UNRAVELING SPONTANEOUSLY BROKEN ABELIAN CHERN-SIMONS THEORIES

In this talk I describe recent work (hep-th/9606029) in which I classi fied all conceivable 2+1 dimensional Chern-Simons (CS) theories with c ontinuous compact abelian gauge group or finite abelian gauge group. T he CS theories with finite abelian gauge group that can be obtained fr om the spontaneous breakdown of a CS theory with gauge group the direc t product of various compact U(1) gauge groups were also identified. T hose that can not be reached in this way are actually the most interes ting 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 g auge group.