Remarks on gauge vortex scattering

TL;DR

This paper discusses the symmetric scattering angles of gauge vortices in the abelian Higgs model, showing that the observed scattering angle of π/n is a consequence of geometric constraints, and extends previous arguments to a more general setting.

Contribution

It generalizes an argument for vortex scattering angles, demonstrating that the π/n scattering result arises from geometric considerations in the abelian Higgs model.

Findings

The π/n scattering angle is one of only two possible outcomes.

The result follows from geometric considerations in the geodesic approximation.

The paper extends previous two-vortex analysis to more general cases.

Abstract

In the abelian Higgs model, among other situations, it has recently been realized that the head-on scattering of $n$ solitons distributed symmetrically around the point of scattering is by an angle $\pi/n$, independant of various details of the scattering. In this note, it is first observed that this result is in fact not entirely surprising: the above is one of only two possible outcomes. Then, a generalization of an argument given by Ruback for the case of two gauge theory vortices in the Bogomol'nyi limit is used to show that in the geodesic approximation the above result follows from purely geometric considerations.