RELATIVISTIC SELF-DUAL CHERN-SIMONS VORTICES WITH ADJOINT COUPLING

We derive a set of self-duality equations for the nonabelian theory of a relativistic charged scalar field coupled to a Chern-Simons gauge f ield via adjoint coupling and with a specific sixth-order potential. S olutions to the self-duality equations saturate the lower bound on the energy, given by the gauge invariant relativistic charge, and the sol utions are static in the sense that tr(phiphidagger) is time independe nt. In the abelian limit this theory reduces to the self-dual Chern-Si mons vortex model of Jackiw and Weinberg, and in the nonrelativistic l imit this theory reduces to the theory of nonrelativistic adjoint coup ling Chern-Simons vortics whose solutions are known to be intimately r elated with integrable models in two dimensions.