A Theory of Giant Vortices

TL;DR

This paper develops an asymptotic theory for giant vortices in the abelian Higgs model, analyzing their properties and solutions for large winding numbers, with explicit corrections and convergence analysis.

Contribution

It introduces an asymptotic expansion approach for giant vortices, providing analytic expressions for solutions and corrections in the large winding number limit.

Findings

Derived asymptotic expressions for vortex solutions.

Analyzed properties of giant vortices for different scalar fields.

Determined the convergence region of the expansion.

Abstract

We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number $n$. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific properties of the giant vortices for charged and neutral scalar fields as well as different integrable limits of the scalar self-coupling are discussed. Asymptotic results and the finite-$n$ corrections to the vortex solutions are derived in analytic form and the convergence region of the expansion is determined.