Higher-Derivative Corrections and AdS$_5$ Black Holes

TL;DR

This paper computes higher-derivative corrections to AdS$_5$ black holes in supergravity, demonstrating agreement with superconformal index results and exploring entropy corrections in holographic duals.

Contribution

It provides a holographic evaluation of the on-shell action and entropy of supersymmetric AdS$_5$ black holes including four-derivative corrections, linking to 4d SCFT anomalies.

Findings

Agreement with superconformal index on the second sheet

Explicit calculation of Wald entropy with corrections

Insights into subleading $1/N$ corrections in holography

Abstract

Using recent results in four-derivative 5d $\mathcal{N}=2$ minimal gauged supergravity, we evaluate the regularized on-shell action of the Euclidean solution in this theory that admits a Lorentzian continuation to an AdS$_5$ black hole with one electric charge and two angular momenta. We focus on the supersymmetric limit of this solution and employ holography to show that the result can be expressed purely in terms of angular momentum fugacities and the 't Hooft anomalies for the $\mathrm{U}(1)_{\mathrm R}$ R-symmetry of the dual 4d $\mathcal{N}=1$ SCFT. This holographic calculation is in perfect agreement with recent studies of the 4d $\mathcal{N}=1$ superconformal index ``on the second sheet''. We illustrate the utility of these results in two classes of 4d $\mathcal{N}=1$ holographic SCFTs that have 't Hooft anomalies with suitable large $N$ behavior that leads to non-trivial corrections at first subleading order in the $1/N$ expansion. We also explicitly calculate the Wald entropy of the black hole solution and delineate the leading four-derivative corrections to the Bekenstein-Hawking entropy.