RENORMALIZATION AND FINITENESS OF TOPOLOGICAL BF THEORIES

We show that the BF theory in any space-time dimension, when quantized in a certain linear covariant gauge, possesses a vector supersymmetry . The generator of the latter together with those of the BRS transform ations and of the translations form the basis of a superalgebra of the Wess-Zumino type. We give a general classification of all possible an omalies and invariant counterterms. Their absence, which amounts to ul traviolet finiteness, follows from purely algebraic arguments in the l ower-dimensional cases.