The Bekenstein–Hawking formula gives a coarse-grained count of the number of microstates of a black hole, and it is remarkable that it may sometimes be reproduced from a microscopic count in string theory. However, the standard approach neglects quantum effects in the bulk which lead to pathologies for both supersymmetric and non-supersymmetric black holes, such as the breakdown of thermodynamics at sufficiently low temperatures.
In this talk, we will explain how a more careful treatment of the gravitational path integral resolves these tensions and leads to new and surprising effects that are completely invisible classically.
For extended supersymmetry, we will find that physically sensible black holes can preserve at most 4 supercharges, with the most exceptional example being black holes in AdS3xS3xS3xS1. This notoriously poorly understood background in string theory has a nonlinear large N=4 superconformal symmetry, but we are nevertheless able to make novel predictions for the BPS and near-BPS spectrum from gravity. Notably, we find discrete jumps in the BPS spectrum as a continuous parameter is adjusted-- a quantum gravity effect for which no microscopic derivation is currently known. This result is corroborated by constructing a family of non-extremal supersymmetric black holes that contribute to a supersymmetric index yet possess a temperature-dependent free energy.