The phase structure of Causal Dynamical Triangulations with toroidal spatial topology

TL;DR

This paper explores how the topology of space influences the phase structure of four-dimensional Causal Dynamical Triangulations, confirming the presence of four phases with toroidal topology and showing similarities to spherical topology.

Contribution

It provides the first detailed phase diagram of CDT with toroidal spatial topology, demonstrating the robustness of phase structure across different topologies.

Findings

All four phases observed in spherical topology are confirmed in toroidal topology.

The phase diagram for toroidal topology closely resembles that of spherical topology.

Topology has a significant impact but does not alter the fundamental phase structure.

Abstract

We investigate the impact of topology on the phase structure of four-dimensional Causal Dynamical Triangulations (CDT). Using numerical Monte Carlo simulations we study CDT with toroidal spatial topology. We confirm existence of all four distinct phases of quantum geometry earlier observed in CDT with spherical spatial topology. We plot the toroidal CDT phase diagram and find that it looks very similar to the case of the spherical spatial topology.