Phases of Giant Magnetic Vortex Strings

TL;DR

This paper analyzes giant magnetic vortex strings in Abelian Higgs models, revealing exact solutions, universality classes, and phase distinctions in the large flux limit through combined analytic and numerical methods.

Contribution

It provides a systematic analysis of giant vortex regimes, classifies solutions into universality classes, and clarifies stability and binding energies in these regimes.

Findings

Exact solutions for giant vortices are obtained.

Different universality classes emerge based on Higgs potential properties.

Large-n limit reveals sharply distinct phases and stability characteristics.

Abstract

We consider Abrikosov-Nielsen-Olesen magnetic vortex strings in 3+1 dimensional Abelian Higgs models. We systematically analyze the giant vortex regime using a combination of analytic and numerical methods. In this regime the strings are infinitely long, axially symmetric, and support a large magnetic flux n along the symmetry axis in their core that causes them to spread out in the transverse directions. Extending previous observations, we show that the non-linear equations governing giant vortices can essentially be solved exactly. The solutions fall into different universality classes, reflecting the properties of the Higgs potential, that become sharply distinct phases in the large-n limit. We use this understanding to shed light on the binding energies and stability of vortex strings in each universality class.