BOGOMOLNYI EQUATIONS FOR NON-ABELIAN CHERN-SIMONS-HIGGS THEORIES

We study the non-abelian Chern-Simons theory with spontaneous symmetry breaking. We find Bogomol'nyi type or self-dual equations for a particular choice of the Higgs potential; the corresponding vortex solutions for G = SU(2) carry both quantized electric charge Q = -en/2 and angular momentum J = nm2/4 (e is the fundamental charge, n is an integer associated with the Chern-Simons coefficient, and m is another integer which labels the topological sector). We propose a straightforward generalization to the SU(N) case.