Generalized gravitational entropy without replica symmetry

TL;DR

This paper extends the generalized entropy framework to cases without replica symmetry, allowing solutions beyond general relativity and applying it to Einstein-Gauss-Bonnet gravity to derive conditions for holographic entanglement entropy.

Contribution

It introduces a flexible ansatz for the replica metric that does not require replica symmetry, enabling analysis of gravitational theories beyond Einstein gravity.

Findings

Replica symmetry breaking terms are allowed by field equations.

Holographic entanglement entropy in Einstein-Gauss-Bonnet gravity is evaluated on extremal surfaces.

The approach generalizes the entropy construction beyond traditional symmetry assumptions.

Abstract

We explore several extensions of the generalized entropy construction of Lewkowycz and Maldacena, including a formulation that does not rely on preserving replica symmetry in the bulk. We show that an appropriately general ansatz for the analytically continued replica metric gives us the flexibility needed to solve the gravitational field equations beyond general relativity. As an application of this observation we study Einstein-Gauss-Bonnet gravity with a small Gauss-Bonnet coupling and derive the condition that the holographic entanglement entropy must be evaluated on a surface which extremizes the Jacobson-Myers entropy. We find that in both general relativity and Einstein-Gauss-Bonnet gravity replica symmetry breaking terms are permitted by the field equations, suggesting that they do not generically vanish.