Topology induced first-order phase transitions in lattice quantum gravity

TL;DR

This paper investigates how the topology of space influences the nature of phase transitions in lattice quantum gravity models, specifically within the framework of Causal Dynamical Triangulations on a three-torus topology.

Contribution

It completes the phase diagram analysis of CDT for three-torus topology and shows that the order of phase transitions depends on the spatial topology.

Findings

Phase transitions' order varies with topology

Phase diagram for three-torus topology is completed

Topology influences spacetime geometry transitions

Abstract

Causal Dynamical Triangulations (CDT) is a lattice formulation of quantum gravity, suitable for Monte-Carlo simulations which have been used to study the phase diagram of the model. It has four phases characterized by different dominant geometries, denoted phase $A$, $B$, $C$ and $C_b$. In this article we analyse the $A-B$ and the $B-C$ {phase} transitions in the case where the topology of space is that of the three-torus. This completes the phase diagram of CDT for such a spatial topology. We observe that the order of a phase transition of spacetime geometries can depend on the topology of spacetime.