Black hole microstates in AdS 4 from supersymmetric localization

This paper addresses a long standing problem, the counting of the microstates of supersymmetric asymptotically ads black holes in terms of a holographically dual field theory. we focus on a class of asymptotically ads4 static black holes preserving two real supercharges which are dual to a topologically twisted deformation of the abjm theory. we evaluate in the large n limit the topologically twisted index of the abjm theory and we show that it correctly reproduces the entropy of the ads4 black holes. an extremization of the index with respect to a set of chemical potentials is required. we interpret it as the selection of the exact r-symmetry of the superconformal quantum mechanics describing the horizon of the black hole.