3d Gravity as a random ensemble

Abstract

We give further evidence that the matrix-tensor model studied in \cite{belin2023} is dual to AdS${}_3$ gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random Hamiltonians, in which the matrix and tensor provide random CFT${}_2$ data subject to a potential that incorporates the bootstrap constraints. We show how the Feynman rules of the ensemble produce a sum over all three-manifolds and how surgery is implemented by the matrix integral. The partition functions of the resulting 3d gravity theory agree with Virasoro TQFT (VTQFT) on a fixed, hyperbolic manifold. However, on non-hyperbolic geometries, our 3d gravity theory differs from VTQFT, leading to a difference in the eigenvalue statistics of the associated ensemble. As explained in \cite{belin2023}, the Schwinger-Dyson (SD) equations of the matrix-tensor integral play a crucial role in understanding how gravity emerges in the limit that the ensemble localizes to exact CFT's. We show how the SD equations can be translated into a combinatorial problem about three-manifolds.

Published version

References in corpus (16)

• Poincare Series, 3D Gravity and CFT Spectroscopy
• Semiclassical 3D gravity as an average of large-c CFTs
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• Solving 3d Gravity with Virasoro TQFT
• The Virasoro Minimal String
• Space-Time Geometry of Topological phases
• Gravity factorized
• A proposal for 3d quantum gravity and its bulk factorization
• OPE statistics from higher-point crossing
• A principle of maximum ignorance for semiclassical gravity
• 3d gravity from Virasoro TQFT: Holography, wormholes and knots
• Multiboundary wormholes and OPE statistics
• Symmetries and spectral statistics in chaotic conformal field theories
• A note on the bulk interpretation of the Quantum Extremal Surface formula
• Euclidean wormholes in two-dimensional CFTs from quantum chaos and number theory
• Symmetries and spectral statistics in chaotic conformal field theories II: Maass cusp forms and arithmetic chaos

Cited by in corpus (10)

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• Modular-invariant random matrix theory and AdS${}_3$ wormholes
• Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$c$ CFT Ensemble
• Anyon Condensation in Virasoro TQFT: Wormhole Factorization
• Discrete JT gravity as an Ising model
• Open-closed 3d gravity as a random ensemble
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• Crystalline Spectral Form Factors
• A universal sum over topologies in 3d gravity