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

A renormalizable rigid supersymmetry for the four dimensional antisymmetric tensor field model in a curved space–time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the vector parameter of the supersymmetry is a covariantly constant vector field. 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 is performed in a pure algebraic manner by using the rigid supersymmetry. 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.