AdS$_3$ wormholes from a modular bootstrap

TL;DR

This paper uses a modular bootstrap approach to determine the path integral of 3D gravity on torus times an interval, revealing universal features and connections to random matrix theory for CFT ensembles.

Contribution

It introduces a modular bootstrap method for 3D gravity path integrals, fixing the amplitude using consistency conditions and comparing it to the Narain ensemble.

Findings

The amplitude is fully determined by bootstrap constraints.

At low temperature, the gravity result matches a random matrix theory approximation.

The behavior is conjectured to be universal for large central charge CFT ensembles with chaotic spectra.

Abstract

In recent work we computed the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. Here we employ a modular bootstrap to show that the amplitude is completely fixed by consistency conditions and a few basic inputs from gravity. This bootstrap is notably for an ensemble of CFTs, rather than for a single instance. We also compare the 3d gravity result with the Narain ensemble. The former is well-approximated at low temperature by a random matrix theory ansatz, and we conjecture that this behavior is generic for an ensemble of CFTs at large central charge with a chaotic spectrum of heavy operators.