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

TL;DR

This work defines a non-perturbative, modular-invariant lift $RMT_2$ of random-matrix universality for 2D CFTs by a two-step Mellin-space construction and SL$(2,\mathbb{Z})$ spectral decomposition, summing over spin sectors and enforcing near-extremal RMT behavior in the scalar sector. The authors demonstrate the lift on the Airy $RMT$ model, revealing a modular-invariant topological expansion in terms of Eisenstein series and Maass cusp forms, and they propose that off-shell $n$-boundary torus wormholes in AdS$_3$ gravity are captured by the $RMT_2$ lift of JT gravity amplitudes, with a concrete replacement rule mapping monomials in the spectral variables to Eisenstein-series factors. For the three-boundary case, a gravity-based heuristic calculation matches the $RMT_2$ result, and explicit JT–$RMT_2$ lifts for $n=4,5$ illustrate the general pattern of Eisenstein-polynomial structures for higher boundaries. Overall, $RMT_2$ provides a modularly consistent framework to bound chaotic spectra in irrational CFTs and to organize multi-boundary wormhole amplitudes in AdS$_3$ gravity, offering a predictive baseline for future gravity calculations beyond JT reductions.

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 $Σ_{0,n} \times S^1$ 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.