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

Understand

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.