalism \"GS formalism\") |\n| [String duality](https:\/\/en.wikipedia.org\/wiki\/String_duality \"String duality\") | [T-duality](https:\/\/en.wikipedia.org\/wiki\/T-duality \"T-duality\") [S-duality](https:\/\/en.wikipedia.org\/wiki\/S-duality \"S-duality\") [U-duality](https:\/\/en.wikipedia.org\/wiki\/U-duality \"U-duality\") [Montonen–Olive duality](https:\/\/en.wikipedia.org\/wiki\/Montonen%E2%80%93Olive_duality \"Montonen–Olive duality\") |\n| Particles and fields | [Graviton](https:\/\/en.wikipedia.org\/wiki\/Graviton \"Graviton\") [Dilaton](https:\/\/en.wikipedia.org\/wiki\/Dilaton \"Dilaton\") [Tachyon](https:\/\/en.wikipedia.org\/wiki\/Tachyon \"Tachyon\") [Ramond–Ramond field](https:\/\/en.wikipedia.org\/wiki\/Ramond%E2%80%93Ramond_field \"Ramond–Ramond field\") [Kalb–Ramond field](https:\/\/en.wikipedia.org\/wiki\/Kalb%E2%80%93Ramond_field \"Kalb–Ramond field\") [Magnetic monopole](https:\/\/en.wikipedia.org\/wiki\/Magnetic_monopole \"Magnetic monopole\") [Dual graviton](https:\/\/en.wikipedia.org\/wiki\/Dual_graviton \"Dual graviton\") [Dual photon](https:\/\/en.wikipedia.org\/wiki\/Dual_photon \"Dual photon\") |\n| [Branes](https:\/\/en.wikipedia.org\/wiki\/Brane \"Brane\") | [D-brane](https:\/\/en.wikipedia.org\/wiki\/D-brane \"D-brane\") [NS5-brane](https:\/\/en.wikipedia.org\/wiki\/NS5-brane \"NS5-brane\") [M2-brane](https:\/\/en.wikipedia.org\/wiki\/M2-brane \"M2-brane\") [M5-brane](https:\/\/en.wikipedia.org\/wiki\/M5-brane \"M5-brane\") [S-brane](https:\/\/en.wikipedia.org\/wiki\/S-brane \"S-brane\") [Black brane](https:\/\/en.wikipedia.org\/wiki\/Black_brane \"Black brane\") [Black holes](https:\/\/en.wikipedia.org\/wiki\/Black_hole \"Black hole\") [Black string](https:\/\/en.wikipedia.org\/wiki\/Black_string \"Black string\") [Brane cosmology](https:\/\/en.wikipedia.org\/wiki\/Brane_cosmology \"Brane cosmology\") [Quiver diagram](https:\/\/en.wikipedia.org\/wiki\/Quiver_diagram \"Quiver diagram\") [Hanany–Witten transition](https:\/\/en.wikipedia.org\/wiki\/Hanany%E2%80%93Witten_transition \"Hanany–Witten transition\") |\n| [Conformal field theory](https:\/\/en.wikipedia.org\/wiki\/Conformal_field_theory \"Conformal field theory\") | [Virasoro algebra](https:\/\/en.wikipedia.org\/wiki\/Virasoro_algebra \"Virasoro algebra\") [Mirror symmetry](https:\/\/en.wikipedia.org\/wiki\/Mirror_symmetry_\\(string_theory\\) \"Mirror symmetry (string theory)\") [Conformal anomaly](https:\/\/en.wikipedia.org\/wiki\/Conformal_anomaly \"Conformal anomaly\") [Conformal algebra](https:\/\/en.wikipedia.org\/wiki\/Conformal_symmetry \"Conformal symmetry\") [Superconformal algebra](https:\/\/en.wikipedia.org\/wiki\/Superconformal_algebra \"Superconformal algebra\") [Vertex operator algebra](https:\/\/en.wikipedia.org\/wiki\/Vertex_operator_algebra \"Vertex operator algebra\") [Loop algebra](https:\/\/en.wikipedia.org\/wiki\/Loop_algebra \"Loop algebra\") [Kac–Moody algebra](https:\/\/en.wikipedia.org\/wiki\/Kac%E2%80%93Moody_algebra \"Kac–Moody algebra\") [Wess–Zumino–Witten model](https:\/\/en.wikipedia.org\/wiki\/Wess%E2%80%93Zumino%E2%80%93Witten_model \"Wess–Zumino–Witten model\") |\n| [Gauge theory](https:\/\/en.wikipedia.org\/wiki\/Gauge_theory \"Gauge theory\") | [Anomalies](https:\/\/en.wikipedia.org\/wiki\/Anomaly_\\(physics\\) \"Anomaly (physics)\") [Instantons](https:\/\/en.wikipedia.org\/wiki\/Instanton \"Instanton\") [Chern–Simons form](https:\/\/en.wikipedia.org\/wiki\/Chern%E2%80%93Simons_form \"Chern–Simons form\") [Bogomol'nyi–Prasad–Sommerfield bound](https:\/\/en.wikipedia.org\/wiki\/Bogomol%27nyi%E2%80%93Prasad%E2%80%93Sommerfield_bound \"Bogomol'nyi–Prasad–Sommerfield bound\") [Exceptional Lie groups](https:\/\/en.wikipedia.org\/wiki\/Exceptional_Lie_group \"Exceptional Lie group\") ([G2](https:\/\/en.wikipedia.org\/wiki\/G2_\\(mathematics\\) \"G2 (mathematics)\"), [F4](https:\/\/en.wikipedia.org\/wiki\/F4_\\(mathematics\\) \"F4 (mathematics)\"), [E6](https:\/\/en.wikipedia.org\/wiki\/E6_\\(mathematics\\) \"E6 (mathematics)\"), [E7](https:\/\/en.wikipedia.org\/wiki\/E7_\\(mathematics\\) \"E7 (mathematics)\"), [E8](https:\/\/en.wikipedia.org\/wiki\/E8_\\(mathematics\\) \"E8 (mathematics)\")) [ADE classification](https:\/\/en.wikipedia.org\/wiki\/ADE_classification \"ADE classification\") [Dirac string](https:\/\/en.wikipedia.org\/wiki\/Dirac_string \"Dirac string\") [*p*\\-form electrodynamics](https:\/\/en.wikipedia.org\/wiki\/P-form_electrodynamics \"P-form electrodynamics\") |\n| Geometry | [Worldsheet](https:\/\/en.wikipedia.org\/wiki\/Worldsheet \"Worldsheet\") [Kaluza–Klein theory](https:\/\/en.wikipedia.org\/wiki\/Kaluza%E2%80%93Klein_theory \"Kaluza–Klein theory\") [Compactification](https:\/\/en.wikipedia.org\/wiki\/Compactification_\\(physics\\) \"Compactification (physics)\") [Why 10 dimensions](https:\/\/en.wikipedia.org\/wiki\/Why_10_dimensions \"Why 10 dimensions\")? [Kähler manifold](https:\/\/en.wikipedia.org\/wiki\/K%C3%A4hler_manifold \"Kähler manifold\") [Ricci-flat manifold](https:\/\/en.wikipedia.org\/wiki\/Ricci-flat_manifold \"Ricci-flat manifold\") [Calabi–Yau manifold](https:\/\/en.wikipedia.org\/wiki\/Calabi%E2%80%93Yau_manifold \"Calabi–Yau manifold\") [Hyperkähler manifold](https:\/\/en.wikipedia.org\/wiki\/Hyperk%C3%A4hler_manifold \"Hyperkähler manifold\") [K3 surface](https:\/\/en.wikipedia.org\/wiki\/K3_surface \"K3 surface\") [G2 manifold](https:\/\/en.wikipedia.org\/wiki\/G2_manifold \"G2 manifold\") [Spin(7)-manifold](https:\/\/en.wikipedia.org\/wiki\/Spin\\(7\\)-manifold \"Spin(7)-manifold\") [Generalized complex manifold](https:\/\/en.wikipedia.org\/wiki\/Generalized_complex_structure \"Generalized complex structure\") [Orbifold](https:\/\/en.wikipedia.org\/wiki\/Orbifold \"Orbifold\") [Conifold](https:\/\/en.wikipedia.org\/wiki\/Conifold \"Conifold\") [Orientifold](https:\/\/en.wikipedia.org\/wiki\/Orientifold \"Orientifold\") [Moduli space](https:\/\/en.wikipedia.org\/wiki\/Moduli_space \"Moduli space\") [Hořava–Witten theory](https:\/\/en.wikipedia.org\/wiki\/Ho%C5%99ava%E2%80%93Witten_theory \"Hořava–Witten theory\") [K-theory (physics)](https:\/\/en.wikipedia.org\/wiki\/K-theory_\\(physics\\) \"K-theory (physics)\") [Twisted K-theory](https:\/\/en.wikipedia.org\/wiki\/Twisted_K-theory \"Twisted K-theory\") |\n| [Supersymmetry](https:\/\/en.wikipedia.org\/wiki\/Supersymmetry \"Supersymmetry\") | [Supergravity](https:\/\/en.wikipedia.org\/wiki\/Supergravity \"Supergravity\") [Eleven-dimensional supergravity](https:\/\/en.wikipedia.org\/wiki\/Eleven-dimensional_supergravity \"Eleven-dimensional supergravity\") [Type I supergravity](https:\/\/en.wikipedia.org\/wiki\/Type_I_supergravity \"Type I supergravity\") [Type IIA supergravity](https:\/\/en.wikipedia.org\/wiki\/Type_IIA_supergravity \"Type IIA supergravity\") [Type IIB supergravity](https:\/\/en.wikipedia.org\/wiki\/Type_IIB_supergravity \"Type IIB supergravity\") [Superspace](https:\/\/en.wikipedia.org\/wiki\/Superspace \"Superspace\") [Lie superalgebra](https:\/\/en.wikipedia.org\/wiki\/Lie_superalgebra \"Lie superalgebra\") [Lie supergroup](https:\/\/en.wikipedia.org\/wiki\/Lie_supergroup \"Lie supergroup\") |\n| [Holography](https:\/\/en.wikipedia.org\/wiki\/Holography \"Holography\") | [Holographic principle](https:\/\/en.wikipedia.org\/wiki\/Holographic_principle \"Holographic principle\") [AdS\/CFT correspondence](https:\/\/en.wikipedia.org\/wiki\/AdS\/CFT_correspondence \"AdS\/CFT correspondence\") |\n| [M-theory](https:\/\/en.wikipedia.org\/wiki\/M-theory \"M-theory\") | [Matrix theory](https:\/\/en.wikipedia.org\/wiki\/Matrix_theory_\\(physics\\) \"Matrix theory (physics)\") [Introduction to M-theory](https:\/\/en.wikipedia.org\/wiki\/Introduction_to_M-theory \"Introduction to M-theory\") |\n| String theorists | [Aganagić](https:\/\/en.wikipedia.org\/wiki\/Mina_Aganagi%C4%87 \"Mina Aganagić\") [Arkani-Hamed](https:\/\/en.wikipedia.org\/wiki\/Nima_Arkani-Hamed \"Nima Arkani-Hamed\") [Atiyah](https:\/\/en.wikipedia.org\/wiki\/Michael_Atiyah \"Michael Atiyah\") [Banks](https:\/\/en.wikipedia.org\/wiki\/Tom_Banks_\\(physicist\\) \"Tom Banks (physicist)\") [Berenstein](https:\/\/en.wikipedia.org\/wiki\/David_Berenstein \"David Berenstein\") [Bousso](https:\/\/en.wikipedia.org\/wiki\/Raphael_Bousso \"Raphael Bousso\") [Curtright](https:\/\/en.wikipedia.org\/wiki\/Thomas_Curtright \"Thomas Curtright\") [Dijkgraaf](https:\/\/en.wikipedia.org\/wiki\/Robbert_Dijkgraaf \"Robbert Dijkgraaf\") [Distler](https:\/\/en.wikipedia.org\/wiki\/Jacques_Distler \"Jacques Distler\") [Douglas](https:\/\/en.wikipedia.org\/wiki\/Michael_R._Douglas \"Michael R. Douglas\") [Duff](https:\/\/en.wikipedia.org\/wiki\/Michael_Duff_\\(physicist\\) \"Michael Duff (physicist)\") [Dvali](https:\/\/en.wikipedia.org\/wiki\/Gia_Dvali \"Gia Dvali\") [Ferrara](https:\/\/en.wikipedia.org\/wiki\/Sergio_Ferrara \"Sergio Ferrara\") [Fischler](https:\/\/en.wikipedia.org\/wiki\/Willy_Fischler \"Willy Fischler\") [Friedan](https:\/\/en.wikipedia.org\/wiki\/Daniel_Friedan \"Daniel Friedan\") [Gates](https:\/\/en.wikipedia.org\/wiki\/Sylvester_James_Gates \"Sylvester James Gates\") [Gliozzi](https:\/\/en.wikipedia.org\/wiki\/Ferdinando_Gliozzi \"Ferdinando Gliozzi\") [Gopakumar](https:\/\/en.wikipedia.org\/wiki\/Rajesh_Gopakumar \"Rajesh Gopakumar\") [Green](https:\/\/en.wikipedia.org\/wiki\/Michael_Green_\\(physicist\\) \"Michael Green (physicist)\") [Greene](https:\/\/en.wikipedia.org\/wiki\/Brian_Greene \"Brian Greene\") [Gross](https:\/\/en.wikipedia.org\/wiki\/David_Gross \"David Gross\") [Gubser](https:\/\/en.wikipedia.org\/wiki\/Steven_Gubser \"Steven Gubser\") [Gukov](https:\/\/en.wikipedia.org\/wiki\/Sergei_Gukov \"Sergei Gukov\") [Guth](https:\/\/en.wikipedia.org\/wiki\/Alan_Guth \"Alan Guth\") [Hanson](https:\/\/en.wikipedia.org\/wiki\/Andrew_J._Hanson \"Andrew J. Hanson\") [Harvey](https:\/\/en.wikipedia.org\/wiki\/Jeffrey_A._Harvey \"Jeffrey A. Harvey\") ['t Hooft](https:\/\/en.wikipedia.org\/wiki\/Gerard_%27t_Hooft \"Gerard 't Hooft\") [Hořava](https:\/\/en.wikipedia.org\/wiki\/Petr_Ho%C5%99ava_\\(theorist\\) \"Petr Hořava (theorist)\") [Gibbons](https:\/\/en.wikipedia.org\/wiki\/Gary_Gibbons \"Gary Gibbons\") [Kachru](https:\/\/en.wikipedia.org\/wiki\/Shamit_Kachru \"Shamit Kachru\") [Kaku](https:\/\/en.wikipedia.org\/wiki\/Michio_Kaku \"Michio Kaku\") [Kallosh](https:\/\/en.wikipedia.org\/wiki\/Renata_Kallosh \"Renata Kallosh\") [Kaluza](https:\/\/en.wikipedia.org\/wiki\/Theodor_Kaluza \"Theodor Kaluza\") [Kapustin](https:\/\/en.wikipedia.org\/wiki\/Anton_Kapustin \"Anton Kapustin\") [Klebanov](https:\/\/en.wikipedia.org\/wiki\/Igor_Klebanov \"Igor Klebanov\") [Knizhnik](https:\/\/en.wikipedia.org\/wiki\/Vadim_Knizhnik \"Vadim Knizhnik\") [Kontsevich](https:\/\/en.wikipedia.org\/wiki\/Maxim_Kontsevich \"Maxim Kontsevich\") [Klein](https:\/\/en.wikipedia.org\/wiki\/Oskar_Klein \"Oskar Klein\") [Linde](https:\/\/en.wikipedia.org\/wiki\/Andrei_Linde \"Andrei Linde\") [Maldacena](https:\/\/en.wikipedia.org\/wiki\/Juan_Mart%C3%ADn_Maldacena \"Juan Martín Maldacena\") [Mandelstam](https:\/\/en.wikipedia.org\/wiki\/Stanley_Mandelstam \"Stanley Mandelstam\") [Marolf](https:\/\/en.wikipedia.org\/wiki\/Donald_Marolf \"Donald Marolf\") [Martinec](https:\/\/en.wikipedia.org\/wiki\/Emil_Martinec \"Emil Martinec\") [Minwalla](https:\/\/en.wikipedia.org\/wiki\/Shiraz_Minwalla \"Shiraz Minwalla\") [Moore](https:\/\/en.wikipedia.org\/wiki\/Greg_Moore_\\(physicist\\) \"Greg Moore (physicist)\") [Motl](https:\/\/en.wikipedia.org\/wiki\/Lubo%C5%A1_Motl \"Luboš Motl\") [Mukhi](https:\/\/en.wikipedia.org\/wiki\/Sunil_Mukhi \"Sunil Mukhi\") [Myers](https:\/\/en.wikipedia.org\/wiki\/Robert_Myers_\\(physicist\\) \"Robert Myers (physicist)\") [Nanopoulos](https:\/\/en.wikipedia.org\/wiki\/Dimitri_Nanopoulos \"Dimitri Nanopoulos\") [Năstase](https:\/\/en.wikipedia.org\/wiki\/Hora%C8%9Biu_N%C4%83stase \"Horațiu Năstase\") [Nekrasov](https:\/\/en.wikipedia.org\/wiki\/Nikita_Nekrasov \"Nikita Nekrasov\") [Neveu](https:\/\/en.wikipedia.org\/wiki\/Andr%C3%A9_Neveu \"André Neveu\") [Nielsen](https:\/\/en.wikipedia.org\/wiki\/Holger_Bech_Nielsen \"Holger Bech Nielsen\") [van Nieuwenhuizen](https:\/\/en.wikipedia.org\/wiki\/Peter_van_Nieuwenhuizen \"Peter van Nieuwenhuizen\") [Novikov](https:\/\/en.wikipedia.org\/wiki\/Sergei_Novikov_\\(mathematician\\) \"Sergei Novikov (mathematician)\") [Olive](https:\/\/en.wikipedia.org\/wiki\/David_Olive \"David Olive\") [Ooguri](https:\/\/en.wikipedia.org\/wiki\/Hirosi_Ooguri \"Hirosi Ooguri\") [Ovrut](https:\/\/en.wikipedia.org\/wiki\/Burt_Ovrut \"Burt Ovrut\") [Polchinski](https:\/\/en.wikipedia.org\/wiki\/Joseph_Polchinski \"Joseph Polchinski\") [Polyakov](https:\/\/en.wikipedia.org\/wiki\/Alexander_Markovich_Polyakov \"Alexander Markovich Polyakov\") [Rajaraman](https:\/\/en.wikipedia.org\/wiki\/Arvind_Rajaraman \"Arvind Rajaraman\") [Ramond](https:\/\/en.wikipedia.org\/wiki\/Pierre_Ramond \"Pierre Ramond\") [Randall](https:\/\/en.wikipedia.org\/wiki\/Lisa_Randall \"Lisa Randall\") [Randjbar-Daemi](https:\/\/en.wikipedia.org\/wiki\/Seifallah_Randjbar-Daemi \"Seifallah Randjbar-Daemi\") [Roček](https:\/\/en.wikipedia.org\/wiki\/Martin_Ro%C4%8Dek \"Martin Roček\") [Rohm](https:\/\/en.wikipedia.org\/wiki\/Ryan_Rohm \"Ryan Rohm\") [Sagnotti](https:\/\/en.wikipedia.org\/wiki\/Augusto_Sagnotti \"Augusto Sagnotti\") [Scherk](https:\/\/en.wikipedia.org\/wiki\/Jo%C3%ABl_Scherk \"Joël Scherk\") [Schwarz](https:\/\/en.wikipedia.org\/wiki\/John_Henry_Schwarz \"John Henry Schwarz\") [Seiberg](https:\/\/en.wikipedia.org\/wiki\/Nathan_Seiberg \"Nathan Seiberg\") [Sen](https:\/\/en.wikipedia.org\/wiki\/Ashoke_Sen \"Ashoke Sen\") [Shenker](https:\/\/en.wikipedia.org\/wiki\/Stephen_Shenker \"Stephen Shenker\") [Siegel](https:\/\/en.wikipedia.org\/wiki\/Warren_Siegel \"Warren Siegel\") [Silverstein](https:\/\/en.wikipedia.org\/wiki\/Eva_Silverstein \"Eva Silverstein\") [Sơn](https:\/\/en.wikipedia.org\/wiki\/%C4%90%C3%A0m_Thanh_S%C6%A1n \"Đàm Thanh Sơn\") [Staudacher](https:\/\/en.wikipedia.org\/wiki\/Matthias_Staudacher \"Matthias Staudacher\") [Steinhardt](https:\/\/en.wikipedia.org\/wiki\/Paul_Steinhardt \"Paul Steinhardt\") [Strominger](https:\/\/en.wikipedia.org\/wiki\/Andrew_Strominger \"Andrew Strominger\") [Sundrum](https:\/\/en.wikipedia.org\/wiki\/Raman_Sundrum \"Raman Sundrum\") [Susskind](https:\/\/en.wikipedia.org\/wiki\/Leonard_Susskind \"Leonard Susskind\") [Townsend](https:\/\/en.wikipedia.org\/wiki\/Paul_Townsend \"Paul Townsend\") [Trivedi](https:\/\/en.wikipedia.org\/wiki\/Sandip_Trivedi \"Sandip Trivedi\") [Turok](https:\/\/en.wikipedia.org\/wiki\/Neil_Turok \"Neil Turok\") [Vafa](https:\/\/en.wikipedia.org\/wiki\/Cumrun_Vafa \"Cumrun Vafa\") [Veneziano](https:\/\/en.wikipedia.org\/wiki\/Gabriele_Veneziano \"Gabriele Veneziano\") [Verlinde](https:\/\/en.wikipedia.org\/wiki\/Erik_Verlinde \"Erik Verlinde\") [Verlinde](https:\/\/en.wikipedia.org\/wiki\/Herman_Verlinde \"Herman Verlinde\") [Wess](https:\/\/en.wikipedia.org\/wiki\/Julius_Wess \"Julius Wess\") [Witten](https:\/\/en.wikipedia.org\/wiki\/Edward_Witten \"Edward Witten\") [Yau](https:\/\/en.wikipedia.org\/wiki\/Shing-Tung_Yau \"Shing-Tung Yau\") [Yoneya](https:\/\/en.wikipedia.org\/wiki\/Tamiaki_Yoneya \"Tamiaki Yoneya\") [Zamolodchikov](https:\/\/en.wikipedia.org\/wiki\/Alexander_Zamolodchikov \"Alexander Zamolodchikov\") [Zamolodchikov](https:\/\/en.wikipedia.org\/wiki\/Alexei_Zamolodchikov \"Alexei Zamolodchikov\") [Zaslow](https:\/\/en.wikipedia.org\/wiki\/Eric_Zaslow \"Eric Zaslow\") [Zumino](https:\/\/en.wikipedia.org\/wiki\/Bruno_Zumino \"Bruno Zumino\") [Zwiebach](https:\/\/en.wikipedia.org\/wiki\/Barton_Zwiebach \"Barton Zwiebach\") 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Wikipedia® is a registered trademark of the [Wikimedia Foundation, Inc.](https:\/\/wikimediafoundation.org\/), a non-profit organization.