Modular-Invariant Random Matrix Theory and AdS_{3} Wormholes

We develop a nonperturbative definition of RMT_{2}: 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 RMT_{2}, 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 RMT_{2} lift of two-point correlations of the GUE Airy model. We propose that in AdS_{3} pure gravity, semiclassical amplitudes for off-shell n-boundary torus wormholes with topology Σ_{0,n}×S^{1} are given by the RMT_{2} lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT_{2} result.