Zero Modes of Rotationally Symmetric Generalized Vortices and Vortex Scattering

TL;DR

This paper investigates zero modes of rotationally symmetric vortices in generalized Abelian Higgs models, revealing that n vortices have 2n modes and exhibit a /n rotational symmetry during head-on collisions.

Contribution

It demonstrates that all such vortices possess 2n zero modes and formulates a symmetric Cauchy problem for vortex scattering, advancing understanding of vortex dynamics.

Findings

n vortices have 2n zero modes

Vortex scattering solutions exhibit /n symmetry

Formulation of a symmetric Cauchy problem for vortex collisions

Abstract

Zero modes of rotationally symmetric vortices in a hierarchy of generalized Abelian Higgs models are studied. Under the finite-energy and the smoothness condition, it is shown, that in all models, $n$ self-dual vortices superimposed at the origin have $2n$ modes. The relevance of these modes for vortex scattering is discussed, first in the context of the slow-motion approximation. Then a corresponding Cauchy problem for an all head-on collision of $n$ vortices is formulated. It is shown that the solution of this Cauchy problem has a $\frac{\pi}{n}$ symmetry.