We develop a nonperturbative definition of ${\mathrm{RMT}}_2$: 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 ${\mathrm{RMT}}_2$, 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 $\mathrm{SL}(2,\mathbb{Z})$ spectral decomposition employed in previous work. As a demonstration we perform the explicit ${\mathrm{RMT}}_2$ lift of two-point correlations of the GUE Airy model. We propose that in ${\mathrm{AdS}}_3$ pure gravity, semiclassical amplitudes for off-shell $n$-boundary torus wormholes with topology ${\mathrm{\Sigma }}_{0,n}\times S^1$ are given by the ${\mathrm{RMT}}_2$ lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the ${\mathrm{RMT}}_2$ result.

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• Conformal field theory
• Gauge-gravity dualities
• Quantum gravity
• Random matrix theory