Replica wormholes from Liouville theory

Shinji Hirano,Tsunehide Kuroki

doi:10.1007/jhep01(2022)094

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 2d conformal field theory (CFT) description, namely, the Liouville theory coupled to the (2, p) minimal matter in the p → ∞ 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.

Highlights

Of the SSS matrix model in [21]
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 2d conformal field theory (CFT) description, namely, the Liouville theory coupled to the (2, p) minimal matter in the p → ∞ 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

Summary

Disk partition function

Our first task is to start creating a precise dictionary between the JT gravity and the Liouville CFT [12, 13, 27]. Our goal is to establish the correspondence between the parameters listed in table 2 For this purpose we examine the most elementary quantity in the JT gravity, namely, the disk partition function [11]. On the Liouville theory side, one needs to fix the boundary length dτ ebφ(τ ). Where ZLdisk( ) is the “marked” Liouville disk partition function × ZmdiskZgdisk and the matter and ghost disk partition functions, ZmdiskZgdisk, will be normalized to 1. The Laplace transform of the ∂sU (0) from μB to corresponds to the JT gravity disk partition function. The JT disk partition function (2.12) must be matched to the “marked” Liouville disk partition function with a fixed boundary length : ZLdisk( ) = N dELe− EL ∂sU (0) =. These contributions are trivial and can be absorbed into the normalization

Semiclassical Liouville analysis

Replica wormholes

A single cosmic brane

Two cosmic branes

Marginal defect deformation

Discussions