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{{Short description|Collection of possible string theory vacua}}
{{String theory|cTopic=Theory}}

In [[string theory]], the '''string theory landscape''' (or '''landscape of vacua''') is the collection of possible [[false vacuum|false vacua]],<ref name=Ashok>The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10<sup>500</sup>. See [[Michael R. Douglas|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).</ref> together comprising a collective "landscape" of choices of parameters governing [[Compactification (physics)|compactifications]].

The term "landscape" comes from the notion of a [[fitness landscape]] in [[evolutionary biology]].<ref>{{cite book |first=Jim |last=Baggott |year=2018 |title=Quantum Space Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe |location= |publisher=Oxford University Press |isbn=978-0-19-253681-5 |page=288 |url=https://books.google.com/books?id=HwN6DwAAQBAJ&pg=PA288 }}</ref>  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]].<ref>L. Smolin, "Did the universe evolve?", ''Classical and Quantum Gravity'' '''9''', 173–191 (1992). L. Smolin, ''[[The Life of the Cosmos]]'' (Oxford, 1997)</ref>

==Compactified Calabi–Yau manifolds<!--'KKLT mechanism' redirects here-->==
{{main|Compactification (physics)}}

In string theory the number of [[flux vacua]] is commonly thought to be roughly <math>10^{500}</math>,<ref>{{cite journal|title=The landscape and the multiverse: What's the problem?|journal=Synthese|date=2021|last1=Read|first1=James|last2=Le Bihan|first2=Baptiste|volume=199|issue=3–4|pages=7749–7771|doi=10.1007/s11229-021-03137-0|s2cid=234815857|doi-access=free}}</ref> but could be <math>10^{272,000}</math><ref>{{cite journal|title=The F-theory geometry with most flux vacua|date=2015|last1=Taylor| first1=Washington|last2=Wang|first2=Yi-Nan|doi=10.1007/JHEP12(2015)164|journal=Journal of High Energy Physics|volume=2015|issue=12|pages=164|arxiv=1511.03209 |bibcode=2015JHEP...12..164T|s2cid=41149049}}</ref> or higher. The large number of possibilities arises from choices of [[Calabi–Yau manifold]]s and choices of generalized [[magnetic flux]]es over various [[Homology (mathematics)|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]].<ref>{{cite journal|title=Computational complexity of the landscape|year=2007|author1=Frederik Denef|last2=Douglas | first2=Michael R.|doi=10.1016/j.aop.2006.07.013|journal=Annals of Physics|volume=322|issue=5|pages=1096–1142|arxiv=hep-th/0602072|bibcode = 2007AnPhy.322.1096D |s2cid=281586}}</ref> This is a version of the [[subset sum problem]].

A possible mechanism of string theory vacuum stabilization, now known as the '''KKLT mechanism'''<!--boldface per WP:R#PLA-->, was proposed in 2003 by [[Shamit Kachru]], [[Renata Kallosh]], [[Andrei Linde]], and [[Sandip Trivedi]].<ref>{{cite journal|title=de Sitter Vacua in String Theory|journal=Physical Review D|volume=68|issue=4|pages=046005|arxiv=hep-th/0301240|author=Kachru, Shamit|author2=Kallosh, Renata|author3=Linde, Andrei|author4=Trivedi, Sandip P.|year=2003|doi=10.1103/PhysRevD.68.046005|bibcode=2003PhRvD..68d6005K|s2cid=119482182}}</ref>

==Fine-tuning by the anthropic principle==
{{main|Fine-tuning (physics)|Anthropic principle}}

[[Fine-tuning (physics)|Fine-tuning]] of constants like the [[cosmological constant]] or the [[Higgs boson]] mass are 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|date=May 2017}} that this is not the case, and that many different vacua are physically realized.<ref>L. Susskind, "The anthropic landscape of string theory", {{arxiv|hep-th/0302219}}.</ref> 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.

===Weinberg model===
{{main|Bayesian probability}}

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.<ref>S. Weinberg, "Anthropic bound on the cosmological constant", ''Phys. Rev. Lett.'' '''59''', 2607 (1987).</ref>

Weinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts{{which|date=May 2017}} have been made to apply similar reasoning to models of particle physics.<ref>S. M. Carroll, "Is our universe natural?" (2005) {{arxiv|hep-th/0512148}} reviews a number of proposals in preprints dated 2004/5.</ref>

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 size|sample]] from a [[probability distribution|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 <math>P(x)</math> of observing some fundamental parameters <math>x</math> is given by,
:<math>P(x)=P_{\mathrm{prior}}(x)\times P_{\mathrm{selection}}(x),</math>
where <math>P_\mathrm{prior}</math> is the prior probability, from fundamental theory, of the parameters <math>x</math> and <math>P_\mathrm{selection}</math> is the "anthropic selection function", determined by the number of "observers" that would occur in the universe with parameters <math>x</math>.{{citation needed|date=May 2016}}

