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Hyperbolic compactification of M-theory and de Sitter quantum gravity

by G. Bruno De Luca, Eva Silverstein, Gonzalo Torroba

This Submission thread is now published as SciPost Phys. 12, 083 (2022)

Submission summary

As Contributors: Eva Silverstein · Gonzalo Torroba
Arxiv Link: (pdf)
Date accepted: 2022-02-14
Date submitted: 2022-02-02 14:42
Submitted by: Torroba, Gonzalo
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We present a mechanism for accelerated expansion of the universe in the generic case of negative-curvature compactifications of M-theory, with minimal ingredients. M-theory on a hyperbolic manifold with small closed geodesics supporting Casimir energy -- along with a single classical source (7-form flux) -- contains an immediate 3-term structure for volume stabilization at positive potential energy. Hyperbolic manifolds are well-studied mathematically, with an important rigidity property at fixed volume. They and their Dehn fillings to more general Einstein spaces exhibit explicit discrete parameters that yield small closed geodesics supporting Casimir energy. The off-shell effective potential derived by M. Douglas incorporates the warped product structure via the constraints of general relativity, screening negative energy. Analyzing the fields sourced by the localized Casimir energy and the available discrete choices of manifolds and fluxes, we find a regime where the net curvature, Casimir energy, and flux compete at large radius and stabilize the volume. Further metric and form field deformations are highly constrained by hyperbolic rigidity and warping effects, leading to calculations giving strong indications of a positive Hessian, and residual tadpoles are small. We test this via explicit back reacted solutions and perturbations in patches including the Dehn filling regions, initiate a neural network study of further aspects of the internal fields, and derive a Maldacena-Nunez style no-go theorem for Anti-de Sitter extrema. A simple generalization incorporating 4-form flux produces axion monodromy inflation. As a relatively simple de Sitter uplift of the large-N M2-brane theory, the construction applies to de Sitter holography as well as to cosmological modeling, and introduces new connections between mathematics and the physics of string/M theory compactifications.

Published as SciPost Phys. 12, 083 (2022)

Author comments upon resubmission

We thank the referee for their efforts reviewing our paper and for their comments and questions. We have updated the paper in a few places based on their input. We have also replied to the referee reports separately.

List of changes

1) We have emphasized the variational nature of the parameter $B_\star$ in the new footnote 13.
2) In order to avoid potential confusions and emphasize that our mechanism uses a large $K/a$, we have introduced the parameter $a$ from the beginning in Sec. 2. We refer there to the later Sec. 4 where we argue that it is possible to obtain $a\ll1$ with explicit discrete parameters in our construction. This decreases the relative strength of the curvature contribution, and allows the Casimir energy to compete without requiring sub-Planckian Casimir circles.
3) We have added in the conclusion section some comments on possible research directions for obtaining a realistic matter content. Since many of the existing constructions of this in other classes of compactifications are local, it appears possible to incorporate them here as well as potentially new mechanisms related to the geometry of hyperbolic manifolds and orbifolds. Not having delved into this in great detail yet, we still leave it as a future direction in this paper.

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