Replica analysis of entanglement properties

TL;DR

This paper systematically analyzes entanglement entropy in curved backgrounds using the replica method, providing analytic expansions and exploring its behavior in black hole backgrounds to understand entanglement islands.

Contribution

It develops a general replica-based framework for entanglement entropy in curved spaces, extending previous results and analyzing black hole entanglement properties.

Findings

Analytic $(q-1)$ expansion of Rènyi entropy $S_q$

Behavior of entanglement entropy in black hole backgrounds

Insights into entanglement islands

Abstract

In this paper we develop a systematic analysis of the properties of entanglement entropy in curved backgrounds using the replica approach. We explore the analytic $(q-1)$ expansion of R\'enyi entropy $S_q$ and its variations; our setup applies to generic variations, from symmetry transformations to variations of the background metric or entangling region. Our methodology elegantly reproduces and generalises results from the literature on entanglement entropy in different dimensions, backgrounds, and states. We use our analytic expansions to explore the behaviour of entanglement entropy in static black hole backgrounds under specific scaling transformations, and we explain why this behaviour is key to determining whether there are islands of entanglement.