Abstract. We study the ultraviolet and the infrared behavior of 2D topological BF-Theory coupled to vector and scalar fields. This model is equivalent to 2D gravity coupled to topological matter. Using techniques of the algebraic renormalization program we show that this model is anomaly free and ultraviolet as well as infrared finite at all orders of perturbation theory.

We discuss the ultraviolet finiteness of the two-dimensional BF model coupled to topological matter quantized in the axial gauge. This noncovariant gauge fixing avoids the infrared problem in the two-dimensional space-time. The BF model together with the matter coupling is obtained by dimensional reduction of the ordinary three-dimensional BF model. This procedure furnishes the usual linear vector supersymmetry and an additional scalar supersymmetry. The whole symmetry content of the model allows to apply the standard algebraic renormalization procedure which we use to prove that this model is ultraviolet finite and anomaly free to all orders of perturbation theory.