Influence of center vortex interactions on the static potentials

TL;DR

This paper investigates how center vortex interactions influence static potentials in SU(4) Yang-Mills theory, revealing adherence to Casimir scaling at intermediate distances and N-ality at large distances, enhancing understanding of confinement mechanisms.

Contribution

It introduces a detailed analysis of vacuum domain interactions in SU(4) theory, highlighting their role in static potential behavior and confinement properties.

Findings

Attractions within vacuum domains follow Casimir scaling.

Repulsions can decompose domains into center vortices with minimal flux.

Static potentials exhibit N-ality at asymptotic distances.

Abstract

We analyze the static potentials induced by vacuum domains for various representations in SU($4$) Yang-Mills theory within the framework of the domain structure model. By studying the interactions within the vacuum domains, we can uncover fundamental properties of the static potentials. It appears that attractions within the vacuum domains strongly adhere to Casimir scaling at intermediate distances. Conversely, the repulsions within the vacuum domains may decompose them into center vortices with the lowest magnitude of center vortex fluxes, thereby exhibiting $N$-ality at asymptotic distances.