These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:{{citation needed|date=May 2016}}{{year needed|date=May 2016}}

* The  function <math>P_\mathrm{prior}</math> is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way.
* The function <math>P_\mathrm{selection}</math> 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===
[[Max Tegmark|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.<ref>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 [http://www.math.columbia.edu/~woit/wordpress/?p=310].</ref>

Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.<ref>See, ''e.g.'' {{cite journal|year=2007|title=A measure of the multiverse|author1=Alexander Vilenkin|doi=10.1088/1751-8113/40/25/S22|journal=Journal of Physics A: Mathematical and Theoretical|volume=40|issue=25|pages=6777–6785|arxiv=hep-th/0609193|bibcode = 2007JPhA...40.6777V |s2cid=119390736}}</ref>

A problem with many of the simplified approaches people{{who|date=March 2016}} 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.<ref>{{cite journal|title=An observational test for the anthropic origin of the cosmological constant|author=Abraham Loeb|date=2006|journal=Journal of Cosmology and Astroparticle Physics|volume=0605|issue=5|pages=009 |bibcode=2006JCAP...05..009L|arxiv=astro-ph/0604242|doi=10.1088/1475-7516/2006/05/009|s2cid=39340203}}</ref><ref>{{cite journal|title=Anthropic prediction for Lambda and the Q catastrophe|author=Jaume Garriga|author2=Alexander Vilenkin|name-list-style=amp|date=2006|volume=163|pages=245–57|journal=Prog. Theor. Phys. Suppl.|doi=10.1143/PTPS.163.245 |arxiv = hep-th/0508005 |bibcode = 2006PThPS.163..245G |s2cid=118936307}}</ref><ref>{{cite journal|title=Probabilities in the Bousso-Polchinski multiverse|author=Delia Schwartz-Perlov|author2=Alexander Vilenkin|name-list-style=amp|date=2006|journal=Journal of Cosmology and Astroparticle Physics|volume=0606|issue=6|pages=010 |bibcode=2006JCAP...06..010S|arxiv=hep-th/0601162|doi=10.1088/1475-7516/2006/06/010|s2cid=119337679}}</ref>

===Interpretation===
Few dispute the large number of metastable vacua.{{citation needed|date=May 2017}} The existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial.{{elucidate|date=May 2017}}

====Cosmological constant problem====
[[Andrei Linde]], [[Sir Martin Rees]] and [[Leonard Susskind]] advocate it as a solution to the [[cosmological constant problem]].{{citation needed|date=August 2018}}

===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<ref>M. R. Douglas, "Statistical analysis of the supersymmetry breaking scale", {{arxiv|hep-th/0405279}}.</ref> and others to propose that the SUSY breaking scale is distributed as a power
law in the landscape <math>P_{prior}\sim m_{soft}^{2n_F+n_D-1} </math> where <math>n_F</math> is the number of F-breaking fields 
(distributed as complex numbers) and <math>n_D</math> is the number of D-breaking fields (distributed as real numbers).
Next, one may impose the Agrawal, Barr, Donoghue, Seckel (ABDS) anthropic requirement<ref>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}}</ref> 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.<ref>H. Baer, V. Barger, H. Serce and K. Sinha, "Higgs and superparticle mass predictions from the landscape", ''JHEP'' '''03''', 002 (2018), {{arxiv|1712.01399}} .</ref>
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====
[[David Gross]] suggests{{citation needed|date=May 2017}} 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.

====Popular reception====
There are several popular books about the anthropic principle in cosmology.<ref>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).</ref> The authors of two physics blogs, [[Lubos Motl]] and [[Peter Woit]], are opposed to this use of the anthropic principle.{{why|date=May 2017}}<ref>Motl's blog criticized the anthropic principle and Woit's [http://www.math.columbia.edu/~woit/blog/ blog] frequently attacks the anthropic string landscape.</ref>

==See also==
* [[Swampland (physics)|Swampland]]
* [[String theory#Extra dimensions|Extra dimensions]]

==References==
{{Reflist|30em}}

==External links==
* [http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=hep-th&level=1&index1=5460697 String landscape; moduli stabilization; flux vacua; flux compactification] on [[arxiv.org]].
* {{cite journal |title= On the computation of non-perturbative effective potentials in the string theory landscape |first1= Mirjam |last1= Cvetič|author1-link= Mirjam Cvetič |first2= Iñaki |last2= García-Etxebarria |first3= James |last3= Halverson |doi= 10.1002/prop.201000093 |journal= Fortschritte der Physik |volume= 59 |issue= 3–4 |pages= 243–283 |date= March 2011 |arxiv = 1009.5386 |bibcode = 2011ForPh..59..243C |s2cid= 46634583 }}

{{String theory topics |state=collapsed}}

{{DEFAULTSORT:String Theory Landscape}}
[[Category:Physical cosmology]]
[[Category:String theory]]
[[Category:Multiverse]]