Remarks on a compact Abelian Higgs model

Aspects of screening and confinement are re-examined for a recently proposed compact Abelian Higgs model with a $θ$-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 rôle 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.

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