AdS$_5$ Black Hole Entropy near the BPS Limit

TL;DR

The paper develops a coherent framework to study AdS_5 black holes near the BPS limit by combining gravitational thermodynamics with a nearBPS extension of the N=4 SYM partition function. It identifies two independent deformations from the BPS surface: nonzero temperature and a constraint-violating deformation parameterized by φ, and it formulates a nearBPS free-energy extremization that reproduces the gravity results for mass and entropy. A key outcome is the equality of heat capacity and electric capacitance, C_T = C_φ, and the introduction of the height function h to quantify constraint violations, linking the microphysics to the gravity side via a first-law structure that holds beyond strict BPS. The results offer a principled route to extend BPS microstate counting into a near-supersymmetric regime, providing insight into near-extremal holography and suggesting directions for a fuller microscopic understanding of nearBPS degrees of freedom.

Abstract

We analyze AdS$_5$ black holes that are nearly supersymmetric. They depart from the BPS limit in two distinct ways: a temperature takes them above extremality and a potential violates a certain constraint. We study the thermodynamics of these deformations and their interplay in detail. We discuss recent microscopic computations of BPS black hole entropy in $\mathcal{N}=4$ SYM and generalize methods to the nearBPS regime by relaxing constraints imposed by supersymmetry. The computations recover gravitational results from microscopics also for nearBPS black holes.