Yang--Mills topology on four-dimensional triangulations

TL;DR

This paper investigates the topological properties of 4D SU(N) gauge theories coupled to gravity within the Causal Dynamical Triangulations framework, revealing that topology emerges only in the semiclassical phase of spacetime.

Contribution

It introduces a discretized topological charge for CDT and demonstrates its emergence in the C-phase, linking topology to semiclassical spacetime in quantum gravity.

Findings

Topology emerges in the C-phase of CDT.

Discretized topological charge is consistent with continuum limits.

A visualization tool for topological structures is developed.

Abstract

We consider 4D $SU(N)$ gauge theories coupled to gravity in the Causal Dynamical Triangulations (CDT) approach, focusing on the topological classification of the gauge path integral over fixed triangulations. We discretize the topological charge and, after checking the emergence of topology and the continuum scaling on flat triangulations, we show that topology emerges on thermalized triangulations only in the so-called $C$-phase of CDT, thus enforcing the link between such phase and semiclassical spacetime. We also provide a tool to visualize the topological structures.