\n\n- [Privacy policy](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Policy:Privacy_policy)\n- [About Wikipedia](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:About)\n- [Disclaimers](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:General_disclaimer)\n- [Contact Wikipedia](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Contact_us)\n- [Legal & safety contacts](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Legal:Wikimedia_Foundation_Legal_and_Safety_Contact_Information)\n- [Code of Conduct](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Policy:Universal_Code_of_Conduct)\n- [Developers](https:\/\/developer.wikimedia.org\/)\n- [Statistics](https:\/\/stats.wikimedia.org\/#\/en.wikipedia.org)\n- [Cookie statement](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Policy:Cookie_statement)\n- [Mobile view](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&mobileaction=toggle_view_mobile)\n\n- [![Wikimedia Foundation](https:\/\/en.wikipedia.org\/static\/images\/footer\/wikimedia.svg)](https:\/\/www.wikimedia.org\/)\n- [![Powered by MediaWiki](https:\/\/en.wikipedia.org\/w\/resources\/assets\/mediawiki_compact.svg)](https:\/\/www.mediawiki.org\/)\n\nSearch\n\nToggle the table of contents\n\nString theory landscape\n\n7 languages\n\n[Add topic](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape)","attrs_readable_markdown":"From Wikipedia, the free encyclopedia\n\nIn [string theory](https:\/\/en.wikipedia.org\/wiki\/String_theory \"String theory\"), the **string theory landscape** (or **landscape of vacua**) is the collection of possible [false vacua](https:\/\/en.wikipedia.org\/wiki\/False_vacuum \"False vacuum\"),[\\[1\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-Ashok-1) together comprising a collective \"landscape\" of choices of parameters governing [compactifications](https:\/\/en.wikipedia.org\/wiki\/Compactification_\\(physics\\) \"Compactification (physics)\").\n\nThe term \"landscape\" comes from the notion of a [fitness landscape](https:\/\/en.wikipedia.org\/wiki\/Fitness_landscape \"Fitness landscape\") in [evolutionary biology](https:\/\/en.wikipedia.org\/wiki\/Evolutionary_biology \"Evolutionary biology\").[\\[2\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-2) It was first applied to cosmology by [Lee Smolin](https:\/\/en.wikipedia.org\/wiki\/Lee_Smolin \"Lee Smolin\") in his book *[The Life of the Cosmos](https:\/\/en.wikipedia.org\/wiki\/The_Life_of_the_Cosmos \"The Life of the Cosmos\")* (1997), and was first used in the context of string theory by [Leonard Susskind](https:\/\/en.wikipedia.org\/wiki\/Leonard_Susskind \"Leonard Susskind\").[\\[3\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-3)\n\n## Compactified Calabi–Yau manifolds\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=1 \"Edit section: Compactified Calabi–Yau manifolds\")\\]\n\nIn string theory, the estimated count of distinct flux vacua is commonly stated as having a lower bound of ![{\\\\displaystyle 10^{500}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/9fc79f91eb42fdee58d7e3e2d441013ad2488959),[\\[4\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-4) but more recently this has been revised to ![{\\\\displaystyle 10^{272,000}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c7ea2462969aa025b37c43ee26b6a3e026316b53),[\\[5\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-5) and the true number may still be far higher. The large number of possibilities arises from choices of [Calabi–Yau manifolds](https:\/\/en.wikipedia.org\/wiki\/Calabi%E2%80%93Yau_manifold \"Calabi–Yau manifold\") and choices of generalized [magnetic fluxes](https:\/\/en.wikipedia.org\/wiki\/Magnetic_flux \"Magnetic flux\") over various [homology](https:\/\/en.wikipedia.org\/wiki\/Homology_\\(mathematics\\) \"Homology (mathematics)\") cycles, found in [F-theory](https:\/\/en.wikipedia.org\/wiki\/F-theory \"F-theory\").\n\nIf there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is [NP complete](https:\/\/en.wikipedia.org\/wiki\/NP_complete \"NP complete\").[\\[6\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-6) This is a version of the [subset sum problem](https:\/\/en.wikipedia.org\/wiki\/Subset_sum_problem \"Subset sum problem\").\n\nA possible mechanism of string theory vacuum stabilization, now known as the **KKLT mechanism**, was proposed in 2003 by [Shamit Kachru](https:\/\/en.wikipedia.org\/wiki\/Shamit_Kachru \"Shamit Kachru\"), [Renata Kallosh](https:\/\/en.wikipedia.org\/wiki\/Renata_Kallosh \"Renata Kallosh\"), [Andrei Linde](https:\/\/en.wikipedia.org\/wiki\/Andrei_Linde \"Andrei Linde\"), and [Sandip Trivedi](https:\/\/en.wikipedia.org\/wiki\/Sandip_Trivedi \"Sandip Trivedi\").[\\[7\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-7)\n\n## Fine-tuning by the anthropic principle\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=2 \"Edit section: Fine-tuning by the anthropic principle\")\\]\n\n[Fine-tuning](https:\/\/en.wikipedia.org\/wiki\/Fine-tuning_\\(physics\\) \"Fine-tuning (physics)\") of constants like the [cosmological constant](https:\/\/en.wikipedia.org\/wiki\/Cosmological_constant \"Cosmological constant\") or the [Higgs boson](https:\/\/en.wikipedia.org\/wiki\/Higgs_boson \"Higgs boson\") mass is usually assumed to occur for precise physical reasons as opposed to taking their particular values at random. That is, these values should be uniquely consistent with underlying physical laws.\n\nThe number of theoretically allowed configurations has prompted suggestions\\[*[according to whom?](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Manual_of_Style\/Words_to_watch#Unsupported_attributions \"Wikipedia:Manual of Style\/Words to watch\")*\\] that this is not the case, and that many different vacua are physically realized.[\\[8\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-8) The [anthropic principle](https:\/\/en.wikipedia.org\/wiki\/Anthropic_principle \"Anthropic principle\") proposes that fundamental constants may have the values they have because such values are necessary for life (and therefore intelligent observers to measure the constants). The *anthropic landscape* thus refers to the collection of those portions of the landscape that are suitable for supporting intelligent life.\n\nIn 1987, [Steven Weinberg](https:\/\/en.wikipedia.org\/wiki\/Steven_Weinberg \"Steven Weinberg\") proposed that the observed value of the [cosmological constant](https:\/\/en.wikipedia.org\/wiki\/Cosmological_constant \"Cosmological constant\") was so small because it is impossible for life to occur in a universe with a much larger cosmological constant.[\\[9\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-9)\n\nWeinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts\\[*[which?](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Avoid_weasel_words \"Wikipedia:Avoid weasel words\")*\\] have been made to apply similar reasoning to models of particle physics.[\\[10\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-10)\n\nSuch attempts are based in the general ideas of [Bayesian probability](https:\/\/en.wikipedia.org\/wiki\/Bayesian_probability \"Bayesian probability\"); interpreting probability in a context where it is only possible to draw one [sample](https:\/\/en.wikipedia.org\/wiki\/Sample_size \"Sample size\") from a [distribution](https:\/\/en.wikipedia.org\/wiki\/Probability_distribution \"Probability distribution\") is problematic in [frequentist probability](https:\/\/en.wikipedia.org\/wiki\/Frequentist_probability \"Frequentist probability\") but not in Bayesian probability, which is not defined in terms of the frequency of repeated events.\n\nIn such a framework, the probability ![{\\\\displaystyle P(x)}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/89833156eff2c51bfb8750db3306a0544ce34e14) of observing some fundamental parameters ![{\\\\displaystyle x}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/87f9e315fd7e2ba406057a97300593c4802b53e4) is given by,\n\n![{\\\\displaystyle P(x)=P\\_{\\\\mathrm {prior} }(x)\\\\times P\\_{\\\\mathrm {selection} }(x),}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/cd5c5e9caa69d16bda58b1d40e39d5f19308f211)\n\nwhere ![{\\\\displaystyle P\\_{\\\\mathrm {prior} }}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/8b9334b97d41d76b64c846d2c73f5e8009acde1e) is the prior probability, from fundamental theory, of the parameters ![{\\\\displaystyle x}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/87f9e315fd7e2ba406057a97300593c4802b53e4) and ![{\\\\displaystyle P\\_{\\\\mathrm {selection} }}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f83c7cd3c00307571cd5af18a6f4029cf1252faa) is the \"anthropic selection function\", determined by the number of \"observers\" that would occur in the universe with parameters ![{\\\\displaystyle x}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/87f9e315fd7e2ba406057a97300593c4802b53e4).\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\nThese probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\\[*[year needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Manual_of_Style\/Dates_and_numbers \"Wikipedia:Manual of Style\/Dates and numbers\")*\\]\n\n- The function ![{\\\\displaystyle P\\_{\\\\mathrm {prior} }}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/8b9334b97d41d76b64c846d2c73f5e8009acde1e) is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way.\n- The function ![{\\\\displaystyle P\\_{\\\\mathrm {selection} }}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f83c7cd3c00307571cd5af18a6f4029cf1252faa) is completely unknown, since so little is known about the origin of life. Simplified criteria (such as the number of galaxies) must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable universe.\n\n### Simplified approaches\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=4 \"Edit section: Simplified approaches\")\\]\n\n[Tegmark](https:\/\/en.wikipedia.org\/wiki\/Max_Tegmark \"Max Tegmark\") *et al.* have recently considered these objections and proposed a simplified anthropic scenario for [axion](https:\/\/en.wikipedia.org\/wiki\/Axion \"Axion\") [dark matter](https:\/\/en.wikipedia.org\/wiki\/Dark_matter \"Dark matter\") in which they argue that the first two of these problems do not apply.[\\[11\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-11)\n\nVilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.[\\[12\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-12)\n\nA problem with many of the simplified approaches people\\[*[who?](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Manual_of_Style\/Words_to_watch#Unsupported_attributions \"Wikipedia:Manual of Style\/Words to watch\")*\\] have tried is that they \"predict\" a cosmological constant that is too large by a factor of 10–1000 orders of magnitude (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed.[\\[13\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-13)[\\[14\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-14)[\\[15\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-15)\n\nFew dispute the large number of metastable vacua.\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\] The existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial.\\[*[further explanation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Please_clarify \"Wikipedia:Please clarify\")*\\]\n\n#### Cosmological constant problem\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=6 \"Edit section: Cosmological constant problem\")\\]\n\n[Andrei Linde](https:\/\/en.wikipedia.org\/wiki\/Andrei_Linde \"Andrei Linde\"), [Sir Martin Rees](https:\/\/en.wikipedia.org\/wiki\/Sir_Martin_Rees \"Sir Martin Rees\") and [Leonard Susskind](https:\/\/en.wikipedia.org\/wiki\/Leonard_Susskind \"Leonard Susskind\") advocate it as a solution to the [cosmological constant problem](https:\/\/en.wikipedia.org\/wiki\/Cosmological_constant_problem \"Cosmological constant problem\").\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\n### Weak scale supersymmetry from the landscape\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=7 \"Edit section: Weak scale supersymmetry from the landscape\")\\]\n\nThe string landscape ideas can be applied to the notion of weak scale supersymmetry and the Little Hierarchy problem. For string vacua which include the MSSM (Minimal Supersymmetric Standard Model) as the low energy effective field theory, all values of SUSY breaking fields are expected to be equally likely on the landscape. This led Douglas[\\[16\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-16) and others to propose that the SUSY breaking scale is distributed as a power law in the landscape ![{\\\\displaystyle P\\_{prior}\\\\sim m\\_{soft}^{2n\\_{F}+n\\_{D}-1}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f84426fcffb7b6d00faa610a5ab08a8680d127a5) where ![{\\\\displaystyle n\\_{F}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/ccc36cc9554ca4e1cf9ece1b4bba77c31dba3389) is the number of F-breaking fields (distributed as complex numbers) and ![{\\\\displaystyle n\\_{D}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/b21e96ed85525311a68773d60c9abc849ad8cb50) is the number of D-breaking fields (distributed as real numbers). Next, one may impose the Agrawal, Barr, Donoghue, Seckel (ABDS) anthropic requirement[\\[17\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-17) that the derived weak scale lie within a factor of a few of our measured value (lest nuclei as needed for life as we know it become unstable (the atomic principle)). Combining these effects with a mild power-law draw to large soft SUSY breaking terms, one may calculate the Higgs boson and superparticle masses expected from the landscape.[\\[18\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-18) The Higgs mass probability distribution peaks around 125 GeV while sparticles (with the exception of light higgsinos) tend to lie well beyond current LHC search limits. This approach is an example of the application of stringy naturalness.\n\n#### Scientific relevance\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=String_theory_landscape&action=edit&section=8 \"Edit section: Scientific relevance\")\\]\n\n[David Gross](https:\/\/en.wikipedia.org\/wiki\/David_Gross \"David Gross\") suggests\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\] that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the [Smolin–Susskind debate](https:\/\/en.wikipedia.org\/wiki\/Smolin%E2%80%93Susskind_debate \"Smolin–Susskind debate\") on the merits of the landscape.\n\nThere are several popular books about the anthropic principle in cosmology.[\\[19\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-19) The authors of two physics blogs, [Lubos Motl](https:\/\/en.wikipedia.org\/wiki\/Lubos_Motl \"Lubos Motl\") and [Peter Woit](https:\/\/en.wikipedia.org\/wiki\/Peter_Woit \"Peter Woit\"), are opposed to this use of the anthropic principle.\\[*[why?](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Please_clarify \"Wikipedia:Please clarify\")*\\][\\[20\\]](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_note-20)\n\n- [Swampland](https:\/\/en.wikipedia.org\/wiki\/Swampland_\\(physics\\) \"Swampland (physics)\")\n- [Extra dimensions](https:\/\/en.wikipedia.org\/wiki\/String_theory#Extra_dimensions \"String theory\")\n- [M-theory](https:\/\/en.wikipedia.org\/wiki\/M-theory \"M-theory\")\n\n1. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-Ashok_1-0)** The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See [M. Douglas](https:\/\/en.wikipedia.org\/wiki\/Michael_R._Douglas \"Michael R. Douglas\"), \"The statistics of string \/ M theory vacua\", *JHEP* **0305**, 46 (2003). [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0303194](https:\/\/arxiv.org\/abs\/hep-th\/0303194); S. Ashok and M. Douglas, \"Counting flux vacua\", *JHEP* **0401**, 060 (2004).\n2. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-2)**\n   Baggott, Jim (2018). [*Quantum Space Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe*](https:\/\/books.google.com\/books?id=HwN6DwAAQBAJ&pg=PA288). Oxford University Press. p. 288. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n   \n   [978-0-19-253681-5](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-0-19-253681-5 \"Special:BookSources\/978-0-19-253681-5\")\n   \n   .\n3. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-3)** L. Smolin, \"Did the universe evolve?\", *Classical and Quantum Gravity* **9**, 173–191 (1992). L. Smolin, *[The Life of the Cosmos](https:\/\/en.wikipedia.org\/wiki\/The_Life_of_the_Cosmos \"The Life of the Cosmos\")* (Oxford, 1997)\n4. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-4)**\n   Read, James; Le Bihan, Baptiste (2021). [\"The landscape and the multiverse: What's the problem?\"](https:\/\/doi.org\/10.1007%2Fs11229-021-03137-0). *Synthese*. **199** (3–4\\): 7749–7771\\. [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1007\/s11229-021-03137-0](https:\/\/doi.org\/10.1007%2Fs11229-021-03137-0). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [234815857](https:\/\/api.semanticscholar.org\/CorpusID:234815857).\n5. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-5)**\n   Taylor, Washington; Wang, Yi-Nan (2015). \"The F-theory geometry with most flux vacua\". *Journal of High Energy Physics*. **2015** (12): 164. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1511\\.03209](https:\/\/arxiv.org\/abs\/1511.03209). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2015JHEP...12..164T](https:\/\/ui.adsabs.harvard.edu\/abs\/2015JHEP...12..164T). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1007\/JHEP12(2015)164](https:\/\/doi.org\/10.1007%2FJHEP12%282015%29164). