# Critical Phenomena in Causal Dynamical Triangulations

## TL;DR

This paper investigates how the topology of space influences phase transitions in four-dimensional causal dynamical triangulations, finding that the order of the phase transition remains unaffected by topology differences.

## Contribution

It provides a systematic comparison of phase transitions in CDT with spherical and toroidal topologies, revealing topology does not alter the transition order.

## Key findings

- The phase transition order is unaffected by topology differences.
- Classical geometries differ significantly between topologies.
- Topology may influence geometrical details but not critical phenomena.

## Abstract

Four-dimensional CDT (causal dynamical triangulations) is a lattice theory of geometries which one might use in an attempt to define quantum gravity non-perturbatively, following the standard procedures of lattice field theory. Being a theory of geometries, the phase transitions which in usual lattice field theories are used to define the continuum limit of the lattice theory will in the CDT case be transitions between different types of geometries. This picture is interwoven with the topology of space which is kept fixed in the lattice theory, the reason being that "classical" geometries around which the quantum fluctuations take place depend crucially on the imposed topology. Thus it is possible that the topology of space can influence the phase transitions and the corresponding critical phenomena used to extract continuum physics. In this article we perform a systematic comparison between a CDT phase transition where space has spherical topology and the "same" transition where space has toroidal topology. The "classical" geometries around which the systems fluctuate are very different it the two cases, but we find that the order of phase transition is not affected by this.