Vortices and Impurities

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.