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [41149049](https:\/\/api.semanticscholar.org\/CorpusID:41149049).\n6. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-6)**\n   Frederik Denef; Douglas, Michael R. (2007). \"Computational complexity of the landscape\". *Annals of Physics*. **322** (5): 1096–1142\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0602072](https:\/\/arxiv.org\/abs\/hep-th\/0602072). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2007AnPhy.322.1096D](https:\/\/ui.adsabs.harvard.edu\/abs\/2007AnPhy.322.1096D). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/j.aop.2006.07.013](https:\/\/doi.org\/10.1016%2Fj.aop.2006.07.013). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [281586](https:\/\/api.semanticscholar.org\/CorpusID:281586).\n7. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-7)**\n   Kachru, Shamit; Kallosh, Renata; Linde, Andrei; Trivedi, Sandip P. (2003). \"de Sitter Vacua in String Theory\". *Physical Review D*. **68** (4) 046005. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0301240](https:\/\/arxiv.org\/abs\/hep-th\/0301240). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2003PhRvD..68d6005K](https:\/\/ui.adsabs.harvard.edu\/abs\/2003PhRvD..68d6005K). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1103\/PhysRevD.68.046005](https:\/\/doi.org\/10.1103%2FPhysRevD.68.046005). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [119482182](https:\/\/api.semanticscholar.org\/CorpusID:119482182).\n8. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-8)** L. Susskind, \"The anthropic landscape of string theory\", [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0302219](https:\/\/arxiv.org\/abs\/hep-th\/0302219).\n9. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-9)** S. Weinberg, \"Anthropic bound on the cosmological constant\", *Phys. Rev. Lett.* **59**, 2607 (1987).\n10. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-10)** S. M. Carroll, \"Is our universe natural?\" (2005) [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0512148](https:\/\/arxiv.org\/abs\/hep-th\/0512148) reviews a number of proposals in preprints dated 2004\/5.\n11. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-11)** M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, \"Dimensionless constants, cosmology and other dark matters\", [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[astro-ph\/0511774](https:\/\/arxiv.org\/abs\/astro-ph\/0511774). F. Wilczek, \"Enlightenment, knowledge, ignorance, temptation\", [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-ph\/0512187](https:\/\/arxiv.org\/abs\/hep-ph\/0512187). See also the discussion at [\\[1\\]](http:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=310).\n12. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-12)**\n    See, *e.g.*\n    \n    Alexander Vilenkin (2007). \"A measure of the multiverse\". *Journal of Physics A: Mathematical and Theoretical*. **40** (25): 6777–6785\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0609193](https:\/\/arxiv.org\/abs\/hep-th\/0609193). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2007JPhA...40.6777V](https:\/\/ui.adsabs.harvard.edu\/abs\/2007JPhA...40.6777V). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1088\/1751-8113\/40\/25\/S22](https:\/\/doi.org\/10.1088%2F1751-8113%2F40%2F25%2FS22). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [119390736](https:\/\/api.semanticscholar.org\/CorpusID:119390736).\n13. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-13)**\n    Abraham Loeb (2006). \"An observational test for the anthropic origin of the cosmological constant\". *Journal of Cosmology and Astroparticle Physics*. **0605** (5): 009. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[astro-ph\/0604242](https:\/\/arxiv.org\/abs\/astro-ph\/0604242). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2006JCAP...05..009L](https:\/\/ui.adsabs.harvard.edu\/abs\/2006JCAP...05..009L). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1088\/1475-7516\/2006\/05\/009](https:\/\/doi.org\/10.1088%2F1475-7516%2F2006%2F05%2F009). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [39340203](https:\/\/api.semanticscholar.org\/CorpusID:39340203).\n14. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-14)**\n    Jaume Garriga & Alexander Vilenkin (2006). \"Anthropic prediction for Lambda and the Q catastrophe\". *Prog. Theor. Phys. Suppl*. **163**: 245–57\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0508005](https:\/\/arxiv.org\/abs\/hep-th\/0508005). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2006PThPS.163..245G](https:\/\/ui.adsabs.harvard.edu\/abs\/2006PThPS.163..245G). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1143\/PTPS.163.245](https:\/\/doi.org\/10.1143%2FPTPS.163.245). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [118936307](https:\/\/api.semanticscholar.org\/CorpusID:118936307).\n15. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-15)**\n    Delia Schwartz-Perlov & Alexander Vilenkin (2006). \"Probabilities in the Bousso-Polchinski multiverse\". *Journal of Cosmology and Astroparticle Physics*. **0606** (6): 010. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0601162](https:\/\/arxiv.org\/abs\/hep-th\/0601162). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2006JCAP...06..010S](https:\/\/ui.adsabs.harvard.edu\/abs\/2006JCAP...06..010S). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1088\/1475-7516\/2006\/06\/010](https:\/\/doi.org\/10.1088%2F1475-7516%2F2006%2F06%2F010). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [119337679](https:\/\/api.semanticscholar.org\/CorpusID:119337679).\n16. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-16)** M. R. Douglas, \"Statistical analysis of the supersymmetry breaking scale\", [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-th\/0405279](https:\/\/arxiv.org\/abs\/hep-th\/0405279).\n17. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-17)** V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel, \"Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking\", *Phys. Rev. Lett.* **80**, 1822 (1998).[arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-ph\/9801253](https:\/\/arxiv.org\/abs\/hep-ph\/9801253)\n18. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-18)** H. Baer, V. Barger, H. Serce and K. Sinha, \"Higgs and superparticle mass predictions from the landscape\", *JHEP* **03**, 002 (2018), [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1712\\.01399](https:\/\/arxiv.org\/abs\/1712.01399) .\n19. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-19)** L. Susskind, *The cosmic landscape: string theory and the illusion of intelligent design* (Little, Brown, 2005). M. J. Rees, *Just six numbers: the deep forces that shape the universe* (Basic Books, 2001). R. Bousso and J. Polchinski, \"The string theory landscape\", *Sci. Am.* **291**, 60–69 (2004).\n20. **[^](https:\/\/en.wikipedia.org\/wiki\/String_theory_landscape#cite_ref-20)** Motl's blog criticized the anthropic principle and Woit's [blog](http:\/\/www.math.columbia.edu\/~woit\/blog\/) frequently attacks the anthropic string landscape.\n\n- [String landscape; moduli stabilization; flux vacua; flux compactification](http:\/\/xstructure.inr.ac.ru\/x-bin\/theme2.py?arxiv=hep-th&level=1&index1=5460697) on [arxiv.org](https:\/\/en.wikipedia.org\/wiki\/Arxiv.org \"Arxiv.org\").\n- [Cvetič, Mirjam](https:\/\/en.wikipedia.org\/wiki\/Mirjam_Cveti%C4%8D \"Mirjam Cvetič\"); García-Etxebarria, Iñaki; Halverson, James (March 2011). \"On the computation of non-perturbative effective potentials in the string theory landscape\". *Fortschritte der Physik*. **59** (3–4\\): 243–283\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1009\\.5386](https:\/\/arxiv.org\/abs\/1009.5386). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2011ForPh..59..243C](https:\/\/ui.adsabs.harvard.edu\/abs\/2011ForPh..59..243C). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1002\/prop.201000093](https:\/\/doi.org\/10.1002%2Fprop.201000093). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [46634583](https:\/\/api.semanticscholar.org\/CorpusID:46634583).","meta_canonical":null}

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Boilerpipe Text	From Wikipedia, the free encyclopedia In string theory , the string theory landscape (or landscape of vacua ) is the collection of possible false vacua , [ 1 ] together comprising a collective "landscape" of choices of parameters governing compactifications . The term "landscape" comes from the notion of a fitness landscape in evolutionary biology . [ 2 ] It was first applied to cosmology by Lee Smolin in his book The Life of the Cosmos (1997), and was first used in the context of string theory by Leonard Susskind . [ 3 ] Compactified Calabi–Yau manifolds [ edit ] In string theory, the estimated count of distinct flux vacua is commonly stated as having a lower bound of , [ 4 ] but more recently this has been revised to , [ 5 ] and the true number may still be far higher. The large number of possibilities arises from choices of Calabi–Yau manifolds and choices of generalized magnetic fluxes over various homology cycles, found in F-theory . If there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is NP complete . [ 6 ] This is a version of the subset sum problem . A possible mechanism of string theory vacuum stabilization, now known as the KKLT mechanism , was proposed in 2003 by Shamit Kachru , Renata Kallosh , Andrei Linde , and Sandip Trivedi . [ 7 ] Fine-tuning by the anthropic principle [ edit ] Fine-tuning of constants like the cosmological constant or the Higgs boson mass is usually assumed to occur for precise physical reasons as opposed to taking their particular values at random. That is, these values should be uniquely consistent with underlying physical laws. The number of theoretically allowed configurations has prompted suggestions [ according to whom? ] that this is not the case, and that many different vacua are physically realized. [ 8 ] The anthropic principle proposes that fundamental constants may have the values they have because such values are necessary for life (and therefore intelligent observers to measure the constants). The anthropic landscape thus refers to the collection of those portions of the landscape that are suitable for supporting intelligent life. In 1987, Steven Weinberg proposed that the observed value of the cosmological constant was so small because it is impossible for life to occur in a universe with a much larger cosmological constant. [ 9 ] Weinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts [ which? ] have been made to apply similar reasoning to models of particle physics. [ 10 ] Such attempts are based in the general ideas of Bayesian probability ; interpreting probability in a context where it is only possible to draw one sample from a distribution is problematic in frequentist probability but not in Bayesian probability, which is not defined in terms of the frequency of repeated events. In such a framework, the probability of observing some fundamental parameters is given by, where is the prior probability, from fundamental theory, of the parameters and is the "anthropic selection function", determined by the number of "observers" that would occur in the universe with parameters . [ citation needed ] These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that: [ citation needed ] [ year needed ] The function is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way. The function is completely unknown, since so little is known about the origin of life. Simplified criteria (such as the number of galaxies) must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable universe. Simplified approaches [ edit ] Tegmark et al. have recently considered these objections and proposed a simplified anthropic scenario for axion dark matter in which they argue that the first two of these problems do not apply. [ 11 ] Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum. [ 12 ] A problem with many of the simplified approaches people [ who? ] have tried is that they "predict" a cosmological constant that is too large by a factor of 10–1000 orders of magnitude (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed. [ 13 ] [ 14 ] [ 15 ] Few dispute the large number of metastable vacua. [ citation needed ] The existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial. [ further explanation needed ] Cosmological constant problem [ edit ] Andrei Linde , Sir Martin Rees and Leonard Susskind advocate it as a solution to the cosmological constant problem . [ citation needed ] Weak scale supersymmetry from the landscape [ edit ] The string landscape ideas can be applied to the notion of weak scale supersymmetry and the Little Hierarchy problem. For string vacua which include the MSSM (Minimal Supersymmetric Standard Model) as the low energy effective field theory, all values of SUSY breaking fields are expected to be equally likely on the landscape. This led Douglas [ 16 ] and others to propose that the SUSY breaking scale is distributed as a power law in the landscape where is the number of F-breaking fields (distributed as complex numbers) and is the number of D-breaking fields (distributed as real numbers). Next, one may impose the Agrawal, Barr, Donoghue, Seckel (ABDS) anthropic requirement [ 17 ] that the derived weak scale lie within a factor of a few of our measured value (lest nuclei as needed for life as we know it become unstable (the atomic principle)). Combining these effects with a mild power-law draw to large soft SUSY breaking terms, one may calculate the Higgs boson and superparticle masses expected from the landscape. [ 18 ] The Higgs mass probability distribution peaks around 125 GeV while sparticles (with the exception of light higgsinos) tend to lie well beyond current LHC search limits. This approach is an example of the application of stringy naturalness. Scientific relevance [ edit ] David Gross suggests [ citation needed ] that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the Smolin–Susskind debate on the merits of the landscape. There are several popular books about the anthropic principle in cosmology. [ 19 ] The authors of two physics blogs, Lubos Motl and Peter Woit , are opposed to this use of the anthropic principle. [ why? ] [ 20 ] Swampland Extra dimensions M-theory ^ The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10 500 . See M. Douglas , "The statistics of string / M theory vacua", JHEP 0305 , 46 (2003). arXiv : hep-th/0303194 ; S. Ashok and M. Douglas, "Counting flux vacua", JHEP 0401 , 060 (2004). ^ Baggott, Jim (2018). Quantum Space Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe . Oxford University Press. p. 288. ISBN 978-0-19-253681-5 . ^ L. Smolin, "Did the universe evolve?", Classical and Quantum Gravity 9 , 173–191 (1992). L. Smolin, The Life of the Cosmos (Oxford, 1997) ^ Read, James; Le Bihan, Baptiste (2021). "The landscape and the multiverse: What's the problem?" . Synthese . 199 ( 3– 4): 7749– 7771. doi : 10.1007/s11229-021-03137-0 . S2CID 234815857 . ^ Taylor, Washington; Wang, Yi-Nan (2015). "The F-theory geometry with most flux vacua". Journal of High Energy Physics . 2015 (12): 164. arXiv : 1511.03209 . Bibcode : 2015JHEP...12..164T . doi : 10.1007/JHEP12(2015)164 . S2CID 41149049 . ^ Frederik Denef; Douglas, Michael R. (2007). "Computational complexity of the landscape". Annals of Physics . 322 (5): 1096– 1142. arXiv : hep-th/0602072 . Bibcode : 2007AnPhy.322.1096D . doi : 10.1016/j.aop.2006.07.013 . S2CID 281586 . ^ Kachru, Shamit; Kallosh, Renata; Linde, Andrei; Trivedi, Sandip P. (2003). "de Sitter Vacua in String Theory". Physical Review D . 68 (4) 046005. arXiv : hep-th/0301240 . Bibcode : 2003PhRvD..68d6005K . doi : 10.1103/PhysRevD.68.046005 . S2CID 119482182 . ^ L. Susskind, "The anthropic landscape of string theory", arXiv : hep-th/0302219 . ^ S. Weinberg, "Anthropic bound on the cosmological constant", Phys. Rev. Lett. 59 , 2607 (1987). ^ S. M. Carroll, "Is our universe natural?" (2005) arXiv : hep-th/0512148 reviews a number of proposals in preprints dated 2004/5. ^ M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, "Dimensionless constants, cosmology and other dark matters", arXiv : astro-ph/0511774 . F. Wilczek, "Enlightenment, knowledge, ignorance, temptation", arXiv : hep-ph/0512187 . See also the discussion at [1] . ^ See, e.g. Alexander Vilenkin (2007). "A measure of the multiverse". Journal of Physics A: Mathematical and Theoretical . 40 (25): 6777– 6785. arXiv : hep-th/0609193 . Bibcode : 2007JPhA...40.6777V . doi : 10.1088/1751-8113/40/25/S22 . S2CID 119390736 . ^ Abraham Loeb (2006). "An observational test for the anthropic origin of the cosmological constant". Journal of Cosmology and Astroparticle Physics . 0605 (5): 009. arXiv : astro-ph/0604242 . Bibcode : 2006JCAP...05..009L . doi : 10.1088/1475-7516/2006/05/009 . S2CID 39340203 . ^ Jaume Garriga & Alexander Vilenkin (2006). "Anthropic prediction for Lambda and the Q catastrophe". Prog. Theor. Phys. Suppl . 163 : 245– 57. arXiv : hep-th/0508005 . Bibcode : 2006PThPS.163..245G . doi : 10.1143/PTPS.163.245 . S2CID 118936307 . ^ Delia Schwartz-Perlov & Alexander Vilenkin (2006). "Probabilities in the Bousso-Polchinski multiverse". Journal of Cosmology and Astroparticle Physics . 0606 (6): 010. arXiv : hep-th/0601162 . Bibcode : 2006JCAP...06..010S . doi : 10.1088/1475-7516/2006/06/010 . S2CID 119337679 . ^ M. R. Douglas, "Statistical analysis of the supersymmetry breaking scale", arXiv : hep-th/0405279 . ^ V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel, "Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking", Phys. Rev. Lett. 80 , 1822 (1998). arXiv : hep-ph/9801253 ^ H. Baer, V. Barger, H. Serce and K. Sinha, "Higgs and superparticle mass predictions from the landscape", JHEP 03 , 002 (2018), arXiv : 1712.01399 . ^ L. Susskind, The cosmic landscape: string theory and the illusion of intelligent design (Little, Brown, 2005). M. J. Rees, Just six numbers: the deep forces that shape the universe (Basic Books, 2001). R. Bousso and J. Polchinski, "The string theory landscape", Sci. Am. 291 , 60–69 (2004). ^ Motl's blog criticized the anthropic principle and Woit's blog frequently attacks the anthropic string landscape. String landscape; moduli stabilization; flux vacua; flux compactification on arxiv.org . Cvetič, Mirjam ; García-Etxebarria, Iñaki; Halverson, James (March 2011). "On the computation of non-perturbative effective potentials in the string theory landscape". Fortschritte der Physik . 59 ( 3– 4): 243– 283. arXiv : 1009.5386 . Bibcode : 2011ForPh..59..243C . doi : 10.1002/prop.201000093 . S2CID 46634583 .
