A bstract The off-shell free energy of supersymmetric black holes in AdS 5 is constructed and the phase diagram in various limiting cases is investigated, including in the presence of higher derivative corrections, with particular emphasis on BPS thermodynamics. Starting from Landau’s theory, an exact method is systematically developed to construct the off shell BPS free energy, which in certain limiting cases, can be rearranged in terms of an effective energy and entropy of the system, with the latter being conjugate to an effective BPS temperature. The off-shell BPS phase diagram shows features which resemble the phases of general AdS Schwarzschild black holes, with some nuances in the asymptotic structure, modified by four-derivative corrections. Using AdS/CFT, phenomenological effective potentials in the boundary gauge theory are proposed, dual to both general black holes and their BPS counterparts. The saddle points of the effective potential capture the various locally stable and unstable phases of the gauge theory at finite temperature and chemical potential.
Sahu et al. (Wed,) studied this question.