IAS Physics Group Meeting

Abstract: We develop a non-perturbative definition of RMT2: a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its n-point spectral correlations admit a prescribed modular-invariant lift to RMT2, which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the SL(2,Z) spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT2 lift of two-point correlations of the GUE Airy model. We propose that in AdS3 pure gravity, semiclassical amplitudes for off-shell n-boundary torus wormholes with topology Σ0,n×S1 are given by the RMT2 lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT2 result.