Markdown	[Jump to content](https://en.wikipedia.org/wiki/String_theory_landscape#bodyContent) Main menu Main menu move to sidebar hide Navigation - [Main page](https://en.wikipedia.org/wiki/Main_Page "Visit the main page [z]") - [Contents](https://en.wikipedia.org/wiki/Wikipedia:Contents "Guides to browsing Wikipedia") - [Current events](https://en.wikipedia.org/wiki/Portal:Current_events "Articles related to current events") - [Random article](https://en.wikipedia.org/wiki/Special:Random "Visit a randomly selected article [x]") - [About Wikipedia](https://en.wikipedia.org/wiki/Wikipedia:About "Learn about Wikipedia and how it works") - [Contact us](https://en.wikipedia.org/wiki/Wikipedia:Contact_us "How to contact Wikipedia") Contribute - [Help](https://en.wikipedia.org/wiki/Help:Contents "Guidance on how to use and edit Wikipedia") - [Learn to edit](https://en.wikipedia.org/wiki/Help:Introduction "Learn how to edit Wikipedia") - [Community portal](https://en.wikipedia.org/wiki/Wikipedia:Community_portal "The hub for editors") - [Recent changes](https://en.wikipedia.org/wiki/Special:RecentChanges "A list of recent changes to Wikipedia [r]") - [Upload file](https://en.wikipedia.org/wiki/Wikipedia:File_upload_wizard "Add images or other media for use on Wikipedia") - [Special pages](https://en.wikipedia.org/wiki/Special:SpecialPages "A list of all special pages [q]") [![](https://en.wikipedia.org/static/images/icons/enwiki-25.svg) ![Wikipedia](https://en.wikipedia.org/static/images/mobile/copyright/wikipedia-wordmark-en-25.svg) ![The Free Encyclopedia](https://en.wikipedia.org/static/images/mobile/copyright/wikipedia-tagline-en-25.svg)](https://en.wikipedia.org/wiki/Main_Page) [Search](https://en.wikipedia.org/wiki/Special:Search "Search Wikipedia [f]") Appearance - [Donate](https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en) - [Create account](https://en.wikipedia.org/w/index.php?title=Special:CreateAccount&returnto=String+theory+landscape "You are encouraged to create an account and log in; however, it is not mandatory") - [Log in](https://en.wikipedia.org/w/index.php?title=Special:UserLogin&returnto=String+theory+landscape "You're encouraged to log in; however, it's not mandatory. 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[o]") ## Contents move to sidebar hide - [(Top)](https://en.wikipedia.org/wiki/String_theory_landscape) - [1 Compactified Calabi–Yau manifolds](https://en.wikipedia.org/wiki/String_theory_landscape#Compactified_Calabi%E2%80%93Yau_manifolds) - [2 Fine-tuning by the anthropic principle](https://en.wikipedia.org/wiki/String_theory_landscape#Fine-tuning_by_the_anthropic_principle) Toggle Fine-tuning by the anthropic principle subsection - [2\.1 Weinberg model](https://en.wikipedia.org/wiki/String_theory_landscape#Weinberg_model) - [2\.2 Simplified approaches](https://en.wikipedia.org/wiki/String_theory_landscape#Simplified_approaches) - [2\.3 Interpretation](https://en.wikipedia.org/wiki/String_theory_landscape#Interpretation) - [2\.3.1 Cosmological constant problem](https://en.wikipedia.org/wiki/String_theory_landscape#Cosmological_constant_problem) - [2\.4 Weak scale supersymmetry from the landscape](https://en.wikipedia.org/wiki/String_theory_landscape#Weak_scale_supersymmetry_from_the_landscape) - [2\.4.1 Scientific relevance](https://en.wikipedia.org/wiki/String_theory_landscape#Scientific_relevance) - [2\.4.2 Popular reception](https://en.wikipedia.org/wiki/String_theory_landscape#Popular_reception) - [3 See also](https://en.wikipedia.org/wiki/String_theory_landscape#See_also) - [4 References](https://en.wikipedia.org/wiki/String_theory_landscape#References) - [5 External links](https://en.wikipedia.org/wiki/String_theory_landscape#External_links) Toggle the table of contents # String theory landscape 7 languages - [Беларуская](https://be.wikipedia.org/wiki/%D0%9B%D0%B0%D0%BD%D0%B4%D1%88%D0%B0%D1%84%D1%82_%D1%82%D1%8D%D0%BE%D1%80%D1%8B%D1%96_%D1%81%D1%82%D1%80%D1%83%D0%BD "Ландшафт тэорыі струн – Belarusian") - [Deutsch](https://de.wikipedia.org/wiki/Stringlandschaft "Stringlandschaft – German") - [Eesti](https://et.wikipedia.org/wiki/Stringiteooria_maastik "Stringiteooria maastik – Estonian") - [한국어](https://ko.wikipedia.org/wiki/%EB%81%88_%EC%9D%B4%EB%A1%A0_%ED%92%8D%EA%B2%BD "끈 이론 풍경 – Korean") - 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[Get shortened URL](https://en.wikipedia.org/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FString_theory_landscape) Print/export - [Download as PDF](https://en.wikipedia.org/w/index.php?title=Special:DownloadAsPdf&page=String_theory_landscape&action=show-download-screen "Download this page as a PDF file") - [Printable version](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&printable=yes "Printable version of this page [p]") In other projects - [Wikidata item](https://www.wikidata.org/wiki/Special:EntityPage/Q4253887 "Structured data on this page hosted by Wikidata [g]") Appearance move to sidebar hide From Wikipedia, the free encyclopedia Collection of possible string theory vacua \| [String theory](https://en.wikipedia.org/wiki/String_theory "String theory") \| \|---\| \| [![](https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Calabi_yau_formatted.svg/120px-Calabi_yau_formatted.svg.png)](https://en.wikipedia.org/wiki/File:Calabi_yau_formatted.svg) \| \| Fundamental objects \| \| [String](https://en.wikipedia.org/wiki/String_\(physics\) "String (physics)") [Cosmic string](https://en.wikipedia.org/wiki/Cosmic_string "Cosmic string") [Brane](https://en.wikipedia.org/wiki/Brane "Brane") [D-brane](https://en.wikipedia.org/wiki/D-brane "D-brane") \| \| Perturbative theory \| \| [Bosonic](https://en.wikipedia.org/wiki/Bosonic_string_theory "Bosonic string theory") [Superstring](https://en.wikipedia.org/wiki/Superstring_theory "Superstring theory") ([Type I](https://en.wikipedia.org/wiki/Type_I_string_theory "Type I string theory"), [Type II](https://en.wikipedia.org/wiki/Type_II_string_theory "Type II string theory"), [Heterotic](https://en.wikipedia.org/wiki/Heterotic_string_theory "Heterotic string theory")) \| \| Non-perturbative results \| \| [S-duality](https://en.wikipedia.org/wiki/S-duality "S-duality") [T-duality](https://en.wikipedia.org/wiki/T-duality "T-duality") [U-duality](https://en.wikipedia.org/wiki/U-duality "U-duality") [M-theory](https://en.wikipedia.org/wiki/M-theory "M-theory") [F-theory](https://en.wikipedia.org/wiki/F-theory "F-theory") [AdS/CFT correspondence](https://en.wikipedia.org/wiki/AdS/CFT_correspondence "AdS/CFT correspondence") \| \| Phenomenology \| \| [Phenomenology](https://en.wikipedia.org/wiki/String_phenomenology "String phenomenology") [Cosmology](https://en.wikipedia.org/wiki/String_cosmology "String cosmology") [Brane cosmology](https://en.wikipedia.org/wiki/Brane_cosmology "Brane cosmology") [Landscape]() \| \| Mathematics \| \| [Geometric Langlands correspondence](https://en.wikipedia.org/wiki/Geometric_Langlands_correspondence "Geometric Langlands correspondence") [Mirror symmetry](https://en.wikipedia.org/wiki/Mirror_symmetry_\(string_theory\) "Mirror symmetry (string theory)") [Monstrous moonshine](https://en.wikipedia.org/wiki/Monstrous_moonshine "Monstrous moonshine") [Vertex algebra](https://en.wikipedia.org/wiki/Vertex_algebra "Vertex algebra") [K-theory](https://en.wikipedia.org/wiki/K-theory_\(physics\) "K-theory (physics)") \| \| Related concepts [Theory of everything](https://en.wikipedia.org/wiki/Theory_of_everything "Theory of everything") [Conformal field theory](https://en.wikipedia.org/wiki/Conformal_field_theory "Conformal field theory") [Quantum gravity](https://en.wikipedia.org/wiki/Quantum_gravity "Quantum gravity") [Supersymmetry](https://en.wikipedia.org/wiki/Supersymmetry "Supersymmetry") [Supergravity](https://en.wikipedia.org/wiki/Supergravity "Supergravity") [Twistor string theory](https://en.wikipedia.org/wiki/Twistor_string_theory "Twistor string theory") [N = 4 supersymmetric Yang–Mills theory](https://en.wikipedia.org/wiki/N_%3D_4_supersymmetric_Yang%E2%80%93Mills_theory "N = 4 supersymmetric Yang–Mills theory") [Kaluza–Klein theory](https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory "Kaluza–Klein theory") [Multiverse](https://en.wikipedia.org/wiki/Multiverse "Multiverse") [Holographic principle](https://en.wikipedia.org/wiki/Holographic_principle "Holographic principle") \| \| Theorists [Aganagić](https://en.wikipedia.org/wiki/Mina_Aganagi%C4%87 "Mina Aganagić") [Arkani-Hamed](https://en.wikipedia.org/wiki/Nima_Arkani-Hamed "Nima Arkani-Hamed") [Atiyah](https://en.wikipedia.org/wiki/Michael_Atiyah "Michael Atiyah") [Banks](https://en.wikipedia.org/wiki/Tom_Banks_\(physicist\) "Tom Banks (physicist)") [Berenstein](https://en.wikipedia.org/wiki/David_Berenstein "David Berenstein") [Bousso](https://en.wikipedia.org/wiki/Raphael_Bousso "Raphael Bousso") [Costello](https://en.wikipedia.org/wiki/Kevin_Costello "Kevin Costello") [Curtright](https://en.wikipedia.org/wiki/Thomas_Curtright "Thomas Curtright") [Dijkgraaf](https://en.wikipedia.org/wiki/Robbert_Dijkgraaf "Robbert Dijkgraaf") [Distler](https://en.wikipedia.org/wiki/Jacques_Distler "Jacques Distler") [Douglas](https://en.wikipedia.org/wiki/Michael_R._Douglas "Michael R. Douglas") [Duff](https://en.wikipedia.org/wiki/Michael_Duff_\(physicist\) "Michael Duff (physicist)") [Dvali](https://en.wikipedia.org/wiki/Gia_Dvali "Gia Dvali") [Ferrara](https://en.wikipedia.org/wiki/Sergio_Ferrara "Sergio Ferrara") [Fischler](https://en.wikipedia.org/wiki/Willy_Fischler "Willy Fischler") [Friedan](https://en.wikipedia.org/wiki/Daniel_Friedan "Daniel Friedan") [Gates](https://en.wikipedia.org/wiki/Sylvester_James_Gates "Sylvester James Gates") [Gliozzi](https://en.wikipedia.org/wiki/Ferdinando_Gliozzi "Ferdinando Gliozzi") [Gopakumar](https://en.wikipedia.org/wiki/Rajesh_Gopakumar "Rajesh Gopakumar") [Green](https://en.wikipedia.org/wiki/Michael_Green_\(physicist\) "Michael Green (physicist)") [Greene](https://en.wikipedia.org/wiki/Brian_Greene "Brian Greene") [Gross](https://en.wikipedia.org/wiki/David_Gross "David Gross") [Gubser](https://en.wikipedia.org/wiki/Steven_Gubser "Steven Gubser") [Gukov](https://en.wikipedia.org/wiki/Sergei_Gukov "Sergei Gukov") [Guth](https://en.wikipedia.org/wiki/Alan_Guth "Alan Guth") [Hanson](https://en.wikipedia.org/wiki/Andrew_J._Hanson "Andrew J. Hanson") [Harvey](https://en.wikipedia.org/wiki/Jeffrey_A._Harvey "Jeffrey A. Harvey") [Hořava](https://en.wikipedia.org/wiki/Petr_Ho%C5%99ava_\(theorist\) "Petr Hořava (theorist)") [Horowitz](https://en.wikipedia.org/wiki/Gary_Horowitz "Gary Horowitz") [Gibbons](https://en.wikipedia.org/wiki/Gary_Gibbons "Gary Gibbons") [Kachru](https://en.wikipedia.org/wiki/Shamit_Kachru "Shamit Kachru") [Kaku](https://en.wikipedia.org/wiki/Michio_Kaku "Michio Kaku") [Kallosh](https://en.wikipedia.org/wiki/Renata_Kallosh "Renata Kallosh") [Kaluza](https://en.wikipedia.org/wiki/Theodor_Kaluza "Theodor Kaluza") [Kapustin](https://en.wikipedia.org/wiki/Anton_Kapustin "Anton Kapustin") [Klebanov](https://en.wikipedia.org/wiki/Igor_Klebanov "Igor Klebanov") [Knizhnik](https://en.wikipedia.org/wiki/Vadim_Knizhnik "Vadim Knizhnik") [Kontsevich](https://en.wikipedia.org/wiki/Maxim_Kontsevich "Maxim Kontsevich") [Klein](https://en.wikipedia.org/wiki/Oskar_Klein "Oskar Klein") [Linde](https://en.wikipedia.org/wiki/Andrei_Linde "Andrei Linde") [Maldacena](https://en.wikipedia.org/wiki/Juan_Mart%C3%ADn_Maldacena "Juan Martín Maldacena") [Mandelstam](https://en.wikipedia.org/wiki/Stanley_Mandelstam "Stanley Mandelstam") [Marolf](https://en.wikipedia.org/wiki/Donald_Marolf "Donald Marolf") [Martinec](https://en.wikipedia.org/wiki/Emil_Martinec "Emil Martinec") [Minwalla](https://en.wikipedia.org/wiki/Shiraz_Minwalla "Shiraz Minwalla") [Moore](https://en.wikipedia.org/wiki/Greg_Moore_\(physicist\) "Greg Moore (physicist)") [Motl](https://en.wikipedia.org/wiki/Lubo%C5%A1_Motl "Luboš Motl") [Mukhi](https://en.wikipedia.org/wiki/Sunil_Mukhi "Sunil Mukhi") [Myers](https://en.wikipedia.org/wiki/Robert_Myers_\(physicist\) "Robert Myers (physicist)") [Nanopoulos](https://en.wikipedia.org/wiki/Dimitri_Nanopoulos "Dimitri Nanopoulos") [Năstase](https://en.wikipedia.org/wiki/Hora%C8%9Biu_N%C4%83stase "Horațiu Năstase") [Nekrasov](https://en.wikipedia.org/wiki/Nikita_Nekrasov "Nikita Nekrasov") [Neveu](https://en.wikipedia.org/wiki/Andr%C3%A9_Neveu "André Neveu") [Nielsen](https://en.wikipedia.org/wiki/Holger_Bech_Nielsen "Holger Bech Nielsen") [van Nieuwenhuizen](https://en.wikipedia.org/wiki/Peter_van_Nieuwenhuizen "Peter van Nieuwenhuizen") [Novikov](https://en.wikipedia.org/wiki/Sergei_Novikov_\(mathematician\) "Sergei Novikov (mathematician)") [Olive](https://en.wikipedia.org/wiki/David_Olive "David Olive") [Ooguri](https://en.wikipedia.org/wiki/Hirosi_Ooguri "Hirosi Ooguri") [Ovrut](https://en.wikipedia.org/wiki/Burt_Ovrut "Burt Ovrut") [Polchinski](https://en.wikipedia.org/wiki/Joseph_Polchinski "Joseph Polchinski") [Polyakov](https://en.wikipedia.org/wiki/Alexander_Markovich_Polyakov "Alexander Markovich Polyakov") [Rajaraman](https://en.wikipedia.org/wiki/Arvind_Rajaraman "Arvind Rajaraman") [Ramond](https://en.wikipedia.org/wiki/Pierre_Ramond "Pierre Ramond") [Randall](https://en.wikipedia.org/wiki/Lisa_Randall "Lisa Randall") [Randjbar-Daemi](https://en.wikipedia.org/wiki/Seifallah_Randjbar-Daemi "Seifallah Randjbar-Daemi") [Roček](https://en.wikipedia.org/wiki/Martin_Ro%C4%8Dek "Martin Roček") [Rohm](https://en.wikipedia.org/wiki/Ryan_Rohm "Ryan Rohm") [Sagnotti](https://en.wikipedia.org/wiki/Augusto_Sagnotti "Augusto Sagnotti") [Scherk](https://en.wikipedia.org/wiki/Jo%C3%ABl_Scherk "Joël Scherk") [Schwarz](https://en.wikipedia.org/wiki/John_Henry_Schwarz "John Henry Schwarz") [Seiberg](https://en.wikipedia.org/wiki/Nathan_Seiberg "Nathan Seiberg") [Sen](https://en.wikipedia.org/wiki/Ashoke_Sen "Ashoke Sen") [Shenker](https://en.wikipedia.org/wiki/Stephen_Shenker "Stephen Shenker") [Siegel](https://en.wikipedia.org/wiki/Warren_Siegel "Warren Siegel") [Silverstein](https://en.wikipedia.org/wiki/Eva_Silverstein "Eva Silverstein") [Sơn](https://en.wikipedia.org/wiki/%C4%90%C3%A0m_Thanh_S%C6%A1n "Đàm Thanh Sơn") [Staudacher](https://en.wikipedia.org/wiki/Matthias_Staudacher "Matthias Staudacher") [Steinhardt](https://en.wikipedia.org/wiki/Paul_Steinhardt "Paul Steinhardt") [Strominger](https://en.wikipedia.org/wiki/Andrew_Strominger "Andrew Strominger") [Sundrum](https://en.wikipedia.org/wiki/Raman_Sundrum "Raman Sundrum") [Susskind](https://en.wikipedia.org/wiki/Leonard_Susskind "Leonard Susskind") ['t Hooft](https://en.wikipedia.org/wiki/Gerard_%27t_Hooft "Gerard 't Hooft") [Townsend](https://en.wikipedia.org/wiki/Paul_Townsend "Paul Townsend") [Trivedi](https://en.wikipedia.org/wiki/Sandip_Trivedi "Sandip Trivedi") [Turok](https://en.wikipedia.org/wiki/Neil_Turok "Neil Turok") [Vafa](https://en.wikipedia.org/wiki/Cumrun_Vafa "Cumrun Vafa") [Veneziano](https://en.wikipedia.org/wiki/Gabriele_Veneziano "Gabriele Veneziano") [Verlinde](https://en.wikipedia.org/wiki/Erik_Verlinde "Erik Verlinde") [Verlinde](https://en.wikipedia.org/wiki/Herman_Verlinde "Herman Verlinde") [Wess](https://en.wikipedia.org/wiki/Julius_Wess "Julius Wess") [Witten](https://en.wikipedia.org/wiki/Edward_Witten "Edward Witten") [Yau](https://en.wikipedia.org/wiki/Shing-Tung_Yau "Shing-Tung Yau") [Yoneya](https://en.wikipedia.org/wiki/Tamiaki_Yoneya "Tamiaki Yoneya") [Zamolodchikov](https://en.wikipedia.org/wiki/Alexander_Zamolodchikov "Alexander Zamolodchikov") [Zamolodchikov](https://en.wikipedia.org/wiki/Alexei_Zamolodchikov "Alexei Zamolodchikov") [Zaslow](https://en.wikipedia.org/wiki/Eric_Zaslow "Eric Zaslow") [Zumino](https://en.wikipedia.org/wiki/Bruno_Zumino "Bruno Zumino") [Zwiebach](https://en.wikipedia.org/wiki/Barton_Zwiebach "Barton Zwiebach") \| \| [History](https://en.wikipedia.org/wiki/History_of_string_theory "History of string theory") [Glossary](https://en.wikipedia.org/wiki/Glossary_of_string_theory "Glossary of string theory") \| \| [v](https://en.wikipedia.org/wiki/Template:String_theory "Template:String theory") [t](https://en.wikipedia.org/wiki/Template_talk:String_theory "Template talk:String theory") [e](https://en.wikipedia.org/wiki/Special:EditPage/Template:String_theory "Special:EditPage/Template:String theory") \| In [string theory](https://en.wikipedia.org/wiki/String_theory "String theory"), the string theory landscape (or landscape of vacua) is the collection of possible [false vacua](https://en.wikipedia.org/wiki/False_vacuum "False vacuum"),[\[1\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-Ashok-1) together comprising a collective "landscape" of choices of parameters governing [compactifications](https://en.wikipedia.org/wiki/Compactification_\(physics\) "Compactification (physics)"). The term "landscape" comes from the notion of a [fitness landscape](https://en.wikipedia.org/wiki/Fitness_landscape "Fitness landscape") in [evolutionary biology](https://en.wikipedia.org/wiki/Evolutionary_biology "Evolutionary biology").