Lorentzian 3d Gravity with Wormholes via Matrix Models

TL;DR

This paper establishes a novel link between 3D Lorentzian quantum gravity and a hermitian two-matrix model, revealing two distinct phases with different geometric properties, including wormholes in the strong-coupling phase.

Contribution

It introduces a non-perturbative matrix model formulation of 3D Lorentzian quantum gravity and identifies its phase structure and geometric implications.

Findings

Two phases of the matrix model with distinct geometries

Weak gravity phase with propagating 2D universes

Strong coupling phase with disintegrated hypersurfaces and wormholes

Abstract

We uncover a surprising correspondence between a non-perturbative formulation of three-dimensional Lorentzian quantum gravity and a hermitian two-matrix model with ABAB-interaction. The gravitational transfer matrix can be expressed as the logarithm of a two-matrix integral, and we deduce from the known structure of the latter that the model has two phases. In the phase of weak gravity, well-defined two-dimensional universes propagate in proper time, whereas in the strong-coupling phase the spatial hypersurfaces disintegrate into many components connected by wormholes.