Semiclassical 3D gravity as an average of large-c CFTs

Abstract

A two-dimensional CFT dual to a semiclassical theory of gravity in three dimensions must have a large central charge $c$ and a sparse low energy spectrum. This constrains the OPE coefficients and density of states of the CFT via the conformal bootstrap. We define an ensemble of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce semiclassical 3D gravity. We analyze a wide variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell action of gravity agrees with the ensemble-averaged CFT at large $c$. The one-loop corrections also match in the cases where they have been computed. We also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger.

96 pages (typos fixed, references added)

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• Multiboundary wormholes and OPE statistics
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• Quantum Chaos on Edge
• 3d Gravity as a random ensemble
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• TQFT gravity and ensemble holography
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Symmetries and spectral statistics in chaotic conformal field theories II: Maass cusp forms and arithmetic chaos
• Black hole wavefunctions and microcanonical states
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
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