Abstract
We present a self-contained treatment of planar gauge theories broken down to some finite residual gauge group H via the Higgs mechanism. The main focus is on the discrete H gauge theory describing the long-distance physics of such a model. The spectrum features global H charges, magnetic vortices, and dyonic combinations. Due to the AharonovBohm effect, these particles exhibit topological interactions. Among other things, we review the Hopf algebra related to this discrete H gauge theory, which provides a unified description of the spin, braid, and fusion properties of the particles in this model. Exotic phenomena such as flux metamorphosis, Alice fluxes, Cheshire charge, (non-)Abelian braid statistics, the generalized spin-statistics connection, and non-Abelian AharonovBohm scattering are explained and illustrated by representative examples.
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