Domain structures and quark potentials in SU($3$) gauge theory

TL;DR

This paper investigates how center vortex configurations influence static potentials in SU(3) gauge theory, demonstrating that including vortex interactions and vacuum domains can produce realistic, convex potentials across different distance regimes.

Contribution

It introduces a phenomenological approach to model vortex interactions and vacuum domains, achieving more accurate static potential predictions in SU(3) Yang-Mills theory.

Findings

Including vortex interactions improves potential modeling.

Vacuum domains are crucial for convex potential behavior.

Ad-hoc probability weights can fit phenomenological data.

Abstract

We analyze the static potentials for various representations in SU($3$) Yang-Mills theory within the framework of the domain model of center vortices. The influence of vortex interactions is investigated on the static potentials. We show that, by ad-hoc choosing the probability weights of the different vortex configurations contributing to the static potential, a phenomenologically satisfactory result for the different representations can be achieved. In particular including vacuum domains, a way to effectively parametrize vortex interactions, is crucial in obtaining an (almost) everywhere convex potential when interpolating between the short distances and the asymptotic regimes.