# Four-dimensional CDT with toroidal topology

## TL;DR

This paper investigates 3+1 dimensional Causal Dynamical Triangulations with toroidal spatial topology, showing that the system fluctuates around a background geometry derived from a minisuperspace action, combining classical and quantum aspects.

## Contribution

It demonstrates how to derive an effective minisuperspace action for CDT with toroidal topology using integration and transfer matrix methods, revealing background fluctuations.

## Key findings

- Background geometry can be understood from a minisuperspace action.
- The system exhibits fluctuations around a dynamically formed background.
- The effective action includes both classical and quantum components.

## Abstract

3+1 dimensional Causal Dynamical Triangulations (CDT) describe a quantum theory of fluctuating geometries without the introduction of a background geometry. If the topology of space is constrained to be that of a three-dimensional torus we show that the system will fluctuate around a dynamically formed background geometry which can be understood from a simple minisuperspace action which contains both a classical part and a quantum part. We determine this action by integrating out degrees of freedom in the full model, as well as by transfer matrix methods.