On consistency of noncommutative chern-simons theory

We consider then on commutative extension of Chern-Simons theory.We show the the theory can be fully expanded in power series of the non commutative parameter 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 order sin h and in theta is confined to a BR Sexactcocycle. 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.