The finiteness of the four dimensional antisymmetric tensor field model in a curved background

A renormalizable local supersymmetry for the four dimensional antisymmetric tensor field model in a curved space–time background will be constructed. Contrary to other topological field theories a closed algebra between the BRS and the superdiffeomorphisms operator is realizable only if the vector parameter of the superdiffeomorphisms obeys a definite constraint. This also guarantees that the corresponding transformations lead to a genuine symmetry of the model. The proof of the ultraviolet finiteness to all orders of perturbation theory will be performed in a pure algebraic manner by using the superdiffeomorphisms. Work supported in part by the “Jubiläumsfonds der Österreichischen Nationalbank” under Contract Grant Number 5393. Work supported in part by the “Fonds zur Förderung der Wissenschaftlichen Forschung” under Contract Grant Number P11354-PHY. Work supported in part by the “Fonds zur Förderung der Wissenschaftlichen Forschung” under Contract Grant Numbers P10268-PHY and P11582-PHY.