Replica Phase Transition with Quantum Gravity Corrections

TL;DR

This paper investigates the phase structure of a boundary effective theory for near-extremal Reissner-Nordstr"om black holes, revealing a phase transition influenced by temperature and coupling constants, inspired by bulk replica wormholes.

Contribution

It introduces a detailed boundary effective theory including a Schwarzian and $U(1)$ mode, analyzing phase transitions with quantum gravity corrections.

Findings

Identifies a phase transition between connected and disconnected geometries.

Derives the entropy from the partition function of the boundary theory.

Shows the phase structure depends on temperature and coupling constants C, K, and E.

Abstract

Motivated by bulk replica wormholes, we study the boundary effective theory that describes the near-horizon fluctuations of a near-extremal Reissner-Nordstr\"om black hole. This theory consists of a Schwarzian mode and a $U(1)$ phase mode. We compute the partition function of this boundary theory on connected geometries, from which the entropy is derived. Our analysis reveals a rich phase structure, in which the dominance of connected or disconnected configurations leads to a phase transition controlled by the temperature and the coupling constants $C$, $K$, and $\mathcal{E}$ of the 1d effective theory.