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Replica Phase Transition with Quantum Gravity Corrections

Jun Nian, Yuan Zhong

Abstract

Motivated by bulk replica wormholes, we study the boundary effective theory that describes the near-horizon fluctuations of a near-extremal Reissner-Nordström 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 replica geometries, from which the entropy is derived. Our analysis reveals a rich phase structure, in which the dominance of connected or disconnected replica configurations leads to a phase transition controlled by the temperature and the coupling constants $C$, $K$, and $\mathcal{E}$ of the 1d effective theory.

Replica Phase Transition with Quantum Gravity Corrections

Abstract

Motivated by bulk replica wormholes, we study the boundary effective theory that describes the near-horizon fluctuations of a near-extremal Reissner-Nordström black hole. This theory consists of a Schwarzian mode and a phase mode. We compute the partition function of this boundary theory on replica geometries, from which the entropy is derived. Our analysis reveals a rich phase structure, in which the dominance of connected or disconnected replica configurations leads to a phase transition controlled by the temperature and the coupling constants , , and of the 1d effective theory.
Paper Structure (4 sections, 40 equations, 3 figures)

This paper contains 4 sections, 40 equations, 3 figures.

Table of Contents

  1. i) Transition on $\beta$.
  2. ii) Transition on $\mathcal{E}$.
  3. iii) Transition on $C/K$ with $C/K \in (0, \mathcal{E}^2)$.
  4. acknowledgments

Figures (3)

  • Figure 1: The connected and disconnected replica geometries
  • Figure 2: The quotient geometry $M_n/Z_n$ can be treated as a trumpet geometry
  • Figure 3: The phase structure on $\beta/K$ and $C/K$ with constant $\mathcal{E}$.