The self-dual Chern-Simons $CP(N)$ models
  We study the Chern-Simons $CP(N)$ models with a global $U(1)$ symmetry and found the self-dual models among them. The Bogomolnyi-type bound in these self-dual models is a nontrivial generalization of that in the pure $CP(N)$ models. Our models have quite a rich vacuum and soliton structure and approach the many known gauged self-dual models in some limit. 
Kyoungtae Kimm, Kimyeong Lee, and Taejin Lee