Absence of higher order corrections to non-commutative Chern-Simons coupling

We analyze the structure of non-commutative pure Chern-Simons theory system atically in the axial gauge. We show that there is no IR/UV mixing in this theory in this gauge. In fact, we show, using the usual BRST identities as well as the identities following from vector supersymmetry, that this is a free theory. As a result, the tree level Chern-Simons coefficient is not re normalized. It also holds that the Chern-Simons coefficient is not modified at finite temperature. As a byproduct of our analysis, we prove that the g hosts completely decouple in the axial gauge in a non-commutative gauge the ory.