${\cal P}-v$ Criticality in Gauged Supergravities

AdS black holes enjoy richer transition behaviors in extended phase space by assuming the cosmological constant and its conjugate quantity as thermodynamic pressure and thermodynamic volume. We study the extended thermodynamics of charged dilatonic AdS black holes in a class of Einstein-Maxwell-Dilaton theories that can be embedded in gauged supergravities in diverse dimensions. We find that new transition behaviors emerge in higher dimensions. First, there exist standard Van der Waals transition in five dimensional dilatonic AdS black hole with two equal charges. Second, there emerge a new phase transition branch in negative pressure region in six and seven dimensional dilatonic black holes with two equal charges. Third, there emerge transition behaviors in higher dimensional black hole with single charge cases that are absent in four dimension.