On random matrix statistics of 3d gravity

TL;DR

The paper demonstrates that 3d gravity on manifolds of the form $Σ_{g,n}×I$ with end-of-the-world branes is exactly dual to the Virasoro minimal string / random matrix model. Using BCFT annulus data and open–closed duality, it derives the disk amplitude and the annulus wormhole cylinder amplitude, showing they reproduce the universal random-matrix expressions, with ensemble type determined by boundary conditions and the mapping class group gauging rendering results finite. For higher-genus, χ<0, amplitudes are rewritten as gravitational inner products of half-Maldacena–Maoz wormholes and shown to coincide with Virasoro minimal string amplitudes, up to a simple topological factor $e^{S_0}=g_ag_b$ and Casimir-energy-induced shifts. Overall, the work provides nonperturbative evidence that 3d gravity with EOW branes is governed by a matrix-model ensemble, linking BCFT, Liouville theory, Virasoro TQFT, and random matrix theory in a coherent holographic framework.

Abstract

We show that 3d gravity on manifolds that are topologically a Riemann surface times an interval $Σ_{g,n}\times I$ with end-of-the-world branes at the ends of the interval is described by a random matrix model, namely the Virasoro minimal string. Because these manifolds have $n$ annular asymptotic boundaries, the path integrals naturally correspond to spectral correlators of open strings upon inverse Laplace transforms. For $g=0$ and $n=2$, we carry out an explicit path integration and find precise agreement with the universal random matrix expression. For Riemann surfaces with negative Euler characteristic, we evaluate the path integral as a gravitational inner product between states prepared by two copies of Virasoro TQFT. Along the way, we clarify the effects of gauging the mapping class group and the connection to chiral 3d gravity.