Vortices and Monopoles in a Harmonic Trap

The Ω-deformation is a harmonic trap, penning certain excitations near the origin in a manner consistent with supersymmetry. Here we explore the dynamics of BPS monopoles and vortices in such a trap. We pay particular attention to monopoles in the Higgs phase, when they are confined to a vortex string. Unusually for BPS solitons, the mass of these confined monopoles is quadratic in the topological charges. We compute an index theorem to determine the number of collective coordinates of confined monopoles. Despite being restricted to move on a line, we find that they have a rich dynamics. As the strength of the trap increases, the number of collective co-ordinates can change, sometimes with constituent monopoles disappearing, sometimes with new ones emerging.We are supported by STFC and by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013), ERC grant agreement STG 279943, “Strongly Coupled Systems”.This is the final version of the article. It was first available from Springer via http://dx.doi.org/10.1007/JHEP12(2015)09