Perturbative Chern-Simons Theory on Noncommutative R^3

A U(N) Chern-Simons theory on noncommutative ${\mathbb{R}}^3$ is constructed as a $\text{q}$-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 ${\text{q}}_{\text{m}\text{n}}$-independent at the one loop level and that the calculations respect the restriction of the topological supersymmetry. Thus the topological $\text{q}$-deformed Chern-Simons theory is an example of a model which is non-singular in the limit $\text{q}\to 0$.