String theory landscape
String theory |
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Fundamental objects |
Perturbative theory |
Non-perturbative results |
Phenomenology |
Mathematics |
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
In string theory the number of flux vacua is commonly thought to be roughly ,[4] but could be [5] or 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
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
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?] 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 order to implement this idea in a concrete physical theory, it is necessary[why?] to postulate a multiverse in which fundamental physical parameters can take different values. This has been realized in the context of eternal inflation.
Weinberg model
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[
Such attempts are based in the general ideas of
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
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]
Interpretation
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
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] 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
Popular reception
There are several popular books about the anthropic principle in cosmology.
See also
References
- arXiv:hep-th/0303194; S. Ashok and M. Douglas, "Counting flux vacua", JHEP 0401, 060 (2004).
- 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)
- S2CID 234815857.
- S2CID 41149049.
- S2CID 281586.
- S2CID 119482182.
- arXiv:hep-th/0302219.
- ^ S. Weinberg, "Anthropic bound on the cosmological constant", Phys. Rev. Lett. 59, 2607 (1987).
- arXiv:hep-th/0512148reviews a number of proposals in preprints dated 2004/5.
- arXiv:hep-ph/0512187. See also the discussion at [1].
- S2CID 119390736.
- S2CID 39340203.
- S2CID 118936307.
- S2CID 119337679.
- 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
- 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.
External links
- String landscape; moduli stabilization; flux vacua; flux compactification on arxiv.org.
- S2CID 46634583.