Holographic Renyi Entropies and Restrictions on Higher Derivative Terms

TL;DR

This paper calculates holographic Re9nyi entropies for boundary CFTs with Einstein-Gauss-Bonnet-Maxwell gravity, revealing causality-based restrictions on higher derivative couplings and indicating potential phase transitions.

Contribution

It provides the first holographic computation of Re9nyi entropies in Gauss-Bonnet gravity, identifying causality constraints and phase transition signatures.

Findings

Violation of Re9nyi entropy inequalities at high Gauss-Bonnet couplings

Restrictions on Gauss-Bonnet coupling coefficients due to negative entropy black holes

Distinct analytic structures indicating possible phase transitions

Abstract

We perform a holographic calculation of the Entanglement R\'enyi entropy $S_q(\mu,\lambda)$, for spherical entangling surfaces in boundary CFT's with Einstein-Gauss-Bonnet-Maxwell holographic gravitational duals. We find that for Gauss-Bonnet couplings $\lambda$, larger than a specific value, but still allowed by causality, a violation of an inequality that R\'enyi entropies must obey by definition occurs. This violation is related to the existence of negative entropy black holes and restricts the coefficient of the Gauss-Bonnet coupling in the bulk theory. Furthermore, we discover a distinction in the analytic structure of the analytic continuation of $S_q(\mu,\lambda)$, between negative and non-negative $\lambda$, suggesting the existence of a phase transition.