THE FINITENESS OF THE 4-DIMENSIONAL ANTISYMMETRIC TENSOR FIELD MODEL IN A CURVED BACKGROUND

A renormalizable rigid supersymmetry for the four-dimensional antisymm etric tensor field model in a curved space-time background is construc ted. A closed algebra between the BRS and the supersymmetry operators is only realizable if the vector parameter of the supersymmetry is a c ovariantly constant vector field. This also guarantees that the corres ponding transformations lead to a genuine symmetry of the model. The p roof of the ultraviolet finiteness to all orders of perturbation theor y is performed in a pure algebraic manner by using the rigid supersymm etry.