# Condensation of Vortex-Strings: Effective Potential Contribution Through Dual Actions

## TL;DR

This paper derives a dual model of the Abelian Higgs model highlighting vortex-strings, enabling quantum field theoretical treatment of topological excitations and their role in phase transitions, with implications for understanding confinement and early universe phenomena.

## Contribution

It introduces a dual formulation of the Abelian Higgs model that explicitly includes vortex-strings, facilitating the study of their quantum effects on phase transitions.

## Key findings

- Vortex-strings contribute nontrivially to phase transitions.
- The dual model provides a framework for quantum analysis of topological excitations.
- Analogies with superconductivity are established.

## Abstract

Topological excitations are believed to play an important role in different areas of physics. For example, one case of topical interest is the use of dual models of quantum cromodynamics to understand properties of its vacuum and confinement through the condensation of magnetic monopoles and vortices. Other applications are related to the role of these topological excitations, nonhomogeneous solutions of the field equations, in phase transitions associated to spontaneous symmetry breaking in gauge theories, whose study is of importance in phase transitions in the early universe, for instance. Here we show a derivation of a model dual to the scalar Abelian Higgs model where its topological excitations, namely vortex-strings, become manifest and can be treated in a quantum field theory way. The derivation of the nontrivial contribution of these vacuum excitations to phase transitions and its analogy with superconductivity is then made possible and they are studied here.