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Journal ArticleDOI

Hierarchies from fluxes in string compactifications

25 Nov 2002-Physical Review D (American Physical Society)-Vol. 66, Iss: 10, pp 106006
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.
Citations
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Journal ArticleDOI
TL;DR: In this article, the authors review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence and tachyon.
Abstract: We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

5,954 citations

Journal ArticleDOI
TL;DR: The metastable de Sitter vacua of type IIB string theory has been constructed in this article, which is a supersymmetric version of the ground state of the original ground state.
Abstract: We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of $\overline{\mathrm{D}3}$-branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological time scale of ${10}^{10}\mathrm{yr}.$ We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.

4,149 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigate the embedding of brane inflation into stable compactifications of string theory and conclude that brane inflaton can only work if restrictive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied.
Abstract: We investigate the embedding of brane inflation into stable compactifications of string theory. At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well known difficulty of brane?antibrane scenarios. Careful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation. We discuss the non-generic conditions under which this problem does not arise. We conclude that brane inflation models can only work if restrictive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied. We argue that this may not be a real problem, given the large range of available fluxes and background geometries in string theory.

1,406 citations


Cites background or methods from "Hierarchies from fluxes in string c..."

  • ...It was shown in [5] that the minimal redshift satisfies r0 R = e 2πK 3gsM (4....

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  • ...Throughout this discussion, we ignore the problem of stabilizing the overall volume modulus, which is unfixed in the constructions of [5]....

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  • ...The axion comes from a four-form potential proportional to a harmonic four-form in the internal manifold [5]....

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  • ...As described in [5], one can use the above construction to compactify the warped deformed conifold solution of Klebanov and Strassler (KS)....

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  • ...We choose to turn on background fluxes: the three-form fluxes F3, H3 present in the theory are placed along cycles in the internal space (and F5 is fixed as in [5])....

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Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this article, the spectrum of density perturbations generated in models of the recently discovered "D-cceleration" mechanism of inflation was analyzed, and it was shown that the model has a strict lower bound on the non-Gaussianity of the CMBR power spectrum at an observable level.
Abstract: We analyze the spectrum of density perturbations generated in models of the recently discovered ''D-cceleration'' mechanism of inflation. In this scenario, strong coupling quantum field theoretic effects sum to provide a DBI-like action for the inflaton. We show that the model has a strict lower bound on the non-Gaussianity of the CMBR power spectrum at an observable level, and is thus falsifiable. This in particular observationally distinguishes this mechanism from traditional slow roll inflation generated by weakly interacting scalar fields. The model also favors a large observable tensor component to the CMBR spectrum.

1,219 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this paper, the weak scale is generated from the Planck scale through an exponential hierarchy, but this exponential arises not from gauge interactions but from the background metric, which is a slice of spacetime.
Abstract: We propose a new higher-dimensional mechanism for solving the hierarchy problem. The weak scale is generated from the Planck scale through an exponential hierarchy. However, this exponential arises not from gauge interactions but from the background metric (which is a slice of ${\mathrm{AdS}}_{5}$ spacetime). We demonstrate a simple explicit example of this mechanism with two 3-branes, one of which contains the standard model fields. The phenomenology of these models is new and dramatic. None of the current constraints on theories with very large extra dimensions apply.

9,088 citations


"Hierarchies from fluxes in string c..." refers background in this paper

  • ...In effect the fluxes produce a model similar to RS1 [1], in which the warp factor does not go to zero but to a small positive value....

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  • ...This mechanism has in particular played a role in the Randall-Sundrum (RS) models [1, 2]....

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  • ...This perturbation is absent in our solution: in supergravity language it is a 3-form flux, but it is not of the form ∗6G(3) = iG(3), 10We should note that, unlike RS1, there is no negative tension brane at the low energy end; rather, there is a KS space....

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  • ...(3.19) In effect the fluxes produce a model similar to RS1 [1], in which the warp factor does not go to zero but to a small positive value.10 The large hierarchy (3.13) has a simple interpretation in terms of a dual gauge theory....

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  • ...There has been a great deal of interest in finding string theory constructions which produce large hierarchies through warping, and in particular reproduce, at long wavelengths, features of the RS1 model [1]....

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Journal ArticleDOI
TL;DR: In this paper, a single 3-brane embedded in five dimensions was shown to reproduce four-dimensional Newtonian and general relativistic gravity to more than adequate precision, even without a gap in the Kaluza-Klein spectrum.
Abstract: Conventional wisdom states that Newton's force law implies only four noncompact dimensions. We demonstrate that this is not necessarily true in the presence of a nonfactorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gravity is reproduced to more than adequate precision.

6,936 citations


"Hierarchies from fluxes in string c..." refers background or methods in this paper

  • ...This is similar to the RS2 model [2], though is a bona-fide compactification, with the compact manifold playing a role roughly analogous to the so-called “Planck brane” of [2], and yielding a finite four-dimensional Planck scale....

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  • ...This mechanism has in particular played a role in the Randall-Sundrum (RS) models [1, 2]....

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Journal ArticleDOI
TL;DR: In this article, a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the ‘t Hooft coupling gsM is large, was proposed.
Abstract: We revisit the singular IIB supergravity solution describing M fractional 3branes on the conifold [hep-th/0002159]. Its 5-form flux decreases, which we explain by showing that the relevant N = 1 SUSY SU(N+M)×SU(N) gauge theory undergoes repeated Seiberg-duality transformations in which N → N − M. Far in the IR the gauge theory confines; its chiral symmetry breaking removes the singularity of hep-th/0002159 by deforming the conifold. We propose a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the ‘t Hooft coupling gsM is large. In the UV it approaches that of hep-th/0002159, incorporating the logarithmic flow of couplings. In the IR the deformation of the conifold gives a geometrical realization of chiral symmetry breaking and confinement. We suggest that pure N = 1 Yang-Mills may be dual to strings propagating at small gsM on a warped deformed conifold. We note also that the standard model itself may lie at the base of a duality cascade.

2,429 citations


"Hierarchies from fluxes in string c..." refers background or methods in this paper

  • ...In the final analysis these branes dissolve into flux, and result in a nonsingular solution that has recently been found by Klebanov and Strassler (KS) [7]....

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  • ...Our motivation stems from the work of Klebanov-Strassler [7]....

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  • ...The exponentially small value of z computed from the superpotential of [9] independently confirms the existence of a hierarchy for reasonable choices of M and N (and represents the small, dynamically generated scale of chiral symmetry breaking in [7])....

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  • ...19) then corresponds precisely to the renormalization group analysis of KS [7]....

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  • ...The modes controlling the complex structure of X, which determine τ via (4.8), are frozen on general grounds by just the Klebanov-Strassler fluxes, as described at the end of §3....

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Journal ArticleDOI
TL;DR: In this paper, it was shown that string theory on AdS5 × X5 can be described by a certain N = 1 supersymmetric gauge theory, which we describe in detail.

1,589 citations


"Hierarchies from fluxes in string c..." refers background in this paper

  • ...A simple means of reducing the symmetry is to place the D3-branes not at a smooth point of the transverse space but at a singularity [10, 11, 12, 13]....

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