Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS$_5$

TL;DR

This paper computes logarithmic corrections to the entropy of rotating AdS$_5$ black holes and strings using both field theory indices and gravity methods, finding perfect agreement and advancing microstate counting precision.

Contribution

It demonstrates the matching of logarithmic entropy corrections from field theory and gravity perspectives for rotating AdS$_5$ black objects, validating the Kerr/CFT approach.

Findings

Exact agreement between field theory and gravity calculations.

Logarithmic corrections derived from superconformal and topologically twisted indices.

Supports the use of Kerr/CFT for precision entropy computations in AdS/CFT.

Abstract

We investigate logarithmic corrections to the entropy of supersymmetric, rotating, asymptotically AdS$_5$ black holes and black strings. Within the framework of the AdS/CFT correspondence, the entropy of these black objects is determined, on the field theory side, by the superconformal index and the refined topologically twisted index of $\mathcal{N}=4$ supersymmetric Yang-Mills theory, respectively. We read off the logarithmic correction from those field-theoretic partition functions. On the gravity side, we take the near-horizon limit and apply the Kerr/CFT correspondence whose associated charged Cardy formula describes the degeneracy of states at subleading order and determines the logarithmic correction to the entropy. We find perfect agreement between these two approaches. Our results provide a window into precision microstate counting and demonstrate the efficacy of low-energy, symmetry-based approaches such as the Kerr/CFT correspondence for asymptotically AdS black objects under certain conditions.