Replica Wormholes from Liouville Theory

TL;DR

This paper explores replica wormholes within JT gravity using Liouville conformal field theory, establishing a detailed correspondence between gravitational replica wormholes and twist operator correlators in 2D CFT.

Contribution

It provides a detailed dictionary linking replica wormholes in JT gravity to twist operators in Liouville CFT, advancing understanding of the black hole information paradox.

Findings

Replica wormholes are generated by twist operators in Liouville CFT.

The gravitational entanglement entropy matches twist operator correlators.

A precise correspondence between bulk gravity and 2D CFT is established.

Abstract

The replica wormholes are a key to the existence of the islands that play a central role in a recent proposal for the resolution of the black hole information paradox. In this paper, we study the replica wormholes in the JT gravity, a model of two-dimensional quantum gravity coupled to a non-dynamical dilaton, by making use of the 2$d$ conformal field theory (CFT) description, namely, the Liouville theory coupled to the $(2,p)$ minimal matter in the $p\to\infty$ limit. In the Liouville CFT description, the replica wormholes are created by the twist operators and the gravitational part of the bulk entanglement entropy can be reproduced from the twist operator correlators. We propose the precise dictionary and show how this correspondence works in detail.