Removing the concavity of the thick center vortex potentials by fluctuating the vortex profile

TL;DR

This paper improves the thick center vortex model by introducing vortex profile fluctuations, which smooths the transition between different distance regimes and respects potential concavity constraints.

Contribution

It demonstrates that allowing vortex profile fluctuations resolves the concavity issues and better connects the intermediate and long-distance behaviors in the model.

Findings

Fluctuating vortex profiles improve the potential's physical behavior.

The model maintains Casimir scaling and N-ality features.

Concavity constraints are satisfied with profile fluctuations.

Abstract

The thick center vortex model reproduces important aspects of the potentials between static quark sources as seen in lattice Yang-Mills calculations: Both the intermediate distance behavior, governed by Casimir scaling, as well as the long distance behavior, governed by N-ality, are obtained. However, when a fixed vortex profile is used, these two distance regimes do not connect naturally to each other. The transition in general violates concavity constraints on the potential, especially for higher representations of the gauge group. We demonstrate how this issue can be alleviated when the vortex profile is allowed to fluctuate within this simple model.