Perturbative Chern-Simons Theory on Noncommutative R^3

Abstract

A U(N) Chern-Simons theory on noncommutative $\mathbb{R}^{3}$ is constructed as a $\q$-deformed field theory. The model is characterized by two symmetries: the BRST-symmetry and the topological linear vector supersymmetry. It is shown that the theory is finite and $\q_{\m\n}$-independent at the one loop level and that the calculations respect the restriction of the topological supersymmetry. Thus the topological $\q$-deformed Chern-Simons theory is an example of a model which is non-singular in the limit $\q \to 0$.