(SPONTANEOUSLY BROKEN) ABELIAN CHERN-SIMONS THEORIES

A detailed analysis of Chern-Simons (CS) theories in which a compact A belian direct product gauge group U(1)(k) is spontaneously broken down to a direct product of cyclic groups H similar or equal to Z(N(1)) x ... x Z(N(k)) is presented, The spectrum features global H charges, vo rtices carrying magnetic flux labeled by the elements of H and dyonic combinations. Due to the Aharonov-Bohm effect these particles exhibit topological interactions. The remnant of the U(1)(k) CS term in the di screte H gauge theory describing the effective long distance physics o f such a model is shown to be a 3-cocycle for H governing the non-triv ial topological interactions for the magnetic fluxes implied by the U( 1)(k) CS term. It is noted that there are in general three types of 3- cocycles for a finite Abelian gauge group H: one type describes topolo gical interactions between vortices carrying flux with respect to the same cyclic group in the direct product H, another type gives rise to topological interactions among vortices carrying flux with respect to two different cyclic factors of H and a third type leading to topologi cal interactions between vortices carrying flux with respect to three different cyclic factors. Among other things, it is demonstrated that only the first two types can be obtained from a spontaneously broken U (1)(k) CS theory, The 3-cocycles that cannot be reached in this way tu rn out to be the most interesting. They render the theory non-Abelian and in general lead to dualities with planar theories with a non-Abeli an finite gauge group. In particular, the CS theory with finite gauge group H similar or equal to Z(2) x Z(2) x Z(2) defined by such a 3-coc ycle is shown to be dual to the planar discrete D-4 gauge theory with D-4 the dihedral group of order 8. (C) 1997 Elsevier Science B.V.