The phase structure and effective action of 3D CDT at higher spatial genus

TL;DR

This study investigates the phase structure and effective action of 3D Causal Dynamical Triangulations (CDT) with various topologies and relaxed conditions, finding that these modifications do not alter the continuum limit or leading-order effective action.

Contribution

It provides the first detailed analysis of how enlarging triangulation ensembles and changing spatial topology affect 3D CDT's phase structure and effective action.

Findings

Phase structure remains qualitatively unchanged under generalizations.

Effective action aligns with continuum Einstein gravity predictions.

Spatial genus variations do not impact the leading-order effective action.

Abstract

We perform a detailed investigation of the phase structure and the semiclassical effective action of (2+1)-dimensional Causal Dynamical Triangulations (CDT) quantum gravity using computer simulations. On the one hand, we study the effect of enlarging the ensemble of triangulations by relaxing the simplicial manifold conditions in a controlled way. On the other hand, we cast a first look at CDT geometries with spatial topology beyond that of the sphere or torus. We measure the phase structure of the model for several triangulation ensembles and spatial topologies, finding evidence that the phase structure is qualitatively unaffected by these generalizations. Furthermore, we determine the effective action for the spatial volumes of the system, again varying the simplicial manifold conditions and the spatial topology. In all cases where we were able to gather sufficient statistics, we found the resulting effective action to be consistent with a minisuperspace action derived from continuum Einstein gravity. We interpret our overall results as evidence that 1) partially relaxing simplicial manifold conditions or changing the spatial genus does not affect the continuum limit of 3D CDT and that 2) increasing the spatial genus of the system likely does not influence the leading-order terms in the emergent effective action.