The statistics of string/M theory vacua
16 Jun 2003-Journal of High Energy Physics (JOURNAL OF HIGH ENERGY PHYSICS)-Vol. 2003, Iss: 05, pp 046-046
TL;DR: In this article, an approach to estimate the number of vacua of string/M theory which can realize the Standard Model is presented. But this approach is limited to string theory.
Abstract: We discuss systematic approaches to the classification of string/M theory vacua, and physical questions this might help us resolve. To this end, we initiate the study of ensembles of effective Lagrangians, which can be used to precisely study the predictive power of string theory, and in simple examples can lead to universality results. Using these ideas, we outline an approach to estimating the number of vacua of string/M theory which can realize the Standard Model.
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TL;DR: In this paper, the authors studied the large volume limit of the scalar potential in Calabi-Yau flux compactifications of type IIB string theory, and they showed that there exists a limit in which the potential approaches zero from below, with an associated non-supersymmetric AdS minimum at exponentially large volume.
Abstract: We study the large volume limit of the scalar potential in Calabi-Yau flux compactifications of type IIB string theory. Under general circumstances there exists a limit in which the potential approaches zero from below, with an associated non-supersymmetric AdS minimum at exponentially large volume. Both this and its de Sitter uplift are tachyon-free, thereby fixing all K?hler and complex structure moduli. Also, for the class of vacua described in this paper, the gravitino mass is independent of the flux discretuum, whereas the ratio of the string scale to the 4d Planck scale is hierarchically small but flux dependent. The inclusion of ?' corrections plays a crucial role in the structure of the potential. We illustrate these ideas through explicit computations for a particular Calabi-Yau manifold.
1,232 citations
TL;DR: In this paper, a pedagogical overview of flux compactifications in string theory is presented, from the basic ideas to the most recent developments, focusing on closed-string fluxes in type-II theories.
1,085 citations
Cites background from "The statistics of string/M theory v..."
...Since all possible vacua are too many (mat be even infinite) Douglas and collaborators [204, 30, 31, 205] have advocated for a statistical study of the “landscape” of vacua, which could give some guidance principle for the search of the right vacuum....
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...[204] gives a first estimate of the fraction of vacua that have Standard Model spectrum (see Ref....
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...While the estimates of Ref [204] are very crude, the conjecture is that ignoring values for the couplings, the fraction of models which realize the standard model spectrum is closer to O(10−10) than to O(10−100)....
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TL;DR: The cosmological constant problem is a failure of naturalness and suggests that a fine-tuning mechanism is at work as discussed by the authors, which may also address the hierarchy problem in string theory.
Abstract: The cosmological constant problem is a failure of naturalness and suggests that a fine-tuning mechanism is at work, which may also address the hierarchy problem. An example — supported by Weinberg's successful prediction of the cosmological constant — is the potentially vast landscape of vacua in string theory, where the existence of galaxies and atoms is promoted to a vacuum selection criterion. Then, low energy SUSY becomes unnecessary, and supersymmetry — if present in the fundamental theory — can be broken near the unification scale. All the scalars of the supersymmetric standard model become ultraheavy, except for a single finely tuned Higgs. Yet, the fermions of the supersymmetric standard model can remain light, protected by chiral symmetry, and account for the successful unification of gauge couplings. This framework removes all the difficulties of the SSM: the absence of a light Higgs and sparticles, dimension five proton decay, SUSY flavor and CP problems, and the cosmological gravitino and moduli problems. High-scale SUSY breaking raises the mass of the light Higgs to ~ 120−150 GeV. The gluino is strikingly long lived, and a measurement of its lifetime can determine the ultraheavy scalar mass scale. Measuring the four Yukawa couplings of the Higgs to the gauginos and higgsinos precisely tests for high-scale SUSY. These ideas, if confirmed, will demonstrate that supersymmetry is present but irrelevant for the hierarchy problem — just as it has been irrelevant for the cosmological constant problem — strongly suggesting the existence of a fine-tuning mechanism in nature.