[\[2\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-2) It was first applied to cosmology by [Lee Smolin](https://en.wikipedia.org/wiki/Lee_Smolin "Lee Smolin") in his book [The Life of the Cosmos](https://en.wikipedia.org/wiki/The_Life_of_the_Cosmos "The Life of the Cosmos") (1997), and was first used in the context of string theory by [Leonard Susskind](https://en.wikipedia.org/wiki/Leonard_Susskind "Leonard Susskind").[\[3\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-3) ## Compactified Calabi–Yau manifolds \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=1 "Edit section: Compactified Calabi–Yau manifolds")\] Main article: [Compactification (physics)](https://en.wikipedia.org/wiki/Compactification_\(physics\) "Compactification (physics)") In string theory, the estimated count of distinct flux vacua is commonly stated as having a lower bound of 10 500 {\\displaystyle 10^{500}} ![{\\displaystyle 10^{500}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9fc79f91eb42fdee58d7e3e2d441013ad2488959),[\[4\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-4) but more recently this has been revised to 10 272 , 000 {\\displaystyle 10^{272,000}} ![{\\displaystyle 10^{272,000}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7ea2462969aa025b37c43ee26b6a3e026316b53),[\[5\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-5) and the true number may still be far higher. The large number of possibilities arises from choices of [Calabi–Yau manifolds](https://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold "Calabi–Yau manifold") and choices of generalized [magnetic fluxes](https://en.wikipedia.org/wiki/Magnetic_flux "Magnetic flux") over various [homology](https://en.wikipedia.org/wiki/Homology_\(mathematics\) "Homology (mathematics)") cycles, found in [F-theory](https://en.wikipedia.org/wiki/F-theory "F-theory"). If there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is [NP complete](https://en.wikipedia.org/wiki/NP_complete "NP complete").[\[6\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-6) This is a version of the [subset sum problem](https://en.wikipedia.org/wiki/Subset_sum_problem "Subset sum problem"). A possible mechanism of string theory vacuum stabilization, now known as the KKLT mechanism, was proposed in 2003 by [Shamit Kachru](https://en.wikipedia.org/wiki/Shamit_Kachru "Shamit Kachru"), [Renata Kallosh](https://en.wikipedia.org/wiki/Renata_Kallosh "Renata Kallosh"), [Andrei Linde](https://en.wikipedia.org/wiki/Andrei_Linde "Andrei Linde"), and [Sandip Trivedi](https://en.wikipedia.org/wiki/Sandip_Trivedi "Sandip Trivedi").[\[7\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-7) ## Fine-tuning by the anthropic principle \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=2 "Edit section: Fine-tuning by the anthropic principle")\] Main articles: [Fine-tuning (physics)](https://en.wikipedia.org/wiki/Fine-tuning_\(physics\) "Fine-tuning (physics)") and [Anthropic principle](https://en.wikipedia.org/wiki/Anthropic_principle "Anthropic principle") [Fine-tuning](https://en.wikipedia.org/wiki/Fine-tuning_\(physics\) "Fine-tuning (physics)") of constants like the [cosmological constant](https://en.wikipedia.org/wiki/Cosmological_constant "Cosmological constant") or the [Higgs boson](https://en.wikipedia.org/wiki/Higgs_boson "Higgs boson") mass is usually assumed to occur for precise physical reasons as opposed to taking their particular values at random. That is, these values should be uniquely consistent with underlying physical laws. The number of theoretically allowed configurations has prompted suggestions\[[according to whom?](https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions "Wikipedia:Manual of Style/Words to watch")\] that this is not the case, and that many different vacua are physically realized.[\[8\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-8) The [anthropic principle](https://en.wikipedia.org/wiki/Anthropic_principle "Anthropic principle") proposes that fundamental constants may have the values they have because such values are necessary for life (and therefore intelligent observers to measure the constants). The anthropic landscape thus refers to the collection of those portions of the landscape that are suitable for supporting intelligent life. ### Weinberg model \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=3 "Edit section: Weinberg model")\] In 1987, [Steven Weinberg](https://en.wikipedia.org/wiki/Steven_Weinberg "Steven Weinberg") proposed that the observed value of the [cosmological constant](https://en.wikipedia.org/wiki/Cosmological_constant "Cosmological constant") was so small because it is impossible for life to occur in a universe with a much larger cosmological constant.[\[9\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-9) Weinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts\[[which?](https://en.wikipedia.org/wiki/Wikipedia:Avoid_weasel_words "Wikipedia:Avoid weasel words")\] have been made to apply similar reasoning to models of particle physics.[\[10\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-10) Such attempts are based in the general ideas of [Bayesian probability](https://en.wikipedia.org/wiki/Bayesian_probability "Bayesian probability"); interpreting probability in a context where it is only possible to draw one [sample](https://en.wikipedia.org/wiki/Sample_size "Sample size") from a [distribution](https://en.wikipedia.org/wiki/Probability_distribution "Probability distribution") is problematic in [frequentist probability](https://en.wikipedia.org/wiki/Frequentist_probability "Frequentist probability") but not in Bayesian probability, which is not defined in terms of the frequency of repeated events. In such a framework, the probability P ( x ) {\\displaystyle P(x)} ![{\\displaystyle P(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/89833156eff2c51bfb8750db3306a0544ce34e14) of observing some fundamental parameters x {\\displaystyle x} ![{\\displaystyle x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4) is given by, P ( x ) \= P p r i o r ( x ) × P s e l e c t i o n ( x ) , {\\displaystyle P(x)=P\_{\\mathrm {prior} }(x)\\times P\_{\\mathrm {selection} }(x),} ![{\\displaystyle P(x)=P\_{\\mathrm {prior} }(x)\\times P\_{\\mathrm {selection} }(x),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd5c5e9caa69d16bda58b1d40e39d5f19308f211) where P p r i o r {\\displaystyle P\_{\\mathrm {prior} }} ![{\\displaystyle P\_{\\mathrm {prior} }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8b9334b97d41d76b64c846d2c73f5e8009acde1e) is the prior probability, from fundamental theory, of the parameters x {\\displaystyle x} ![{\\displaystyle x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4) and P s e l e c t i o n {\\displaystyle P\_{\\mathrm {selection} }} ![{\\displaystyle P\_{\\mathrm {selection} }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f83c7cd3c00307571cd5af18a6f4029cf1252faa) is the "anthropic selection function", determined by the number of "observers" that would occur in the universe with parameters x {\\displaystyle x} ![{\\displaystyle x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4).\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\]\[[year needed](https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers "Wikipedia:Manual of Style/Dates and numbers")\] - The function P p r i o r {\\displaystyle P\_{\\mathrm {prior} }} ![{\\displaystyle P\_{\\mathrm {prior} }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8b9334b97d41d76b64c846d2c73f5e8009acde1e) is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way. - The function P s e l e c t i o n {\\displaystyle P\_{\\mathrm {selection} }} ![{\\displaystyle P\_{\\mathrm {selection} }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f83c7cd3c00307571cd5af18a6f4029cf1252faa) is completely unknown, since so little is known about the origin of life. Simplified criteria (such as the number of galaxies) must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable universe. ### Simplified approaches \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=4 "Edit section: Simplified approaches")\] [Tegmark](https://en.wikipedia.org/wiki/Max_Tegmark "Max Tegmark") et al. have recently considered these objections and proposed a simplified anthropic scenario for [axion](https://en.wikipedia.org/wiki/Axion "Axion") [dark matter](https://en.wikipedia.org/wiki/Dark_matter "Dark matter") in which they argue that the first two of these problems do not apply.[\[11\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-11) Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.[\[12\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-12) A problem with many of the simplified approaches people\[[who?](https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions "Wikipedia:Manual of Style/Words to watch")\] have tried is that they "predict" a cosmological constant that is too large by a factor of 10–1000 orders of magnitude (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed.[\[13\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-13)[\[14\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-14)[\[15\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-15) ### Interpretation \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=5 "Edit section: Interpretation")\] Few dispute the large number of metastable vacua.\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] The existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial.\[[further explanation needed](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify "Wikipedia:Please clarify")\] #### Cosmological constant problem \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=6 "Edit section: Cosmological constant problem")\] [Andrei Linde](https://en.wikipedia.org/wiki/Andrei_Linde "Andrei Linde"), [Sir Martin Rees](https://en.wikipedia.org/wiki/Sir_Martin_Rees "Sir Martin Rees") and [Leonard Susskind](https://en.wikipedia.org/wiki/Leonard_Susskind "Leonard Susskind") advocate it as a solution to the [cosmological constant problem](https://en.wikipedia.org/wiki/Cosmological_constant_problem "Cosmological constant problem").\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] ### Weak scale supersymmetry from the landscape \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=7 "Edit section: Weak scale supersymmetry from the landscape")\] The string landscape ideas can be applied to the notion of weak scale supersymmetry and the Little Hierarchy problem. For string vacua which include the MSSM (Minimal Supersymmetric Standard Model) as the low energy effective field theory, all values of SUSY breaking fields are expected to be equally likely on the landscape. This led Douglas[\[16\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-16) and others to propose that the SUSY breaking scale is distributed as a power law in the landscape P p r i o r ∼ m s o f t 2 n F \+ n D − 1 {\\displaystyle P\_{prior}\\sim m\_{soft}^{2n\_{F}+n\_{D}-1}} ![{\\displaystyle P\_{prior}\\sim m\_{soft}^{2n\_{F}+n\_{D}-1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f84426fcffb7b6d00faa610a5ab08a8680d127a5) where n F {\\displaystyle n\_{F}} ![{\\displaystyle n\_{F}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ccc36cc9554ca4e1cf9ece1b4bba77c31dba3389) is the number of F-breaking fields (distributed as complex numbers) and n D {\\displaystyle n\_{D}} ![{\\displaystyle n\_{D}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b21e96ed85525311a68773d60c9abc849ad8cb50) is the number of D-breaking fields (distributed as real numbers). Next, one may impose the Agrawal, Barr, Donoghue, Seckel (ABDS) anthropic requirement[\[17\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-17) that the derived weak scale lie within a factor of a few of our measured value (lest nuclei as needed for life as we know it become unstable (the atomic principle)). Combining these effects with a mild power-law draw to large soft SUSY breaking terms, one may calculate the Higgs boson and superparticle masses expected from the landscape.[\[18\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-18) The Higgs mass probability distribution peaks around 125 GeV while sparticles (with the exception of light higgsinos) tend to lie well beyond current LHC search limits. This approach is an example of the application of stringy naturalness. #### Scientific relevance \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=8 "Edit section: Scientific relevance")\] [David Gross](https://en.wikipedia.org/wiki/David_Gross "David Gross") suggests\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the [Smolin–Susskind debate](https://en.wikipedia.org/wiki/Smolin%E2%80%93Susskind_debate "Smolin–Susskind debate") on the merits of the landscape. #### Popular reception \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=9 "Edit section: Popular reception")\] There are several popular books about the anthropic principle in cosmology.[\[19\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-19) The authors of two physics blogs, [Lubos Motl](https://en.wikipedia.org/wiki/Lubos_Motl "Lubos Motl") and [Peter Woit](https://en.wikipedia.org/wiki/Peter_Woit "Peter Woit"), are opposed to this use of the anthropic principle.\[[why?](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify "Wikipedia:Please clarify")\][\[20\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-20) ## See also \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=10 "Edit section: See also")\] - [![icon](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/40px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png)](https://en.wikipedia.org/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg)[Physics portal](https://en.wikipedia.org/wiki/Portal:Physics "Portal:Physics") - [Swampland](https://en.wikipedia.org/wiki/Swampland_\(physics\) "Swampland (physics)") - [Extra dimensions](https://en.wikipedia.org/wiki/String_theory#Extra_dimensions "String theory") - [M-theory](https://en.wikipedia.org/wiki/M-theory "M-theory") ## References \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=11 "Edit section: References")\] 1. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-Ashok_1-0) The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See [M. Douglas](https://en.wikipedia.org/wiki/Michael_R._Douglas "Michael R. Douglas"), "The statistics of string / M theory vacua", JHEP 0305, 46 (2003). [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0303194](https://arxiv.org/abs/hep-th/0303194); S. Ashok and M. Douglas, "Counting flux vacua", JHEP 0401, 060 (2004). 2. