Modular-invariant random matrix theory and AdS${}_3$ wormholes

Abstract

We develop a non-perturbative 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 $\text{SL}(2,\mathbb{Z})$ 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 ${\Sigma }_{0,n}\times S^1$ 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.

11 pages; v2: added clarification regarding spinning sectors

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Cited by in corpus (3)

• Open-closed 3d gravity as a random ensemble
• A universal sum over topologies in 3d gravity
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity