on consistency of non commutative Chern-Simons theory-JHEP 10:038, 2007

We consider the noncommutative extension of Chern-Simons theory. We show the the theory can be fully expanded in power series of the noncommutative parameter θ and that no non-analytical sector exists. The theory appears to be unstable under radiative corrections, but we show that the infinite set of instabilities, to all orders in and in θ, is confined to a BRS exact cocycle. We show also that the theory is anomaly free. The quantum theory cannot be written in terms of the Groenewald-Moyal star product, and hence doubts arise on the interpretation of the noncommutative nature of the underlying spacetime. Nonetheless, the deformed theory is well defined as a quantum field theory, and the beta function of the Chern-Simons coupling constant vanishes, as in the ordinary Chern-Simons theory