Kadanoff Seminar: AdS_3/RMT_2 beyond the ramp. - Gabriele di Ubaldo, UC Berkeley

AdS_3/RMT_2 beyond the ramp.

In 2307.03707 we introduced a framework for random matrix theory (RMT) in AdS_3 quantum gravity and chaotic 2D CFTs that is manifestly conformal and modular invariant. On the CFT side this leads to a 2d CFT trace formula, analogous to the Gutzwiller trace formula for chaotic quantum systems, which we use to derive necessary and sufficient conditions  for an individual 2d CFT to have RMT statistics. Applied pure 3D gravity, we obtain a microscopic CFT understanding of the off-shell Cotler-Jensen torus wormhole. This wormhole is shown to be exactly dual to RMT_2: the minimal modular invariant completion of the RMT two-point correlator. In work to appear soon, we construct and establish RMT_2 as a modular invariant RMT ensemble which minimally uplifts to 3D the near-extremal dynamics of 2D theories like JT gravity. We construct a modular invariant spectral form factor describing the full ramp-plateau transition. Seen as a candidate SFF of pure 3D gravity, the plateau indicates the discreteness of  black hole microstates. We give predictions for n-boundary wormholes in pure 3D gravity and in the n=3 case we exhibit matching with a gravitational computation. Applied to chaotic CFTs we derive further constraints for a CFT to satify RMT universality in the form of asymptotic sum rules for CFT data.