On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity

TL;DR

This paper investigates the properties of spatial hypersurfaces in three-dimensional Lorentzian quantum gravity using numerical methods, revealing a universality class match with 2D Euclidean quantum gravity above a phase transition.

Contribution

It provides the first detailed numerical analysis of spatial slices in 3D Lorentzian quantum gravity and identifies their universality class in certain phases.

Findings

Spatial slices match 2D Euclidean quantum gravity above the phase transition.

Below the transition, slices exhibit behavior indicating a new quantum system.

Measured quantum observables include entropy exponent, Hausdorff dimensions, and Ricci curvature.

Abstract

Three-dimensional Lorentzian quantum gravity, expressed as the continuum limit of a nonperturbative sum over spacetimes, is tantalizingly close to being amenable to analytical methods, and some of its properties have been described in terms of effective matrix and other models. To gain a more detailed understanding of three-dimensional quantum gravity, we perform a numerical investigation of the nature of spatial hypersurfaces in three-dimensional Causal Dynamical Triangulations (CDT). We measure and analyze several quantum observables, the entropy exponent, the local and global Hausdorff dimensions, and the quantum Ricci curvature of the spatial slices, and try to match them with known continuum properties of systems of two-dimensional quantum geometry. Above the first-order phase transition of CDT quantum gravity, we find strong evidence that the spatial dynamics lies in the same universality class as two-dimensional Euclidean (Liouville) quantum gravity. Below the transition, the behaviour of the spatial slices does not match that of any known quantum gravity model. This may indicate the existence of a new type of two-dimensional quantum system, induced by the more complex nature of the embedding three-dimensional quantum geometry.