Nearly BPS black holes and the spectrum of N=4 Yang Mills

<!--HTML--><p>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. 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. Using this approach, holography predicts the presence of a gap between the BPS black holes and the lightest near-BPS black holes, and the spectrum of near-BPS states that lie above this gap. We will also discuss stringy and non-perturbative corrections that can affect the black hole spectrum.</p>