Modular-invariant random matrix theory and AdS₃ wormholes

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.