Berry Picking: Random Wave Chaos Hierarchy for BPS Microstate Geometries

Abstract

We estimate the strength of chaos of probe waves and probe geodesics in different smooth supergravity backgrounds of decreasing supersymmetry and/or increasing length of the AdS throat in the interior. Since BPS spectra are highly degenerate and thus do not display the level repulsion that ordinarily diagnoses chaos, we propose compliance with the Berry random wave hypothesis for probe wavefunctions as a new notion of BPS chaos suited to the supergravity regime. The wave chaos becomes stronger and stronger with less supersymmetry and longer throats (i.e., as we approach black hole solutions). Geodesic motion shows the opposite trend, becoming more and more regular. We explain this dichotomy by the existence of stable periodic orbits inside long throats while the overall measure of KAM tori decreases. Computing the Rényi entropies for the dual CFT states in the weak coupling regime, we show that they do not have such universal behavior.

40 pages, 9 figures; this version: additional explanations in section 5, improved figures, additional discussion in section 6