Generalized 2-D BF model quantized in the axial gauge

We discuss the uv finiteness of the two-dimensional BF model coupled to top ological matter quantized in the axial gauge. This noncovariant gauge fixin g avoids the ir problem in the two-dimensional space-time. The BF model tog ether with the matter coupling is obtained by dimensional reduction of the ordinary three-dimensional BF model. This procedure furnishes the usual lin ear vector supersymmetry and an additional scalar supersymmetry. The whole symmetry content of the model allows one to apply the standard algebraic re normalization procedure which we use to prove that this model is uv finite and anomaly free to all orders of perturbation theory.