Close Encounters of the Wormhole Kind

Black holes are expected to exhibit universal 'random matrix' behavior at late times, indicative of quantum chaos. The approach to a late-time plateau in the spectral form factor (SFF) is a probe of this behavior. In this talk we study the SFF in double-scaled matrix integrals, dual to two-dimensional black holes, and conjecture a formula for the SFF in the limit of large time, large density of states, and fixed temperature. This formula provides a convergent expansion for the plateau as a sum over spacetime topologies (spacetime wormholes). To understand the origin of this series, we compare to the semiclassical theory of “encounters” in periodic orbits. In Jackiw-Teitelboim (JT) gravity, encounters correspond to portions of the moduli space integral that mutually cancel (in the orientable case) but individually grow at low energies. At genus one we show how the full moduli space integral resolves the low energy region and gives a finite nonzero answer.