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Abstract
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 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 was are actually the most interesting since they lead to nonabelian pheomena 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.
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