What becomes of vortices when they grow giant

TL;DR

This paper develops a systematic large-$n$ expansion for vortex solutions in the abelian Higgs model, providing analytic asymptotic forms and demonstrating accuracy even for small winding numbers.

Contribution

It introduces a new effective field theory framework for giant vortices and derives analytic solutions in the large-$n$ limit, applicable to other topological solitons.

Findings

Asymptotic form of giant vortices obtained

Analytic solutions for critical coupling vortices derived

Approximation remains accurate down to $n=1$

Abstract

We discuss vortex solutions of the abelian Higgs model in the limit of large winding number $n$. We suggest a framework where a topological quantum number $n$ is associated with a ratio of dynamical scales and a systematic expansion in inverse powers of $n$ is then derived in the spirit of effective field theory. The general asymptotic form of ${\it giant}$ vortices is obtained. For critical coupling the axially symmetric vortices become ${\it integrable}$ in the large-$n$ limit and we present the corresponding analytic solution. The method provides simple asymptotic formulae for the vortex shape and parameters with accuracy that can be systematically improved, and can be applied to topological solitons of other models. After including the next-to-leading terms the approximation works remarkably well down to $n=1$.