Vortices and Impurities

TL;DR

This paper studies how impurities affect vortex dynamics in gauge theories, revealing that electric impurities introduce a magnetic connection while magnetic impurities distort the moduli space metric, with implications for vortex bound states.

Contribution

It provides a detailed analysis of vortex moduli space modifications due to electric and magnetic impurities, including a D-brane perspective and bound state computations.

Findings

Electric impurities add a magnetic connection to vortex dynamics.

Magnetic impurities distort the vortex moduli space metric.

Vortices can be modeled as associated with a second frozen gauge group.

Abstract

We describe the BPS dynamics of vortices in the presence of impurities. We argue that a moduli space of solitons survives the addition of both electric and magnetic impurities. However, dynamics on the moduli space is altered. In the case of electric impurities, the metric remains unchanged but the dynamics is accompanied by a connection term, acting as an effective magnetic field over the moduli space. We give an expression for this connection and compute the vortex-impurity bound states in simple cases. In contrast, magnetic impurities distort the metric on the moduli space. We show that magnetic impurities can be viewed as vortices associated to a second, frozen, gauge group. We provide a D-brane description of the dynamics of vortices in product gauge groups and show how one can take the limit such that a subset of the vortices freeze.