Noncommutative relativistic \(U(N)\) Chern-Simons solitons. (English) Zbl 1193.35167
Summary: We investigate the BPS soliton solutions of \(U(N)\) Chern-Simons gauge theory coupled to a scalar field in a noncommutative plane. With a scalar field in the fundamental representation, we show that the BPS equation becomes that of the Abelian Chern-Simons theory in the unitary gauge. We also find a class of particular solutions for the BPS equation with a scalar field in the adjoint representation.
MSC:
| 35Q51 | Soliton equations |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T75 | Noncommutative geometry methods in quantum field theory |
| 35C08 | Soliton solutions |
| 35A08 | Fundamental solutions to PDEs |
