Logarithmic Black Hole Entropy Corrections and Holographic R\'enyi Entropy

TL;DR

This paper investigates quantum corrections to black hole entropy and their impact on holographic Rènyi entropies in CFTs with gravity duals, revealing universal logarithmic corrections across various gravity theories and spacetime dimensions.

Contribution

It extends the calculation of holographic Rènyi entropies by including logarithmic corrections to black hole entropy derived from horizon symmetries and the Cardy formula.

Findings

Logarithmic corrections to black hole entropy are proportional to horizon area logarithm.

These corrections induce similar logarithmic terms in Rènyi entropies for CFTs with gravity duals.

Corrections are present in both Einstein and Gauss-Bonnet gravity models.

Abstract

The entanglement and R\'{e}nyi 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 horizon area. With the corrected black hole entropy expression, we then find corrections to the R\'{e}nyi entropies. We calculate these corrections for both Einstein as well as Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order $G_{D}^0$ and it seems to be a general feature of entanglement and R\'{e}nyi entropies for CFTs with gravity duals. In particular, there is a logarithmic correction to the entropy in odd boundary spacetime dimensions as well.