Corrections to AdS$_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity

TL;DR

This paper computes higher-derivative corrections to AdS$_5$ black hole thermodynamics in supergravity, matching results with dual superconformal index calculations and deriving explicit entropy corrections, especially in supersymmetric and extremal cases.

Contribution

It provides the first detailed analysis of four-derivative corrections to AdS$_5$ black holes, connecting supergravity corrections with dual field theory indices and simplifying the on-shell action via field redefinitions.

Findings

Corrections to black hole entropy and charges are explicitly computed.

Matching of supergravity results with dual superconformal index on the second sheet.

Simplified form of the on-shell action using field redefinitions.

Abstract

We study four-derivative corrections to five-dimensional minimal gauged supergravity. We evaluate the on-shell action of the AdS$_5$ black hole solution with two independent angular momenta and one electric charge at linear order in the corrections. After imposing supersymmetry, we are able to recast the action in terms of the supersymmetric chemical potentials and match the result obtained from the dual superconformal index on the second sheet. To achieve this, we exploit the freedom to implement field redefinitions to recast the action in a much simpler form, as well as the fact that the two-derivative solution is enough. We use the on-shell action to determine the corrections to the black hole thermodynamics, including those to the entropy and the charges. We then specialize to the supersymmetric and extremal case and find a simple expression for the microcanonical entropy. In particular, for the case with one independent angular momentum the corrections are entirely encoded in the dual superconformal anomaly coefficients. We corroborate this result for the entropy by constructing the corrected near-horizon solution and applying Wald's formula.