Black Hole Microstate Counting from Gravity

Finding a gravitational description of black hole microstates is an important problem in quantum gravity. In this talk we describe how to reproduce the integer number of black hole microstates using the Gibbons-Hawking gravitational path integral. This is done for a specific class of supersymmetric black holes in four dimensions arising from toroidal compactifications of string theory: first by applying localization to the gravitational path integral that computes the index (including a careful evaluation of one-loop determinants), and second by comparing the index with the degeneracy.