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-2) Baggott, Jim (2018). [Quantum Space Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe](https://books.google.com/books?id=HwN6DwAAQBAJ&pg=PA288). Oxford University Press. p. 288. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-0-19-253681-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-253681-5 "Special:BookSources/978-0-19-253681-5") . 3. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-3) L. Smolin, "Did the universe evolve?", Classical and Quantum Gravity 9, 173–191 (1992). L. Smolin, [The Life of the Cosmos](https://en.wikipedia.org/wiki/The_Life_of_the_Cosmos "The Life of the Cosmos") (Oxford, 1997) 4. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-4) Read, James; Le Bihan, Baptiste (2021). ["The landscape and the multiverse: What's the problem?"](https://doi.org/10.1007%2Fs11229-021-03137-0). Synthese. 199 (3–4\): 7749–7771\. [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1007/s11229-021-03137-0](https://doi.org/10.1007%2Fs11229-021-03137-0). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [234815857](https://api.semanticscholar.org/CorpusID:234815857). 5. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-5) Taylor, Washington; Wang, Yi-Nan (2015). "The F-theory geometry with most flux vacua". Journal of High Energy Physics. 2015 (12): 164. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1511\.03209](https://arxiv.org/abs/1511.03209). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2015JHEP...12..164T](https://ui.adsabs.harvard.edu/abs/2015JHEP...12..164T). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1007/JHEP12(2015)164](https://doi.org/10.1007%2FJHEP12%282015%29164). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [41149049](https://api.semanticscholar.org/CorpusID:41149049). 6. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-6) Frederik Denef; Douglas, Michael R. (2007). "Computational complexity of the landscape". Annals of Physics. 322 (5): 1096–1142\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0602072](https://arxiv.org/abs/hep-th/0602072). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2007AnPhy.322.1096D](https://ui.adsabs.harvard.edu/abs/2007AnPhy.322.1096D). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/j.aop.2006.07.013](https://doi.org/10.1016%2Fj.aop.2006.07.013). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [281586](https://api.semanticscholar.org/CorpusID:281586). 7. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-7) Kachru, Shamit; Kallosh, Renata; Linde, Andrei; Trivedi, Sandip P. (2003). "de Sitter Vacua in String Theory". Physical Review D. 68 (4) 046005. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0301240](https://arxiv.org/abs/hep-th/0301240). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2003PhRvD..68d6005K](https://ui.adsabs.harvard.edu/abs/2003PhRvD..68d6005K). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1103/PhysRevD.68.046005](https://doi.org/10.1103%2FPhysRevD.68.046005). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [119482182](https://api.semanticscholar.org/CorpusID:119482182). 8. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-8) L. Susskind, "The anthropic landscape of string theory", [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0302219](https://arxiv.org/abs/hep-th/0302219). 9. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-9) S. Weinberg, "Anthropic bound on the cosmological constant", Phys. Rev. Lett. 59, 2607 (1987). 10. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-10) S. M. Carroll, "Is our universe natural?" (2005) [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0512148](https://arxiv.org/abs/hep-th/0512148) reviews a number of proposals in preprints dated 2004/5. 11. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-11) M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, "Dimensionless constants, cosmology and other dark matters", [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[astro-ph/0511774](https://arxiv.org/abs/astro-ph/0511774). F. Wilczek, "Enlightenment, knowledge, ignorance, temptation", [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-ph/0512187](https://arxiv.org/abs/hep-ph/0512187). See also the discussion at [\[1\]](http://www.math.columbia.edu/~woit/wordpress/?p=310). 12. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-12) See, e.g. Alexander Vilenkin (2007). "A measure of the multiverse". Journal of Physics A: Mathematical and Theoretical. 40 (25): 6777–6785\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0609193](https://arxiv.org/abs/hep-th/0609193). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2007JPhA...40.6777V](https://ui.adsabs.harvard.edu/abs/2007JPhA...40.6777V). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1088/1751-8113/40/25/S22](https://doi.org/10.1088%2F1751-8113%2F40%2F25%2FS22). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [119390736](https://api.semanticscholar.org/CorpusID:119390736). 13. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-13) Abraham Loeb (2006). "An observational test for the anthropic origin of the cosmological constant". Journal of Cosmology and Astroparticle Physics. 0605 (5): 009. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[astro-ph/0604242](https://arxiv.org/abs/astro-ph/0604242). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2006JCAP...05..009L](https://ui.adsabs.harvard.edu/abs/2006JCAP...05..009L). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1088/1475-7516/2006/05/009](https://doi.org/10.1088%2F1475-7516%2F2006%2F05%2F009). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [39340203](https://api.semanticscholar.org/CorpusID:39340203). 14. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-14) Jaume Garriga & Alexander Vilenkin (2006). "Anthropic prediction for Lambda and the Q catastrophe". Prog. Theor. Phys. Suppl. 163: 245–57\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0508005](https://arxiv.org/abs/hep-th/0508005). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2006PThPS.163..245G](https://ui.adsabs.harvard.edu/abs/2006PThPS.163..245G). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1143/PTPS.163.245](https://doi.org/10.1143%2FPTPS.163.245). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [118936307](https://api.semanticscholar.org/CorpusID:118936307). 15. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-15) Delia Schwartz-Perlov & Alexander Vilenkin (2006). "Probabilities in the Bousso-Polchinski multiverse". Journal of Cosmology and Astroparticle Physics. 0606 (6): 010. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0601162](https://arxiv.org/abs/hep-th/0601162). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2006JCAP...06..010S](https://ui.adsabs.harvard.edu/abs/2006JCAP...06..010S). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1088/1475-7516/2006/06/010](https://doi.org/10.1088%2F1475-7516%2F2006%2F06%2F010). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [119337679](https://api.semanticscholar.org/CorpusID:119337679). 16. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-16) M. R. Douglas, "Statistical analysis of the supersymmetry breaking scale", [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0405279](https://arxiv.org/abs/hep-th/0405279). 17. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-17) V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel, "Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking", Phys. Rev. Lett. 80, 1822 (1998). [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-ph/9801253](https://arxiv.org/abs/hep-ph/9801253) 18. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-18) H. Baer, V. Barger, H. Serce and K. Sinha, "Higgs and superparticle mass predictions from the landscape", JHEP 03, 002 (2018), [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1712\.01399](https://arxiv.org/abs/1712.01399) . 19. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-19) L. Susskind, The cosmic landscape: string theory and the illusion of intelligent design (Little, Brown, 2005). M. J. Rees, Just six numbers: the deep forces that shape the universe (Basic Books, 2001). R. Bousso and J. Polchinski, "The string theory landscape", Sci. Am. 291, 60–69 (2004). 20. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-20) Motl's blog criticized the anthropic principle and Woit's [blog](http://www.math.columbia.edu/~woit/blog/) frequently attacks the anthropic string landscape. ## External links \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=12 "Edit section: External links")\] - [String landscape; moduli stabilization; flux vacua; flux compactification](http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=hep-th&level=1&index1=5460697) on [arxiv.org](https://en.wikipedia.org/wiki/Arxiv.org "Arxiv.org"). - [Cvetič, Mirjam](https://en.wikipedia.org/wiki/Mirjam_Cveti%C4%8D "Mirjam Cvetič"); García-Etxebarria, Iñaki; Halverson, James (March 2011). "On the computation of non-perturbative effective potentials in the string theory landscape". Fortschritte der Physik. 59 (3–4\): 243–283\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1009\.5386](https://arxiv.org/abs/1009.5386). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2011ForPh..59..243C](https://ui.adsabs.harvard.edu/abs/2011ForPh..59..243C). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1002/prop.201000093](https://doi.org/10.1002%2Fprop.201000093). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [46634583](https://api.semanticscholar.org/CorpusID:46634583). \| [v](https://en.wikipedia.org/wiki/Template:String_theory_topics "Template:String theory topics") [t](https://en.wikipedia.org/wiki/Template_talk:String_theory_topics "Template talk:String theory topics") [e](https://en.wikipedia.org/wiki/Special:EditPage/Template:String_theory_topics "Special:EditPage/Template:String theory topics")[String theory](https://en.wikipedia.org/wiki/String_theory "String theory") \| \| \|---\|---\| \| Background \| [Strings](https://en.wikipedia.org/wiki/String_\(physics\) "String (physics)") [Cosmic strings](https://en.wikipedia.org/wiki/Cosmic_string "Cosmic string") [History of string theory](https://en.wikipedia.org/wiki/History_of_string_theory "History of string theory") [First superstring revolution](https://en.wikipedia.org/wiki/First_superstring_revolution "First superstring revolution") [Second superstring revolution](https://en.wikipedia.org/wiki/Second_superstring_revolution "Second superstring revolution") [String theory landscape]() \| \| Theory \| [Nambu–Goto action](https://en.wikipedia.org/wiki/Nambu%E2%80%93Goto_action "Nambu–Goto action") [Polyakov action](https://en.wikipedia.org/wiki/Polyakov_action "Polyakov action") [Bosonic string theory](https://en.wikipedia.org/wiki/Bosonic_string_theory "Bosonic string theory") [Superstring theory](https://en.wikipedia.org/wiki/Superstring_theory "Superstring theory") [Type I string](https://en.wikipedia.org/wiki/Type_I_string_theory "Type I string theory") [Type II string](https://en.wikipedia.org/wiki/Type_II_string_theory "Type II string theory") [Type IIA string](https://en.wikipedia.org/wiki/Type_II_string_theory "Type II string theory") [Type IIB string](https://en.wikipedia.org/wiki/Type_II_string_theory "Type II string theory") [Heterotic string](https://en.wikipedia.org/wiki/Heterotic_string_theory "Heterotic string theory") [N=2 superstring](https://en.wikipedia.org/wiki/N%3D2_superstring "N=2 superstring") [F-theory](https://en.wikipedia.org/wiki/F-theory "F-theory") [String field theory](https://en.wikipedia.org/wiki/String_field_theory "String field theory") [Matrix string theory](https://en.wikipedia.org/wiki/Matrix_string_theory "Matrix string theory") [Non-critical string theory](https://en.wikipedia.org/wiki/Non-critical_string_theory "Non-critical string theory") [Non-linear sigma model](https://en.wikipedia.org/wiki/Non-linear_sigma_model "Non-linear sigma model") [Tachyon condensation](https://en.wikipedia.org/wiki/Tachyon_condensation "Tachyon condensation") [RNS formalism](https://en.wikipedia.org/wiki/RNS_formalism "RNS formalism") [GS formalism](https://en.wikipedia.org/wiki/GS_formalism "GS formalism") \| \| [String duality](https://en.wikipedia.org/wiki/String_duality "String duality") \| [T-duality](https://en.wikipedia.org/wiki/T-duality "T-duality") [S-duality](https://en.wikipedia.org/wiki/S-duality "S-duality") [U-duality](https://en.wikipedia.org/wiki/U-duality "U-duality") [Montonen–Olive duality](https://en.wikipedia.org/wiki/Montonen%E2%80%93Olive_duality "Montonen–Olive duality") \| \| Particles and fields \| [Graviton](https://en.wikipedia.org/wiki/Graviton "Graviton") [Dilaton](https://en.wikipedia.org/wiki/Dilaton "Dilaton") [Tachyon](https://en.wikipedia.org/wiki/Tachyon "Tachyon") [Ramond–Ramond field](https://en.wikipedia.org/wiki/Ramond%E2%80%93Ramond_field "Ramond–Ramond field") [Kalb–Ramond field](https://en.wikipedia.org/wiki/Kalb%E2%80%93Ramond_field "Kalb–Ramond field") [Magnetic monopole](https://en.wikipedia.org/wiki/Magnetic_monopole "Magnetic monopole") [Dual graviton](https://en.wikipedia.org/wiki/Dual_graviton "Dual graviton") [Dual photon](https://en.wikipedia.org/wiki/Dual_photon "Dual photon") \| \| [Branes](https://en.wikipedia.org/wiki/Brane "Brane") \| [D-brane](https://en.wikipedia.org/wiki/D-brane "D-brane") [NS5-brane](https://en.wikipedia.org/wiki/NS5-brane "NS5-brane") [M2-brane](https://en.wikipedia.org/wiki/M2-brane "M2-brane") [M5-brane](https://en.wikipedia.org/wiki/M5-brane "M5-brane") [S-brane](https://en.wikipedia.org/wiki/S-brane "S-brane") [Black brane](https://en.wikipedia.org/wiki/Black_brane "Black brane") [Black holes](https://en.wikipedia.org/wiki/Black_hole "Black hole") [Black string](https://en.wikipedia.org/wiki/Black_string "Black string") [Brane cosmology](https://en.wikipedia.org/wiki/Brane_cosmology "Brane cosmology") [Quiver diagram](https://en.wikipedia.org/wiki/Quiver_diagram "Quiver diagram") [Hanany–Witten transition](https://en.wikipedia.org/wiki/Hanany%E2%80%93Witten_transition "Hanany–Witten transition") \| \| [Conformal field theory](https://en.wikipedia.org/wiki/Conformal_field_theory "Conformal field theory") \| [Virasoro algebra](https://en.wikipedia.org/wiki/Virasoro_algebra "Virasoro algebra") [Mirror symmetry](https://en.wikipedia.org/wiki/Mirror_symmetry_\(string_theory\) "Mirror symmetry (string theory)") [Conformal anomaly](https://en.wikipedia.org/wiki/Conformal_anomaly "Conformal anomaly") [Conformal algebra](https://en.wikipedia.org/wiki/Conformal_symmetry "Conformal symmetry") [Superconformal algebra](https://en.wikipedia.org/wiki/Superconformal_algebra "Superconformal algebra") [Vertex operator algebra](https://en.wikipedia.org/wiki/Vertex_operator_algebra "Vertex operator algebra") [Loop algebra](https://en.wikipedia.org/wiki/Loop_algebra "Loop algebra") [Kac–Moody algebra](https://en.wikipedia.org/wiki/Kac%E2%80%93Moody_algebra "Kac–Moody algebra") [Wess–Zumino–Witten model](https://en.wikipedia.org/wiki/Wess%E2%80%93Zumino%E2%80%93Witten_model "Wess–Zumino–Witten model") \| \| [Gauge theory](https://en.wikipedia.org/wiki/Gauge_theory "Gauge theory") \| [Anomalies](https://en.wikipedia.org/wiki/Anomaly_\(physics\) "Anomaly (physics)") [Instantons](https://en.wikipedia.org/wiki/Instanton "Instanton") [Chern–Simons form](https://en.wikipedia.org/wiki/Chern%E2%80%93Simons_form "Chern–Simons form") [Bogomol'nyi–Prasad–Sommerfield bound](https://en.wikipedia.org/wiki/Bogomol%27nyi%E2%80%93Prasad%E2%80%93Sommerfield_bound "Bogomol'nyi–Prasad–Sommerfield bound") [Exceptional Lie groups](https://en.wikipedia.org/wiki/Exceptional_Lie_group "Exceptional Lie group") ([G2](https://en.wikipedia.org/wiki/G2_\(mathematics\) "G2 (mathematics)"), [F4](https://en.wikipedia.org/wiki/F4_\(mathematics\) "F4 (mathematics)"), [E6](https://en.wikipedia.org/wiki/E6_\(mathematics\) "E6 (mathematics)"), [E7](https://en.wikipedia.org/wiki/E7_\(mathematics\) "E7 (mathematics)"), [E8](https://en.wikipedia.org/wiki/E8_\(mathematics\) "E8 (mathematics)")) [ADE classification](https://en.wikipedia.org/wiki/ADE_classification "ADE classification") [Dirac string](https://en.wikipedia.org/wiki/Dirac_string "Dirac string") [p\-form electrodynamics](https://en.wikipedia.org/wiki/P-form_electrodynamics "P-form electrodynamics") \| \| Geometry \| [Worldsheet](https://en.wikipedia.org/wiki/Worldsheet "Worldsheet") [Kaluza–Klein theory](https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory "Kaluza–Klein theory") [Compactification](https://en.wikipedia.org/wiki/Compactification_\(physics\) "Compactification (physics)") [Why 10 dimensions](https://en.wikipedia.org/wiki/Why_10_dimensions "Why 10 dimensions")? [Kähler manifold](https://en.wikipedia.org/wiki/K%C3%A4hler_manifold "Kähler manifold") [Ricci-flat manifold](https://en.wikipedia.org/wiki/Ricci-flat_manifold "Ricci-flat manifold") [Calabi–Yau manifold](https://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold "Calabi–Yau manifold") [Hyperkähler manifold](https://en.wikipedia.org/wiki/Hyperk%C3%A4hler_manifold "Hyperkähler manifold") [K3 surface](https://en.wikipedia.org/wiki/K3_surface "K3 surface") [G2 manifold](https://en.wikipedia.org/wiki/G2_manifold "G2 manifold") [Spin(7)-manifold](https://en.wikipedia.org/wiki/Spin\(7\)-manifold "Spin(7)-manifold") [Generalized complex manifold](https://en.wikipedia.org/wiki/Generalized_complex_structure "Generalized complex structure") [Orbifold](https://en.wikipedia.org/wiki/Orbifold "Orbifold") [Conifold](https://en.wikipedia.org/wiki/Conifold "Conifold") [Orientifold](https://en.wikipedia.org/wiki/Orientifold "Orientifold") [Moduli space](https://en.wikipedia.org/wiki/Moduli_space "Moduli space") [Hořava–Witten theory](https://en.wikipedia.org/wiki/Ho%C5%99ava%E2%80%93Witten_theory "Hořava–Witten theory") [K-theory (physics)](https://en.wikipedia.org/wiki/K-theory_\(physics\) "K-theory (physics)") [Twisted K-theory](https://en.wikipedia.org/wiki/Twisted_K-theory "Twisted K-theory") \| \| [Supersymmetry](https://en.wikipedia.org/wiki/Supersymmetry "Supersymmetry") \| [Supergravity](https://en.wikipedia.org/wiki/Supergravity "Supergravity") [Eleven-dimensional supergravity](https://en.wikipedia.org/wiki/Eleven-dimensional_supergravity "Eleven-dimensional supergravity") [Type I supergravity](https://en.wikipedia.org/wiki/Type_I_supergravity "Type I supergravity") [Type IIA supergravity](https://en.wikipedia.org/wiki/Type_IIA_supergravity "Type IIA supergravity") [Type IIB supergravity](https://en.wikipedia.org/wiki/Type_IIB_supergravity "Type IIB supergravity") [Superspace](https://en.wikipedia.org/wiki/Superspace "Superspace") [Lie superalgebra](https://en.wikipedia.org/wiki/Lie_superalgebra "Lie superalgebra") [Lie supergroup](https://en.wikipedia.org/wiki/Lie_supergroup "Lie supergroup") \| \| [Holography](https://en.wikipedia.org/wiki/Holography "Holography") \| [Holographic principle](https://en.wikipedia.org/wiki/Holographic_principle "Holographic principle") [AdS/CFT correspondence](https://en.wikipedia.org/wiki/AdS/CFT_correspondence "AdS/CFT correspondence") \| \| [M-theory](https://en.wikipedia.org/wiki/M-theory "M-theory") \| [Matrix theory](https://en.wikipedia.org/wiki/Matrix_theory_\(physics\) "Matrix theory (physics)") [Introduction to M-theory](https://en.wikipedia.org/wiki/Introduction_to_M-theory "Introduction to M-theory") \| \| String theorists \| [Aganagić](https://en.wikipedia.org/wiki/Mina_Aganagi%C4%87 "Mina Aganagić") [Arkani-Hamed](https://en.wikipedia.org/wiki/Nima_Arkani-Hamed "Nima Arkani-Hamed") [Atiyah](https://en.wikipedia.org/wiki/Michael_Atiyah "Michael Atiyah") [Banks](https://en.wikipedia.org/wiki/Tom_Banks_\(physicist\) "Tom Banks (physicist)") [Berenstein](https://en.wikipedia.org/wiki/David_Berenstein "David Berenstein") [Bousso](https://en.wikipedia.org/wiki/Raphael_Bousso "Raphael Bousso") [Curtright](https://en.wikipedia.org/wiki/Thomas_Curtright "Thomas Curtright") [Dijkgraaf](https://en.wikipedia.org/wiki/Robbert_Dijkgraaf "Robbert Dijkgraaf") [Distler](https://en.wikipedia.org/wiki/Jacques_Distler "Jacques Distler") [Douglas](https://en.wikipedia.org/wiki/Michael_R._Douglas "Michael R. Douglas") [Duff](https://en.wikipedia.org/wiki/Michael_Duff_\(physicist\) "Michael Duff (physicist)") [Dvali](https://en.wikipedia.org/wiki/Gia_Dvali "Gia Dvali") [Ferrara](https://en.wikipedia.org/wiki/Sergio_Ferrara "Sergio Ferrara") [Fischler](https://en.wikipedia.org/wiki/Willy_Fischler "Willy Fischler") [Friedan](https://en.wikipedia.org/wiki/Daniel_Friedan "Daniel Friedan") [Gates](https://en.wikipedia.org/wiki/Sylvester_James_Gates "Sylvester James Gates") [Gliozzi](https://en.wikipedia.org/wiki/Ferdinando_Gliozzi "Ferdinando Gliozzi") [Gopakumar](https://en.wikipedia.org/wiki/Rajesh_Gopakumar "Rajesh Gopakumar") [Green](https://en.wikipedia.org/wiki/Michael_Green_\(physicist\) "Michael Green (physicist)") [Greene](https://en.wikipedia.org/wiki/Brian_Greene "Brian Greene") [Gross](https://en.wikipedia.org/wiki/David_Gross "David Gross") [Gubser](https://en.wikipedia.org/wiki/Steven_Gubser "Steven Gubser") [Gukov](https://en.wikipedia.org/wiki/Sergei_Gukov "Sergei Gukov") [Guth](https://en.wikipedia.org/wiki/Alan_Guth "Alan Guth") [Hanson](https://en.wikipedia.org/wiki/Andrew_J._Hanson "Andrew J. Hanson") [Harvey](https://en.wikipedia.org/wiki/Jeffrey_A._Harvey "Jeffrey A. Harvey") ['t Hooft](https://en.wikipedia.org/wiki/Gerard_%27t_Hooft "Gerard 't Hooft") [Hořava](https://en.wikipedia.org/wiki/Petr_Ho%C5%99ava_\(theorist\) "Petr Hořava (theorist)") [Gibbons](https://en.wikipedia.org/wiki/Gary_Gibbons "Gary Gibbons") [Kachru](https://en.wikipedia.org/wiki/Shamit_Kachru "Shamit Kachru") [Kaku](https://en.wikipedia.org/wiki/Michio_Kaku "Michio Kaku") [Kallosh](https://en.wikipedia.org/wiki/Renata_Kallosh "Renata Kallosh") [Kaluza](https://en.wikipedia.org/wiki/Theodor_Kaluza "Theodor Kaluza") [Kapustin](https://en.wikipedia.org/wiki/Anton_Kapustin "Anton Kapustin") [Klebanov](https://en.wikipedia.org/wiki/Igor_Klebanov "Igor Klebanov") [Knizhnik](https://en.wikipedia.org/wiki/Vadim_Knizhnik "Vadim Knizhnik") [Kontsevich](https://en.wikipedia.org/wiki/Maxim_Kontsevich "Maxim Kontsevich") [Klein](https://en.wikipedia.org/wiki/Oskar_Klein "Oskar Klein") [Linde](https://en.wikipedia.org/wiki/Andrei_Linde "Andrei Linde") [Maldacena](https://en.wikipedia.org/wiki/Juan_Mart%C3%ADn_Maldacena "Juan Martín Maldacena") [Mandelstam](https://en.wikipedia.org/wiki/Stanley_Mandelstam "Stanley Mandelstam") [Marolf](https://en.wikipedia.org/wiki/Donald_Marolf "Donald Marolf") [Martinec](https://en.wikipedia.org/wiki/Emil_Martinec "Emil Martinec") [Minwalla](https://en.wikipedia.org/wiki/Shiraz_Minwalla "Shiraz Minwalla") [Moore](https://en.wikipedia.org/wiki/Greg_Moore_\(physicist\) "Greg Moore (physicist)") [Motl](https://en.wikipedia.org/wiki/Lubo%C5%A1_Motl "Luboš Motl") [Mukhi](https://en.wikipedia.org/wiki/Sunil_Mukhi "Sunil Mukhi") [Myers](https://en.wikipedia.org/wiki/Robert_Myers_\(physicist\) "Robert Myers (physicist)") [Nanopoulos](https://en.wikipedia.org/wiki/Dimitri_Nanopoulos "Dimitri Nanopoulos") [Năstase](https://en.wikipedia.org/wiki/Hora%C8%9Biu_N%C4%83stase "Horațiu Năstase") [Nekrasov](https://en.wikipedia.org/wiki/Nikita_Nekrasov "Nikita Nekrasov") [Neveu](https://en.wikipedia.org/wiki/Andr%C3%A9_Neveu "André Neveu") [Nielsen](https://en.wikipedia.org/wiki/Holger_Bech_Nielsen "Holger Bech Nielsen") [van Nieuwenhuizen](https://en.wikipedia.org/wiki/Peter_van_Nieuwenhuizen "Peter van Nieuwenhuizen") [Novikov](https://en.wikipedia.org/wiki/Sergei_Novikov_\(mathematician\) "Sergei Novikov (mathematician)") [Olive](https://en.wikipedia.org/wiki/David_Olive "David Olive") [Ooguri](https://en.wikipedia.org/wiki/Hirosi_Ooguri "Hirosi Ooguri") [Ovrut](https://en.wikipedia.org/wiki/Burt_Ovrut "Burt Ovrut") [Polchinski](https://en.wikipedia.org/wiki/Joseph_Polchinski "Joseph Polchinski") [Polyakov](https://en.wikipedia.org/wiki/Alexander_Markovich_Polyakov "Alexander Markovich Polyakov") [Rajaraman](https://en.wikipedia.org/wiki/Arvind_Rajaraman "Arvind Rajaraman") [Ramond](https://en.wikipedia.org/wiki/Pierre_Ramond "Pierre Ramond") [Randall](https://en.wikipedia.org/wiki/Lisa_Randall "Lisa Randall") [Randjbar-Daemi](https://en.wikipedia.org/wiki/Seifallah_Randjbar-Daemi "Seifallah Randjbar-Daemi") [Roček](https://en.wikipedia.org/wiki/Martin_Ro%C4%8Dek "Martin Roček") [Rohm](https://en.wikipedia.org/wiki/Ryan_Rohm "Ryan Rohm") [Sagnotti](https://en.wikipedia.org/wiki/Augusto_Sagnotti "Augusto Sagnotti") [Scherk](https://en.wikipedia.org/wiki/Jo%C3%ABl_Scherk "Joël Scherk") [Schwarz](https://en.wikipedia.org/wiki/John_Henry_Schwarz "John Henry Schwarz") [Seiberg](https://en.wikipedia.org/wiki/Nathan_Seiberg "Nathan Seiberg") [Sen](https://en.wikipedia.org/wiki/Ashoke_Sen "Ashoke Sen") [Shenker](https://en.wikipedia.org/wiki/Stephen_Shenker "Stephen Shenker") [Siegel](https://en.wikipedia.org/wiki/Warren_Siegel "Warren Siegel") [Silverstein](https://en.wikipedia.org/wiki/Eva_Silverstein "Eva Silverstein") [Sơn](https://en.wikipedia.org/wiki/%C4%90%C3%A0m_Thanh_S%C6%A1n "Đàm Thanh Sơn") [Staudacher](https://en.wikipedia.org/wiki/Matthias_Staudacher "Matthias Staudacher") [Steinhardt](https://en.wikipedia.org/wiki/Paul_Steinhardt "Paul Steinhardt") [Strominger](https://en.wikipedia.org/wiki/Andrew_Strominger "Andrew Strominger") [Sundrum](https://en.wikipedia.org/wiki/Raman_Sundrum "Raman Sundrum") [Susskind](https://en.wikipedia.org/wiki/Leonard_Susskind "Leonard Susskind") [Townsend](https://en.wikipedia.org/wiki/Paul_Townsend "Paul Townsend") [Trivedi](https://en.wikipedia.org/wiki/Sandip_Trivedi "Sandip Trivedi") [Turok](https://en.wikipedia.org/wiki/Neil_Turok "Neil Turok") [Vafa](https://en.wikipedia.org/wiki/Cumrun_Vafa "Cumrun Vafa") [Veneziano](https://en.wikipedia.org/wiki/Gabriele_Veneziano "Gabriele Veneziano") [Verlinde](https://en.wikipedia.org/wiki/Erik_Verlinde "Erik Verlinde") [Verlinde](https://en.wikipedia.org/wiki/Herman_Verlinde "Herman Verlinde") [Wess](https://en.wikipedia.org/wiki/Julius_Wess "Julius Wess") [Witten](https://en.wikipedia.org/wiki/Edward_Witten "Edward Witten") [Yau](https://en.wikipedia.org/wiki/Shing-Tung_Yau "Shing-Tung Yau") [Yoneya](https://en.wikipedia.org/wiki/Tamiaki_Yoneya "Tamiaki Yoneya") [Zamolodchikov](https://en.wikipedia.org/wiki/Alexander_Zamolodchikov "Alexander Zamolodchikov") [Zamolodchikov](https://en.wikipedia.org/wiki/Alexei_Zamolodchikov "Alexei Zamolodchikov") [Zaslow](https://en.wikipedia.org/wiki/Eric_Zaslow "Eric Zaslow") [Zumino](https://en.wikipedia.org/wiki/Bruno_Zumino "Bruno Zumino") [Zwiebach](https://en.wikipedia.org/wiki/Barton_Zwiebach "Barton Zwiebach") \| ![](https://en.wikipedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=1) Retrieved from "<https://en.wikipedia.org/w/index.php?title=String_theory_landscape&oldid=1326812736>" [Categories](https://en.wikipedia.org/wiki/Help:Category "Help:Category"): - [Physical cosmology](https://en.wikipedia.org/wiki/Category:Physical_cosmology "Category:Physical cosmology") - [String theory](https://en.wikipedia.org/wiki/Category:String_theory "Category:String theory") - 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Readable Markdown	From Wikipedia, the free encyclopedia In [string theory](https://en.wikipedia.org/wiki/String_theory "String theory"), the string theory landscape (or landscape of vacua) is the collection of possible [false vacua](https://en.wikipedia.org/wiki/False_vacuum "False vacuum"),[\[1\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-Ashok-1) together comprising a collective "landscape" of choices of parameters governing [compactifications](https://en.wikipedia.org/wiki/Compactification_\(physics\) "Compactification (physics)"). The term "landscape" comes from the notion of a [fitness landscape](https://en.wikipedia.org/wiki/Fitness_landscape "Fitness landscape") in [evolutionary biology](https://en.wikipedia.org/wiki/Evolutionary_biology "Evolutionary biology").[\[2\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-2) It was first applied to cosmology by [Lee Smolin](https://en.wikipedia.org/wiki/Lee_Smolin "Lee Smolin") in his book [The Life of the Cosmos](https://en.wikipedia.org/wiki/The_Life_of_the_Cosmos "The Life of the Cosmos") (1997), and was first used in the context of string theory by [Leonard Susskind](https://en.wikipedia.org/wiki/Leonard_Susskind "Leonard Susskind").[\[3\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-3) ## Compactified Calabi–Yau manifolds \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=1 "Edit section: Compactified Calabi–Yau manifolds")\] In string theory, the estimated count of distinct flux vacua is commonly stated as having a lower bound of ![{\\displaystyle 10^{500}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9fc79f91eb42fdee58d7e3e2d441013ad2488959),[\[4\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-4) but more recently this has been revised to ![{\\displaystyle 10^{272,000}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7ea2462969aa025b37c43ee26b6a3e026316b53),[\[5\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-5) and the true number may still be far higher. The large number of possibilities arises from choices of [Calabi–Yau manifolds](https://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold "Calabi–Yau manifold") and choices of generalized [magnetic fluxes](https://en.wikipedia.org/wiki/Magnetic_flux "Magnetic flux") over various [homology](https://en.wikipedia.org/wiki/Homology_\(mathematics\) "Homology (mathematics)") cycles, found in [F-theory](https://en.wikipedia.org/wiki/F-theory "F-theory"). If there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is [NP complete](https://en.wikipedia.org/wiki/NP_complete "NP complete").[\[6\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-6) This is a version of the [subset sum problem](https://en.wikipedia.org/wiki/Subset_sum_problem "Subset sum problem"). A possible mechanism of string theory vacuum stabilization, now known as the KKLT mechanism, was proposed in 2003 by [Shamit Kachru](https://en.wikipedia.org/wiki/Shamit_Kachru "Shamit Kachru"), [Renata Kallosh](https://en.wikipedia.org/wiki/Renata_Kallosh "Renata Kallosh"), [Andrei Linde](https://en.wikipedia.org/wiki/Andrei_Linde "Andrei Linde"), and [Sandip Trivedi](https://en.wikipedia.org/wiki/Sandip_Trivedi "Sandip Trivedi").[\[7\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-7) ## Fine-tuning by the anthropic principle \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=2 "Edit section: Fine-tuning by the anthropic principle")\] [Fine-tuning](https://en.wikipedia.org/wiki/Fine-tuning_\(physics\) "Fine-tuning (physics)") of constants like the [cosmological constant](https://en.wikipedia.org/wiki/Cosmological_constant "Cosmological constant") or the [Higgs boson](https://en.wikipedia.org/wiki/Higgs_boson "Higgs boson") mass is usually assumed to occur for precise physical reasons as opposed to taking their particular values at random. That is, these values should be uniquely consistent with underlying physical laws. The number of theoretically allowed configurations has prompted suggestions\[[according to whom?](https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions "Wikipedia:Manual of Style/Words to watch")\] that this is not the case, and that many different vacua are physically realized.[\[8\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-8) The [anthropic principle](https://en.wikipedia.org/wiki/Anthropic_principle "Anthropic principle") proposes that fundamental constants may have the values they have because such values are necessary for life (and therefore intelligent observers to measure the constants). The anthropic landscape thus refers to the collection of those portions of the landscape that are suitable for supporting intelligent life. In 1987, [Steven Weinberg](https://en.wikipedia.org/wiki/Steven_Weinberg "Steven Weinberg") proposed that the observed value of the [cosmological constant](https://en.wikipedia.org/wiki/Cosmological_constant "Cosmological constant") was so small because it is impossible for life to occur in a universe with a much larger cosmological constant.[\[9\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-9) Weinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts\[[which?](https://en.wikipedia.org/wiki/Wikipedia:Avoid_weasel_words "Wikipedia:Avoid weasel words")\] have been made to apply similar reasoning to models of particle physics.[\[10\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-10) Such attempts are based in the general ideas of [Bayesian probability](https://en.wikipedia.org/wiki/Bayesian_probability "Bayesian probability"); interpreting probability in a context where it is only possible to draw one [sample](https://en.wikipedia.org/wiki/Sample_size "Sample size") from a [distribution](https://en.wikipedia.org/wiki/Probability_distribution "Probability distribution") is problematic in [frequentist probability](https://en.wikipedia.org/wiki/Frequentist_probability "Frequentist probability") but not in Bayesian probability, which is not defined in terms of the frequency of repeated events. In such a framework, the probability ![{\\displaystyle P(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/89833156eff2c51bfb8750db3306a0544ce34e14) of observing some fundamental parameters ![{\\displaystyle x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4) is given by, ![{\\displaystyle P(x)=P\_{\\mathrm {prior} }(x)\\times P\_{\\mathrm {selection} }(x),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd5c5e9caa69d16bda58b1d40e39d5f19308f211) where ![{\\displaystyle P\_{\\mathrm {prior} }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8b9334b97d41d76b64c846d2c73f5e8009acde1e) is the prior probability, from fundamental theory, of the parameters ![{\\displaystyle x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4) and ![{\\displaystyle P\_{\\mathrm {selection} }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f83c7cd3c00307571cd5af18a6f4029cf1252faa) is the "anthropic selection function", determined by the number of "observers" that would occur in the universe with parameters ![{\\displaystyle x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4).