Holographic Renyi Entropies and Restrictions on Higher Derivative Terms

Abstract

We perform a holographic calculation of the Entanglement Rényi 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 Rényi 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.

arXiv comment15 pages, 8 figures. Talk delivered at the Workshop on Quantum Fields and Strings of the 2014 Corfu Summer Institute; To appear in Proceedings of Science (Proceedings of the Corfu Summer Institute 2014 "School and Workshops on Elementary Particle Physics and Gravity", 3-21 September 2014 Corfu, Greece); This talk draws heavily from arXiv:1404.1309

Cited by in corpus (1)

• On the Rényi entropy of Lifshitz and hyperscaling violating black holes