logo Supersymmetric Black Holes and Automorphic Forms

A central issue in quantum gravity is to understand the microscopic origin of the Bekenstein-Hawking entropy of black holes.
String theory famously reproduces this entropy to leading order, by a rough counting of micro-states with the required charges.
It is important, but notoriously difficult, to extend this agreement beyond the large charge limit.
In certain cases with sufficient (super)symmetry, we argue that the exact numbers of micro-states as a function of the charges are given by Fourier coefficients of certain automorphic forms of the U-duality group.
This provides a physical setting for standard mathematical constructions in the field of automorphic forms, including unipotent representations, adelic spherical vectors, etc.