We study the non-perturbative, instanton-corrected effective action of the N = 2 SU(2) × SU(2) supersymmetric Yang-Mills theory with a massless hypermultiplet in the bifundamental representation. Starting from the appropriate hyperelliptic curve, we determine the periods and the exact holomorphic prepotential in a certain weak coupling expansion. We discuss the dependence of the solution on the parameter q = Λ 2 2 Λ 1 2 and several other interesting properties. * Ulrike.Feichtinger@cern.ch

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.