Replica analysis of entanglement properties

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 (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>q</a:mi><a:mo>−</a:mo><a:mn>1</a:mn></a:mrow></a:math>) expansion of Rényi entropy <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>S</c:mi><c:mi>q</c:mi></c:msub></c:math> 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 generalizes results from the literature on entanglement entropy in different dimensions, backgrounds and states. We use our analytic expansions to explore the behavior of entanglement entropy in static black hole backgrounds under specific scaling transformations, and we explain why this behavior is key to determining whether there are islands of entanglement.