Eur. Phys. J. C (2018) 78: 23
https://doi.org/10.1140/epjc/s10052-017-5511-4

Regular Article - Theoretical Physics

Logarithmic black hole entropy corrections and holographic Rényi entropy

¹ The Institute of Mathematical Sciences, Chennai, 600113, India
² Department of Physics, KU Leuven Campus Kortrijk - KULAK, Etienne Sabbelaan 53 bus 7800, 8500, Kortrijk, Belgium

^* e-mail: subhash.mahapatra@kuleuven.be
^** e-mail: subhashmahapatra@gmail.com

Received: 11 October 2017
Accepted: 29 December 2017
Published online: 12 January 2018

Abstract

The entanglement and Rényi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Rényi entropies. We calculate these corrections for both Einstein and Gauss–Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order . The entropic c-function and the inequalities of the Rényi entropy are also satisfied even with the correction terms.