Sensitivity of BPS microstates by Sean Colin-Ellerin (CERN)

A key signature of chaos in quantum systems is the random matrix behavior in the repulsion of energy levels. Since black holes are expected to be highly chaotic, their energy levels should exhibit such behavior. However, this cannot be true for BPS black holes as the energies of all of their microstates are fixed to be equal by the BPS bound. I will present a new diagnostic of chaos for BPS black holes, namely the sensitivity of their microstates to the couplings of the theory. This sensitivity can be detected by the mixing matrix for this degenerate subspace as one moves on moduli space, known as the Berry curvature. I will show that for fortuitous states in the N=2 supersymmetric SYK model and N=2 JT gravity, which are toy models for the black hole microstates, the Berry curvature has random matrix statistics. On the other hand, for the monotonous states dual to smooth, horizonless supergravity solutions, I will show in many different examples that the curvature is not chaotic at all..