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Small Cosmological Constants in String Theory
TL;DR: In this paper, the superpotential of type IIB string theory was constructed in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces, which admit vacua in which all moduli are stabilized at weak string coupling.
Abstract: We construct supersymmetric $\mathrm{AdS}_4$ vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the $\alpha'$ expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude $ < 10^{-123}$ in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.
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TL;DR: In this article, the authors constructed a vacuum of string theory in which the magnitude of the vacuum energy is $ < 10−123$ in Planck units, and some supersymmetry remains unbroken.
Abstract: We construct a vacuum of string theory in which the magnitude of the vacuum energy is $< 10^{-123}$ in Planck units. Regrettably, the sign of the vacuum energy is negative, and some supersymmetry remains unbroken.
6 citations
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TL;DR: In this paper, the leading corrections in each homology class were computed using a direct world-sheet approach without relying on any duality symmetry or supersymmetry, and the results were in perfect agreement with the earlier predictions.
Abstract: Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.
3 citations
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TL;DR: In this article, the authors study the symmetric square of Picard-Fuchs operators of genus one curves and the thereby induced generalized Clausen identities, allowing the computation of analytic expressions for the periods of all one-parameter K3 manifolds in terms of elliptic integrals.
Abstract: We study the symmetric square of Picard-Fuchs operators of genus one curves and the thereby induced generalized Clausen identities. This allows the computation of analytic expressions for the periods of all one-parameter K3 manifolds in terms of elliptic integrals. The resulting expressions are globally valid throughout the moduli space and allow the explicit inversion of the mirror map and the exact computation of distances, useful for checks of the Swampland Distance Conjecture. We comment on the generalization to multi-parameter models and provide a two-parameter example.
2 citations
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TL;DR: In this article, the authors show that perturbatively flat vacua can be used to obtain very low values of the Gukov-Vafa-Witten superpotential.
Abstract: The magnitude of the vacuum expectation value of the Gukov-Vafa-Witten superpotential $|W_0|$ plays a central role in the phenomenology of type IIB flux compactifications. Recent analytical constructions have shown that perturbatively flat vacua can be used to obtain very low values of $|W_0|$. We present systematic algorithms to carry out exhaustive numerical searches for such vacua. We also analyse them in the statistical context, as part of the entire ensemble of type IIB flux vacua at low $|W_0|$. Our preliminary analysis indicates that these perturbatively flat vacua are statistically sparse in the whole set of vacua at low $|W_0|$ as calculated by Denef and Douglas. Two-moduli examples are used to illustrate these more general findings in specific settings. We find that these simple cases are good examples for existence proofs but they do not feature a large statistical tuning freedom for phenomenological applications.
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TL;DR: In this paper, a class of 4D ''yoga'' models for which the vacuum energies of heavy particles do not gravitate were constructed, and the models contain three ingredients: (i) a relaxation mechanism driven by a scalar field (the ''relaxon'), (ii) a very supersymmetric gravity sector coupled to the Standard Model in which supersymmetry is non-linearly realised, and (iii) an accidental approximate scale invariance expressed through the presence of a low energy dilaton supermultiplet.
Abstract: We construct a class of 4D `yoga' (naturally relaxed) models for which the vacuum energies of heavy particles do not gravitate. The models contain three ingredients: (i) a relaxation mechanism driven by a scalar field (the `relaxon'), (ii) a very supersymmetric gravity sector coupled to the Standard Model in which supersymmetry is non-linearly realised, and (iii) an accidental approximate scale invariance expressed through the presence of a low-energy dilaton supermultiplet. All three are common in higher-dimensional and string constructions. Although none suffices on its own, taken together they predict a current Dark Energy density that is of order $(M_W^2/M_p)^4$ and a gravitino mass of order $M_W^3/M_p^2,$ with $M_W, M_p$ the weak and Planck scales respectively. The dilaton's vev $\tau$ determines the weak scale $M_W \sim M_p/\sqrt\tau$ and because the relevant part of the scalar potential arises as a function of $\ln\tau$ it stabilizes $\tau$ in a local de Sitter minimum with exponentially large fields obtained using input parameters no larger than O(60), thereby explaining both the size of the electroweak hierarchy and the cosmological constant. Scale invariance implies the dilaton couples to matter like a Brans-Dicke scalar with coupling large enough to be naively ruled out by solar-system tests of gravity. Yet because it comes paired with an axion it escapes fifth-force bounds through the novel screening mechanism described in arXiv:2110.10352. Cosmological axio-dilaton evolution provides a natural quintessence model for Dark Energy, whose evolution might realize recent proposals to resolve the Hubble tension, and whose axion contributes to Dark Matter. We summarize some of the remaining challenges, comment on implications for inflation and sketch possible UV completions of our approach.
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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
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
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
TL;DR: In this article, the authors consider F/M/Type IIA theory compactified to four, three, or two dimensions on a Calabi-Yau fourfold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes.
1,516 citations
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01 Jan 2003
TL;DR: In this paper, the authors proved mirror symmetry for supersymmetric sigma models on Calabi-Yau manifolds in 1+1 dimensions and showed that the equivalence of the gauged linear sigma model embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type Standard R -> 1/R duality and dynamical generation of superpotential by vortices.
Abstract: We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type Standard R -> 1/R duality and dynamical generation of superpotential by vortices are crucial in the derivation This provides not only a proof of mirror symmetry in the case of (local and global) Calabi-Yau manifolds, but also for sigma models on manifolds with positive first Chern class, including deformations of the action by holomorphic isometries
1,436 citations