Corrections to the statistical entropy of five dimensional black holes

TL;DR

This paper calculates the sub-leading corrections to the statistical entropy of five-dimensional black holes with three charges, confirming the agreement with macroscopic supergravity results and clarifying the 4d-5d entropy lift.

Contribution

It provides the first detailed comparison of sub-leading entropy corrections between microscopic string theory and macroscopic supergravity for five-dimensional black holes.

Findings

Confirmed agreement between microscopic and macroscopic entropy calculations.

Derived sub-leading corrections to the 4d-5d black hole entropy relation.

Clarified the role of Taub-NUT space in entropy corrections.

Abstract

We compute the statistical entropy of the three charge (D1-D5-p) five dimensional black hole to sub-leading order in a large charge expansion. We find an agreement with the macroscopic calculation of the Wald entropy in R^2 corrected supergravity theory. The two calculations have a overlapping regime of validity which is not the Cardy regime. We use this result to clarify the 4d-5d lift for black holes on Taub-NUT space. In particular, we compute sub-leading corrections to the formula S^{4d} = S^{5d}. In the microscopic analysis, this correction arises from excitations bound to the Taub-NUT space. In the macroscopic picture, the difference is accounted by a mechanism present in a higher derivative theory wherein the geometry of the Taub-NUT space absorbes some of the electric charge.