Center vortices as composites of monopole fluxes

TL;DR

This paper explores the relationship between center vortices and monopole fluxes in non-Abelian gauge theories, demonstrating how monopole fluxes can be combined to reproduce vortex fluxes and analyzing their impact on potential calculations.

Contribution

It introduces a method to construct center vortex fluxes from monopole fractional fluxes for SU(2) and SU(3), linking monopole and vortex models in gauge theories.

Findings

Monopole fractional fluxes can be combined to form vortex fluxes in SU(3).

Potential calculations show monopole fluxes attract each other.

The approach supports the monopole-vortex connection in confinement mechanisms.

Abstract

We study the relation between the flux of a center vortex obtained from the center vortex model and the flux formed between monopoles obtained from the Abelian gauge fixing method. Motivated by the Monte Carlo simulations which have shown that almost all monopoles are sitting on the top of vortices, we construct the fluxes of center vortices for $SU(2)$ and $SU(3)$ gauge groups using fractional fluxes of monopoles. Then, we compute the potentials in the fundamental representation induced by center vortices and fractional fluxes of monopoles. We show that by combining the fractional fluxes of monopoles one can produce the center vortex fluxes for $SU(3)$ gauge group in a "center vortex model". Comparing the potentials, we conclude that the fractional fluxes of monopoles attract each other.