Remarks on a compact Abelian Higgs model

TL;DR

This paper re-examines screening and confinement in a compact Abelian Higgs model with a θ-term, using a gauge-invariant formalism to show the potential includes both Yukawa and linear components, indicating confinement.

Contribution

It introduces a gauge-invariant, path-dependent variables approach to analyze the model, highlighting the role of vortex line stiffness in confinement and potential profiles.

Findings

Static potential is a sum of Yukawa and linear terms.

Vortex line stiffness parameter influences both sectors.

Confinement of static charges is demonstrated.

Abstract

Aspects of screening and confinement are re-examined for a recently proposed compact Abelian Higgs model with a $\theta$-term. Our discussion is accomplished using the gauge-invariant but path-dependent variables formalism, which is an alternative to the Wilson loop approach. We explicitly show that the static potential profile is the sum of an effective-Yukawa and a linear potential, leading to the confinement of static external charges. We point out the central r\^ole of the parameter measuring the stiffness of the vortex lines present in the model in both the Yukawa-like and the confining sectors of the effective inter-particle potential we have computed.