Discrete gauge theories

In these lectures, 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 Aharonov-Bohm
effect, these particles exhibit topological interactions. Among other things,
we review the Hopf algebra related to this discrete $H$ gauge theory, which
provides an 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 nonabelian Aharonov-Bohm scattering are
explained and illustrated by representative examples.