Modular-invariant random matrix theory and AdS3 wormholes

Abstract

We develop a non-perturbative definition of RMT: a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its -point spectral correlations admit a prescribed modular-invariant lift to RMT, 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 spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT lift of two-point correlations of the GUE Airy model. We propose that in AdS pure gravity, semiclassical amplitudes for off-shell -boundary torus wormholes with topology are given by the RMT lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT result.

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Identifiers

ORCID for Felix Haehl: orcid.org/0000-0001-7426-0962

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