Abstract. We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz-and Witten-type. Our method is similar to the derivation of BRSTtransformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges.

We establish the existence of the topological vector supersymmetry in the six dimensional topological field theory for two-form fields introduced by Baulieu and West. We investigate the relation of these symmetries to the twist operation for the (2, 0) supersymmetry and comment on their resemblance to the analogous symmetries in topological Yang-Mills theory. 1

We discuss the algebraic construction of topological models ͑of both Schwarz-and Witten-type͒ within the Batalin-Vilkovisky formalism and we elaborate on a simple description of vector supersymmetry within this framework.

A topological model in three dimensions is proposed. It combines the Chern-Simons action with a BFK-model which was investigated recently by the authors of [1]. The finiteness of the model to all orders of perturbation theory is shown in the framework of algebraic renormalization procedure.

We derive the vector supersymmetry and the L-symmetry transformations for the fields of a generalized topological p-form model of Schwarz-type in d space-time dimensions.