Exact holography for small black holes

Following recent advances on the computation of the Sen's quantum entropy function I will use supersymmetric localization in AdS2xS^2 supergravity to compute exactly the degeneracy of small black holes in N=4 string theory. In this framework I will show that the answer has an OSV type formula with minor but important corrections due to one-loop determinants and additional orbifold saddle points. This can then be compared with an exact microscopic answer given by the Rademacher expansion of the inverse of the Ramanujan function, the index that counts 1/2 BPS states in N=4 string theory. Impressive agreement is found at all orders in the expansion provinding us with a deep insight into the quantum structure of gravity and a non-trivial test of holography.