Cartan Fluxes in $SU(3)$ Lattice Gauge Theory

TL;DR

The paper introduces a new method for detecting topological objects like center vortices and monopoles in lattice Yang-Mills theory, focusing on the $SU(3)$ case using Cartan fluxes after fixing the Maximal Abelian gauge.

Contribution

It presents a novel approach based on Cartan fluxes for identifying topological objects in $SU(N)$ lattice gauge theories, with specific application to $SU(3)$.

Findings

Method effectively detects center vortices and monopoles in $SU(3)$ lattice gauge theory.

Approach generalizes to $SU(N)$ and aligns with existing methods for $SU(2)$.

Provides insights into the interaction and correlation of topological objects.

Abstract

We propose and analyze a new method of detecting center vortices and monopoles in lattice Yang-Mills theory. This procedure is sensitive to the intrinsic degeneracy of the center charges, which play a crucial role in how these topological objects interact and correlate with one another. Our approach is based on fixing the Maximal Abelian gauge (MAG) and decomposing the link configuration in a suitable way to look for so-called Cartan fluxes. Our discussion is general for $SU(N)$ gauge theory, but we focus our applications on the $SU(3)$ case. For the $SU(2)$ case, our proposed parametrization is equivalent to the usual one.