Thermodynamics at the BPS bound for Black Holes in AdS

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.