1,042 citations
TL;DR: In this paper, a review article provides a pedagogical introduction to various classes of chiral string compactifications to four dimensions with D-branes and fluxes with the main concern being to provide all necessary technical tools to explicitly construct four-dimensional orientifold vacua, with the final aim to come as close as possible to the supersymmetric standard model.
1,004 citations
TL;DR: A survey of the landscape of string and M theory vacua can be found in this article, where the authors discuss the potential for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking.
Abstract: We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics We explain how this work implies that there is a ``landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking
919 citations
References
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TL;DR: In this article, it was shown that the large-N limits of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds.
Abstract: We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown bytaking some branes in the full M/string theory and thentaking a low-energy limit where the field theory on thebrane decouples from the bulk. We observe that, in this limit, we can still trust thenear-horizon geometry for large N. The enhancedsupersymmetries of the near-horizon geometry correspondto the extra supersymmetry generators present in thesuperconformal group (as opposed to just the super-Poincaregroup). The 't Hooft limit of 3 + 1 N = 4 super-Yang–Mills at the conformal pointis shown to contain strings: they are IIB strings. Weconjecture that compactifications of M/string theory on various anti-de Sitterspacetimes is dual to various conformal field theories.This leads to a new proposal for a definition ofM-theory which could be extended to include fivenoncompact dimensions.
15,567 citations
Book•
03 Mar 1992
TL;DR: The second edition of this book appeared in 1983 and was based on a series of lectures given at Princeton in 1983 by Julius Wess as discussed by the authors, where the authors presented a general supersymmetric gauge invariant theory of chiral fields interacting with supergravity.
Abstract: The first edition of this book appeared in 1983 and was based on a series of lectures given at Princeton in 1983 by Julius Wess. Since the appearance of the first edition much work has been done on the development of phenomenological models of particle behavior based on the supergravity multiplet. Some experimental searches have been carried out and others are planned for the future. For this reason the second edition of the book goes substantially beyond the first. Six new chapters have been added for a total of twenty-six and five new appendices for a total of seven. The new chapters and appendices are primarily aimed at deriving the most general supersymmetric gauge invariant theory of chiral fields interacting with supergravity and expressing it in component form. The book is divided into three sections. After a brief introduction, the first part of the book deals with a description of N=1 supersymmetric non-abelian rigid gauge theory of chiral fields. The second part of the book develops a local supersymmetric theory which is supergravity. The final part describes the coupling of supersymmetric chiral fields to supergravity in a gauge invariant way. The book may be recommended as a pedagogical introduction tomore » the theory of N=1 supergravity. Together with the appendices is is completely self-contained, both in notation and in the concepts used, requiring only some knowledge of field theory as a background.« less
3,834 citations
TL;DR: The Bekenstein-Hawking area entropy relation S BH = A 4 was derived for a class of five-dimensional extremal black holes in string theory by counting the degeneracy of BPS solition bound states.
3,497 citations
TL;DR: In this article, a superstring theory for E 8 × 8 × E 8 has been constructed, based on SO(32) and the remaining pieces of all the anomalies cancel if the gauge group is SO (32) or E 8×E 8.
2,550 citations
TL;DR: In this article, the authors show that the hierarchy of scales can be fixed by a choice of Ramond-Ramond and Neveu-Schwarz fluxes in the compact manifold, and give examples involving orientifold compactifications of type IIB string theory and F-theory compactifications on Calabi-Yau fourfolds.
Abstract: Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of type-IIB string theory and F-theory compactifications on Calabi-Yau fourfolds. In each case, the hierarchy of scales is fixed by a choice of Ramond-Ramond and Neveu-Schwarz fluxes in the compact manifold. Our solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining $\mathcal{N}=1$ supersymmetric gauge theory, and the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory.
2,548 citations