BRST and anti-BRST symmetry in topological BF theories

We realize the quantization of arbitrary-dimensional non-Abelian EF theories from the point of view of both the BRST symmetry and anti-BRST symmetry. The method relies on the possibility of enlarging the system of fields occurring in such theories by auxiliary fields introduced geometrically in terms of a superspace formalism. The off-shell nilpotency of the BRST and anti-BRST transformations of these fields is automatically guaranteed, thanks to the structure equations and the Bianchi identities. From this follows a direct construction of the BRST invariant full quantum action which leads, after the elimination of the auxiliary fields, to the same quantum action obtained in the context of the Batalin-Vilkovisky formalism. We also discuss how the constructed BRST invariant quantum action is anti-BRST invariant. In addition, we show that the non-Abelian BF theory in any space-time dimension possesses a vector supersymmetry of ghost number +1.