Nearly BPS Black Holes in AdS5 and their Spectrum in N=4 SYM

 In this talk, we will discuss quantum corrections in the gravitational path integral around nearly 1/16-BPS black holes in asymptotically AdS5 x S5 space, dual to heavy operators in N=4 SYM. We argue these quantum corrections come from a version of the N=2 super-Schwarzian theory which captures the breaking of the SU(1,1|1) near horizon symmetry at finite temperature and chemical potential. The quantization of this theory gives a quantum gravitational derivation of the extremal entropy. Additionally, we show the presence of a gap between the BPS black holes and the lightest near-BPS black holes, and we will give a prediction for the spectrum of near-BPS states that lie above this gap. Time permitting, we will discuss stringy and non-perturbative corrections that can affect the black hole spectrum.