AdS3 gravity and random CFT

Jordan Cotler,Kristan Jensen

doi:10.1007/jhep04(2021)033

Jordan Cotler, Kristan Jensen

Open Access

https://doi.org/10.1007/jhep04(2021)033

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Abstract

We compute the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asymptotically Euclidean AdS3 regions with torus boundary. From our results we obtain the spectral correlations between BTZ black hole microstates near threshold, as well as extract the spectral form factor at fixed momentum, which has linear growth in time with small fluctuations around it. The low-energy limit of these correlations is precisely that of a double-scaled random matrix ensemble with Virasoro symmetry. Our findings suggest that if pure three-dimensional gravity has a holographic dual, then the dual is an ensemble which generalizes random matrix theory.

Highlights

There has long been hope that simple models of quantum gravity with negative cosmological constant in less than four spacetime dimensions exist as consistent quantum mechanical models
Our findings suggest that if pure three-dimensional gravity has a holographic dual, the dual is an ensemble which generalizes random matrix theory
Thanks to the topological recursion of matrix integrals [8,9,10,11], Saad, Shenker, and Stanford [7] have demonstrated that this equation holds to all orders in the genus expansion and for all n, and it is in this sense that JT gravity is dual to a certain matrix ensemble

Summary

Introduction

There has long been hope that simple models of quantum gravity with negative cosmological constant in less than four spacetime dimensions exist as consistent quantum mechanical models. As one expects for consistent theories of AdS quantum gravity, it has a holographic dual. Unlike standard examples of AdS/CFT, the holographic dual is not a quantum mechanical system in one lower dimension. The holographic dictionary equates the n-point ensemble average of tr(e−βiH ) in the dual matrix model to the JT path integral with n boundaries of renormalized lengths βi: The solid disk indicates a sum over all geometries which fill in the boundary circles. Thanks to the topological recursion of matrix integrals [8,9,10,11], Saad, Shenker, and Stanford [7] have demonstrated that this equation holds to all orders in the genus expansion and for all n, and it is in this sense that JT gravity is dual to a certain matrix ensemble

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