Perturbative Chern-Simons Theory on Noncommutative R^3

TL;DR

This paper constructs a noncommutative version of Chern-Simons theory on R^3, demonstrating its finiteness and independence from deformation parameters at one loop, with preserved topological symmetries.

Contribution

It introduces a q-deformed, topologically symmetric Chern-Simons model on noncommutative space, showing its finiteness and consistency at the quantum level.

Findings

The theory is finite at one loop.

It is independent of the noncommutative deformation parameter.

Topological supersymmetry is preserved in calculations.

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 $\q \to 0$.