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

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.

Automated summary

This study constrains the OPE coefficients and density of states of the 2D CFT dual to a semiclassical theory of gravity in 3D using the conformal bootstrap. By calculating in an ensemble of CFT data, it reproduces semiclassical 3D gravity. Various gravitational solutions, including wormholes and higher topology spacetimes, are analyzed and shown to agree with the ensemble-averaged CFT. The study also provides a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger with random couplings induced by wormholes.