Resurgence, conformal blocks, and the sum over geometries in quantum gravity

Benjamin, Nathan; Collier, Scott R.; Maloney, Alexander; Meruliya, Viraj

doi:10.1007/jhep05(2023)166

Cited by 9 publications

(1 citation statement)

References 37 publications

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“…33 Such contributions would presumably correspond to doubly non-perturbative effects from the perspective of the 1/c expansion. That the 1/c expansion around a given bulk saddle is asymptotic may be viewed as indicating the need for the sum over geometries itself [133].…”

Section: Summing Over Topologiesmentioning

confidence: 99%

Solving 3d gravity with Virasoro TQFT

Collier,

Eberhardt,

Zhang

2023

SciPost Phys.

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We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as “Virasoro TQFT”. This TQFT is similar, but importantly not equivalent, to SL(2, \mathbb{R}ℝ) Chern-Simons theory. This sharpens the folklore that 3d gravity is related to SL(2, \mathbb{R}ℝ) Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level. Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity. In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the central charge. Mathematically, the relation leads to many nontrivial conjectures for hyperbolic 3-manifolds, Virasoro conformal blocks and crossing kernels.

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Section: Summing Over Topologiesmentioning

confidence: 99%

Solving 3d gravity with Virasoro TQFT

Collier,

Eberhardt,

Zhang

2023

SciPost Phys.

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The semi-classical saddles in three-dimensional gravity via holography and mini-superspace approach

Chen,

Hikida,

Taki

et al. 2024

J. High Energ. Phys.

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We determine the complex geometries dual to the semi-classical saddles in three-dimensional gravity with positive or negative cosmological constant. We examine the semi-classical saddles in Liouville field theory and interpret them in terms of gravity theory. For this, we describe the gravity theory by Chern-Simons theory and classify the possible saddles based on the homotopy group argument. We further realize the semi-classical saddles using the mini-superspace model of quantum gravity and explicitly determine the integral contour. In the case of positive cosmological constant, we recovered the geometry used for no-boundary proposal of Hartle and Hawking. In the case of negative cosmological constant, the geometry can be identified with Euclidean anti-de Sitter space attached with imaginary radius spheres. The geometry should be unphysical and several arguments on this issue are provided. Partial results were already presented in our earlier letter, and more detailed derivations and explanations on the results are given along with additional results. In particular, we reproduce the classical Liouville action from the Chern-Simons formulation of dual gravity theory.

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The universal one-loop effective action with gravity

Larue,

Quevillon

2023

J. High Energ. Phys.

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We complete the so-called Universal One-Loop Effective Action (UOLEA) with effects of gravity and provide a systematic approach to incorporate higher dimensional operators in curved spacetime. The functional determinant stemming from the path integral is computed using the Covariant Derivative Expansion (CDE), in a momentum representation that does not rely on a specific choice of coordinate to be defined, as it often is. This efficient approach manifests an interesting novelty as it allows to integrate out chiral fermions in curved spacetime in a direct manner leading to new operators involving the curvature, and provides a new alternative to the use of Feynman diagrams in that regard. The method presented would very well fit in a code that performs CDE, offering the possibility to integrate out at one-loop fields on a curved spacetime background, including spin-2 fields, like the graviton. Eventually these results should provide an interesting way to study low energy effects of UV completions of gravity.

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Resurgence, conformal blocks, and the sum over geometries in quantum gravity

Cited by 9 publications

References 37 publications

Solving 3d gravity with Virasoro TQFT

Solving 3d gravity with Virasoro TQFT

The semi-classical saddles in three-dimensional gravity via holography and mini-superspace approach

The universal one-loop effective action with gravity

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