Thermodynamics at the BPS bound for Black Holes in AdS

TL;DR

The paper develops a double-scaling framework to define thermodynamics at the BPS bound for AdS black holes and supersymmetric solitons, introducing emergent BPS chemical potentials and the supersymmetric quantum statistical relation. It applies the construction to rotating BTZ and AdS$_5$ BPS black holes, deriving explicit BPS quantities ($E_{bps}$, $J_{bps}$, $Q_{bps}$, $S_{bps}$) and generalized potentials ($w$, $\phi$, $w_1$, $w_2$) that govern a zero-temperature, generalized grand canonical ensemble. The analysis reveals both stable and unstable regimes and first-order phase transitions in the BPS sector, with a simple BTZ example showing $I_{bps}= -\pi^2 k T_+$ and more intricate behavior in AdS$_5$, including zero entropy in certain BPS solitons. These results reinforce the link between gravitational thermodynamics and dual CFT statistical mechanics and provide a foundation for exploring larger 1/16 BPS sectors and possible string corrections within AdS/CFT.

Abstract

In this work we define a new limiting procedure that extends the usual thermodynamics treatment of Black Hole physics, to the supersymmetric regime. This procedure is inspired on equivalent statistical mechanics derivations in the dual CFT theory, where the BPS partition function at zero temperature is obtained by a double scaling limit of temperature and the relevant chemical potentials. In supergravity, the resulting partition function depends on emergent generalized chemical potentials conjugated to the different conserved charges of the BPS solitons. With this new approach, studies on stability and phase transitions of supersymmetric solutions are presented. We find stable and unstable regimes with first order phase transitions, as suggested by previous studies on free supersymmetric Yang Mills theory.