New topological observables in a model of Causal Dynamical Triangulations on a torus

TL;DR

This paper introduces new topological observables in 3+1 dimensional Causal Dynamical Triangulations with torus topology, analyzing their implications for quantum geometry and matter influence.

Contribution

It presents novel topological measures and applies them to study the effects of scalar matter fields on CDT spacetime geometry.

Findings

Topological observables reveal detailed structure of CDT manifolds.

Scalar matter fields influence the quantum Ricci curvature.

New methods improve understanding of CDT topology and matter effects.

Abstract

The structure of simplicial manifolds in a model of Causal Dynamical Triangulations in 3+1 dimensions with the spatial topology of a 3-torus is analyzed with the help of topological observables, such as loops with nonzero winding numbers and coordinates based on scalar fields with jumps at the boundaries of the elementary cell of the torus. The results are given an interpretation and used in the measurements of a more local observable that is the quantum Ricci curvature. We moreover analyze the influence of scalar matter fields on the geometry of CDT spacetimes.