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

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.