AdS black holes, holography and localization

Abstract

I review some recent progresses in counting the number of microstates of AdS supersymmetric black holes in dimension equal or greater than four using holography. The counting is obtained by applying localization and matrix model techniques to the dual field theory. I cover in details the case of dyonic AdS4 black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS5 black holes.