Quantum gravity on a torus

TL;DR

This paper investigates the effects of changing spatial topology in Causal Dynamical Triangulations (CDT) from a 3-sphere to a 3-torus, finding that the phase structure remains unchanged, indicating universality of CDT results.

Contribution

The study demonstrates that the phase structure of CDT is unaffected by topology change from 3-sphere to 3-torus, supporting the universality of the approach.

Findings

Topology change does not alter phase structure.

Phase transitions remain second order.

Results suggest universality of CDT regardless of topology.

Abstract

Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach to quantum gravity where one assumes space-time foliation into spatial hyper-surfaces of fixed topology. Most of the CDT results were obtained for the spatial topology of the 3-sphere. It was shown that CDT has rich phase structure, including the semiclassical phase consistent with Einstein's general relativity. Some of the phase transitions were found to be second (or higher) order which makes a possibility of taking continuum limit viable. Here we present new results of changing the spatial topology to that of the 3-torus. We argue that the topology change does not change the phase structure nor the order of the phase transitions. Therefore CDT results seem to be universal independent of the topology chosen.