Self-dual gauged CPN models

We consider a CPN model with the subgroup SU(r) completely gauged, where 1 < r < N + 1. The gauge field dynamics is solely governed by a nonabelian Chern-Simons term and the global SU(N + 1) symmetry is broken explicitly by introducing a SU(r) invariant scalar potential. We obtain self-dual equations of this gauged CPN model and find that the energy is bounded from below by a linear combination of the topological charge and a global U(1) charge present in the theory. We also discuss on the self-dual soliton solutions of this model.