Abelian Higgs Model Effective Potential in the Presence of Vortices

TL;DR

This paper analyzes the impact of vortex-string topological excitations on the effective potential in the Abelian Higgs model, providing insights into phase transitions at finite temperatures.

Contribution

It introduces a dual transformation approach to explicitly include vortex-string contributions in the effective potential calculation.

Findings

Vortex-string contributions significantly affect the effective potential.

Finite temperature modifies the vortex-induced potential landscape.

The approach clarifies the role of topological excitations in phase transitions.

Abstract

We determine the contribution of nontrivial vacuum (topological) excitations, more specifically vortex--strings of the Abelian Higgs model in 3+1 dimensions, to the functional partition function. By expressing the original action in terms of dual transformed fields we make explicit in the equivalent action the contribution of the vortex--strings excitations of the model. The effective potential of an appropriately defined local vacuum expectation value of the vortex--string field in the dual transformed action is then evaluated both at zero and finite temperatures and its properties discussed in the context of the finite temperature phase transition.