\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\]\[[year needed](https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers "Wikipedia:Manual of Style/Dates and numbers")\] - The function ![{\\displaystyle P\_{\\mathrm {prior} }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8b9334b97d41d76b64c846d2c73f5e8009acde1e) is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way. - The function ![{\\displaystyle P\_{\\mathrm {selection} }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f83c7cd3c00307571cd5af18a6f4029cf1252faa) is completely unknown, since so little is known about the origin of life. Simplified criteria (such as the number of galaxies) must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable universe. ### Simplified approaches \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=4 "Edit section: Simplified approaches")\] [Tegmark](https://en.wikipedia.org/wiki/Max_Tegmark "Max Tegmark") et al. have recently considered these objections and proposed a simplified anthropic scenario for [axion](https://en.wikipedia.org/wiki/Axion "Axion") [dark matter](https://en.wikipedia.org/wiki/Dark_matter "Dark matter") in which they argue that the first two of these problems do not apply.[\[11\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-11) Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.[\[12\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-12) A problem with many of the simplified approaches people\[[who?](https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions "Wikipedia:Manual of Style/Words to watch")\] have tried is that they "predict" a cosmological constant that is too large by a factor of 10–1000 orders of magnitude (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed.[\[13\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-13)[\[14\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-14)[\[15\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-15) Few dispute the large number of metastable vacua.\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] The existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial.\[[further explanation needed](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify "Wikipedia:Please clarify")\] #### Cosmological constant problem \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=6 "Edit section: Cosmological constant problem")\] [Andrei Linde](https://en.wikipedia.org/wiki/Andrei_Linde "Andrei Linde"), [Sir Martin Rees](https://en.wikipedia.org/wiki/Sir_Martin_Rees "Sir Martin Rees") and [Leonard Susskind](https://en.wikipedia.org/wiki/Leonard_Susskind "Leonard Susskind") advocate it as a solution to the [cosmological constant problem](https://en.wikipedia.org/wiki/Cosmological_constant_problem "Cosmological constant problem").\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] ### Weak scale supersymmetry from the landscape \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=7 "Edit section: Weak scale supersymmetry from the landscape")\] The string landscape ideas can be applied to the notion of weak scale supersymmetry and the Little Hierarchy problem. For string vacua which include the MSSM (Minimal Supersymmetric Standard Model) as the low energy effective field theory, all values of SUSY breaking fields are expected to be equally likely on the landscape. This led Douglas[\[16\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-16) and others to propose that the SUSY breaking scale is distributed as a power law in the landscape ![{\\displaystyle P\_{prior}\\sim m\_{soft}^{2n\_{F}+n\_{D}-1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f84426fcffb7b6d00faa610a5ab08a8680d127a5) where ![{\\displaystyle n\_{F}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ccc36cc9554ca4e1cf9ece1b4bba77c31dba3389) is the number of F-breaking fields (distributed as complex numbers) and ![{\\displaystyle n\_{D}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b21e96ed85525311a68773d60c9abc849ad8cb50) is the number of D-breaking fields (distributed as real numbers). Next, one may impose the Agrawal, Barr, Donoghue, Seckel (ABDS) anthropic requirement[\[17\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-17) that the derived weak scale lie within a factor of a few of our measured value (lest nuclei as needed for life as we know it become unstable (the atomic principle)). Combining these effects with a mild power-law draw to large soft SUSY breaking terms, one may calculate the Higgs boson and superparticle masses expected from the landscape.[\[18\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-18) The Higgs mass probability distribution peaks around 125 GeV while sparticles (with the exception of light higgsinos) tend to lie well beyond current LHC search limits. This approach is an example of the application of stringy naturalness. #### Scientific relevance \[[edit](https://en.wikipedia.org/w/index.php?title=String_theory_landscape&action=edit&section=8 "Edit section: Scientific relevance")\] [David Gross](https://en.wikipedia.org/wiki/David_Gross "David Gross") suggests\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the [Smolin–Susskind debate](https://en.wikipedia.org/wiki/Smolin%E2%80%93Susskind_debate "Smolin–Susskind debate") on the merits of the landscape. There are several popular books about the anthropic principle in cosmology.[\[19\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-19) The authors of two physics blogs, [Lubos Motl](https://en.wikipedia.org/wiki/Lubos_Motl "Lubos Motl") and [Peter Woit](https://en.wikipedia.org/wiki/Peter_Woit "Peter Woit"), are opposed to this use of the anthropic principle.\[[why?](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify "Wikipedia:Please clarify")\][\[20\]](https://en.wikipedia.org/wiki/String_theory_landscape#cite_note-20) - [Swampland](https://en.wikipedia.org/wiki/Swampland_\(physics\) "Swampland (physics)") - [Extra dimensions](https://en.wikipedia.org/wiki/String_theory#Extra_dimensions "String theory") - [M-theory](https://en.wikipedia.org/wiki/M-theory "M-theory") 1. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-Ashok_1-0) The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See [M. Douglas](https://en.wikipedia.org/wiki/Michael_R._Douglas "Michael R. Douglas"), "The statistics of string / M theory vacua", JHEP 0305, 46 (2003). [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0303194](https://arxiv.org/abs/hep-th/0303194); S. Ashok and M. Douglas, "Counting flux vacua", JHEP 0401, 060 (2004). 2. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-2) Baggott, Jim (2018). [Quantum Space Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe](https://books.google.com/books?id=HwN6DwAAQBAJ&pg=PA288). Oxford University Press. p. 288. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-0-19-253681-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-253681-5 "Special:BookSources/978-0-19-253681-5") . 3. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-3) L. Smolin, "Did the universe evolve?", Classical and Quantum Gravity 9, 173–191 (1992). L. Smolin, [The Life of the Cosmos](https://en.wikipedia.org/wiki/The_Life_of_the_Cosmos "The Life of the Cosmos") (Oxford, 1997) 4. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-4) Read, James; Le Bihan, Baptiste (2021). ["The landscape and the multiverse: What's the problem?"](https://doi.org/10.1007%2Fs11229-021-03137-0). Synthese. 199 (3–4\): 7749–7771\. [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1007/s11229-021-03137-0](https://doi.org/10.1007%2Fs11229-021-03137-0). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [234815857](https://api.semanticscholar.org/CorpusID:234815857). 5. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-5) Taylor, Washington; Wang, Yi-Nan (2015). "The F-theory geometry with most flux vacua". Journal of High Energy Physics. 2015 (12): 164. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1511\.03209](https://arxiv.org/abs/1511.03209). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2015JHEP...12..164T](https://ui.adsabs.harvard.edu/abs/2015JHEP...12..164T). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1007/JHEP12(2015)164](https://doi.org/10.1007%2FJHEP12%282015%29164). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [41149049](https://api.semanticscholar.org/CorpusID:41149049). 6. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-6) Frederik Denef; Douglas, Michael R. (2007). "Computational complexity of the landscape". Annals of Physics. 322 (5): 1096–1142\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0602072](https://arxiv.org/abs/hep-th/0602072). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2007AnPhy.322.1096D](https://ui.adsabs.harvard.edu/abs/2007AnPhy.322.1096D). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/j.aop.2006.07.013](https://doi.org/10.1016%2Fj.aop.2006.07.013). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [281586](https://api.semanticscholar.org/CorpusID:281586). 7. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-7) Kachru, Shamit; Kallosh, Renata; Linde, Andrei; Trivedi, Sandip P. (2003). "de Sitter Vacua in String Theory". Physical Review D. 68 (4) 046005. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0301240](https://arxiv.org/abs/hep-th/0301240). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2003PhRvD..68d6005K](https://ui.adsabs.harvard.edu/abs/2003PhRvD..68d6005K). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1103/PhysRevD.68.046005](https://doi.org/10.1103%2FPhysRevD.68.046005). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [119482182](https://api.semanticscholar.org/CorpusID:119482182). 8. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-8) L. Susskind, "The anthropic landscape of string theory", [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0302219](https://arxiv.org/abs/hep-th/0302219). 9. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-9) S. Weinberg, "Anthropic bound on the cosmological constant", Phys. Rev. Lett. 59, 2607 (1987). 10. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-10) S. M. Carroll, "Is our universe natural?" (2005) [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0512148](https://arxiv.org/abs/hep-th/0512148) reviews a number of proposals in preprints dated 2004/5. 11. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-11) M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, "Dimensionless constants, cosmology and other dark matters", [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[astro-ph/0511774](https://arxiv.org/abs/astro-ph/0511774). F. Wilczek, "Enlightenment, knowledge, ignorance, temptation", [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-ph/0512187](https://arxiv.org/abs/hep-ph/0512187). See also the discussion at [\[1\]](http://www.math.columbia.edu/~woit/wordpress/?p=310). 12. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-12) See, e.g. Alexander Vilenkin (2007). "A measure of the multiverse". Journal of Physics A: Mathematical and Theoretical. 40 (25): 6777–6785\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0609193](https://arxiv.org/abs/hep-th/0609193). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2007JPhA...40.6777V](https://ui.adsabs.harvard.edu/abs/2007JPhA...40.6777V). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1088/1751-8113/40/25/S22](https://doi.org/10.1088%2F1751-8113%2F40%2F25%2FS22). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [119390736](https://api.semanticscholar.org/CorpusID:119390736). 13. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-13) Abraham Loeb (2006). "An observational test for the anthropic origin of the cosmological constant". Journal of Cosmology and Astroparticle Physics. 0605 (5): 009. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[astro-ph/0604242](https://arxiv.org/abs/astro-ph/0604242). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2006JCAP...05..009L](https://ui.adsabs.harvard.edu/abs/2006JCAP...05..009L). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1088/1475-7516/2006/05/009](https://doi.org/10.1088%2F1475-7516%2F2006%2F05%2F009). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [39340203](https://api.semanticscholar.org/CorpusID:39340203). 14. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-14) Jaume Garriga & Alexander Vilenkin (2006). "Anthropic prediction for Lambda and the Q catastrophe". Prog. Theor. Phys. Suppl. 163: 245–57\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0508005](https://arxiv.org/abs/hep-th/0508005). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2006PThPS.163..245G](https://ui.adsabs.harvard.edu/abs/2006PThPS.163..245G). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1143/PTPS.163.245](https://doi.org/10.1143%2FPTPS.163.245). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [118936307](https://api.semanticscholar.org/CorpusID:118936307). 15. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-15) Delia Schwartz-Perlov & Alexander Vilenkin (2006). "Probabilities in the Bousso-Polchinski multiverse". Journal of Cosmology and Astroparticle Physics. 0606 (6): 010. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0601162](https://arxiv.org/abs/hep-th/0601162). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2006JCAP...06..010S](https://ui.adsabs.harvard.edu/abs/2006JCAP...06..010S). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1088/1475-7516/2006/06/010](https://doi.org/10.1088%2F1475-7516%2F2006%2F06%2F010). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [119337679](https://api.semanticscholar.org/CorpusID:119337679). 16. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-16) M. R. Douglas, "Statistical analysis of the supersymmetry breaking scale", [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-th/0405279](https://arxiv.org/abs/hep-th/0405279). 17. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-17) V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel, "Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking", Phys. Rev. Lett. 80, 1822 (1998).[arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-ph/9801253](https://arxiv.org/abs/hep-ph/9801253) 18. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-18) H. Baer, V. Barger, H. Serce and K. Sinha, "Higgs and superparticle mass predictions from the landscape", JHEP 03, 002 (2018), [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1712\.01399](https://arxiv.org/abs/1712.01399) . 19. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-19) L. Susskind, The cosmic landscape: string theory and the illusion of intelligent design (Little, Brown, 2005). M. J. Rees, Just six numbers: the deep forces that shape the universe (Basic Books, 2001). R. Bousso and J. Polchinski, "The string theory landscape", Sci. Am. 291, 60–69 (2004). 20. [^](https://en.wikipedia.org/wiki/String_theory_landscape#cite_ref-20) Motl's blog criticized the anthropic principle and Woit's [blog](http://www.math.columbia.edu/~woit/blog/) frequently attacks the anthropic string landscape. - [String landscape; moduli stabilization; flux vacua; flux compactification](http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=hep-th&level=1&index1=5460697) on [arxiv.org](https://en.wikipedia.org/wiki/Arxiv.org "Arxiv.org"). - [Cvetič, Mirjam](https://en.wikipedia.org/wiki/Mirjam_Cveti%C4%8D "Mirjam Cvetič"); García-Etxebarria, Iñaki; Halverson, James (March 2011). "On the computation of non-perturbative effective potentials in the string theory landscape". Fortschritte der Physik. 59 (3–4\): 243–283\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1009\.5386](https://arxiv.org/abs/1009.5386). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2011ForPh..59..243C](https://ui.adsabs.harvard.edu/abs/2011ForPh..59..243C). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1002/prop.201000093](https://doi.org/10.1002%2Fprop.201000093). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [46634583](https://api.semanticscholar.org/CorpusID:46634583).
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