João Gomes, Faculdade de Ciências, Universidade do Porto
Recent developments in computing the quantum entropy function of supersymmetric black holes and exact holography

In this talk I will review recent developments in the computation of quantum corrections to the entropy of supersymmetric black holes based on the $Ad S_2/CFT_1$ correspondence. The use of supersymmetric localization of supergravity on $Ad S_2\times S_2$ is able to reduce a path integral over string fields to a finite dimensional integral. This path integral is the quantum version of Wald's entropy. We look in particular to $1/8$ BPS black holes in four dimensional $N=8$ string theory and compare the gravity computation with the well known microscopic answer. We find exact agreement, up to much subleading non-perturbative corrections that can in principle be computed. These results go much beyond the large charge approximation and constitute a first test of exact holography.