Monopole-antimonopole interaction in Abelian Higgs model

TL;DR

This paper investigates the interaction between monopoles and antimonopoles in the Abelian Higgs model, proposing a string representation approach to overcome gauge dependence and infrared issues, and finds the interaction cannot be simply described by massive photon exchange.

Contribution

It introduces a string representation method to analyze monopole-antimonopole interactions in the Abelian Higgs model, addressing gauge and infrared problems.

Findings

Derived a well-defined potential energy expression for static monopole sources.

Showed that monopole-antimonopole interaction cannot be modeled by simple massive photon exchange.

Provided insights into the limitations of the Zwanziger formalism in this context.

Abstract

We consider interaction of a probe monopole-antimonopole pair in the vacuum of the Abelian Higgs model. For simplicity, the mass of the Higgs particle is assumed to be much larger than the mass of the photon (London limit). In case of a massive photon the straightforward application of the Zwanziger formalism to accommodate both magnetic and electric charges is known to result in gauge dependence and infrared instabilities. We argue that the use of the string representation of the Abelian Higgs model allows to ameliorate both difficulties. In particular, we arrive at a well defined expression for the potential energy of the static monopole sources. We argue that the monopole-antimonopole interaction cannot be described by a massive photon exchange with a definite propagator having simple analytical properties.