Topological defects in the abelian Higgs model

TL;DR

This paper rigorously analyzes the dynamics of Nielsen-Olesen vortex lines in the abelian Higgs model, constructing solutions that closely follow the evolution of given string worldsheets.

Contribution

It provides a rigorous mathematical framework for the evolution of vortex lines in the abelian Higgs model, connecting initial data to vortex dynamics.

Findings

Constructed initial data leading to vortex solutions

Solutions remain close to Nielsen-Olesen vortices during evolution

Established a rigorous link between string worldsheet evolution and field solutions

Abstract

We give a rigorous description of the dynamics of the Nielsen-Olesen vortex line. In particular, given a worldsheet of a string, we construct initial data such that the corresponding solution of the abelian Higgs model will concentrate near the evolution of the string. Moreover, the constructed solution stays close to the Nielsen-Olesen vortex solution.