  In this talk I describe recent work (hep-th/9606029) in which I classified
all conceivable 2+1 dimensional Chern-Simons (CS) theories with continuous
compact abelian gauge group or finite abelian gauge group. The CS theories with
finite abelian gauge group that can be obtained from the spontaneous breakdown
of a CS theory with gauge group the direct product of various compact U(1)
gauge groups were also identified. Those that can not be reached in this way
are actually the most interesting since they lead to nonabelian phenomena such
as nonabelian braid statistics, Alice fluxes and Cheshire charges and quite
generally lead to dualities with 2+1 dimensional theories with a nonabelian
finite gauge group.
