Dynamics of vortices with magnetic impurities

TL;DR

This paper studies how magnetic impurities affect the behavior of BPS vortices, providing numerical and exact solutions on different geometries, and showing that impurities can be incorporated into existing models.

Contribution

It introduces methods to analyze vortex dynamics with magnetic impurities, including exact solutions on hyperbolic space and extending previous models to include delta-function impurities.

Findings

Delta-function impurities can be modeled within the moduli space approximation.

Exact solutions for vortices on hyperbolic space with impurities are obtained.

Previous vortex models on the 2-sphere are extended to include impurities.

Abstract

We investigate the dynamics of BPS vortices in the presence of magnetic impurities taking the form of axially-symmetric localised lumps and delta-functions. We present numerical results for vortices on flat space, as well as exact results for vortices on hyperbolic space in the presence of delta-function impurities. In fact, delta-function impurities of appropriate strength can be captured within the moduli space approximation by keeping one or more of the vortices fixed. We also show that previous work on vortices on the 2-sphere extends naturally to the inclusion of delta-function impurities.