EXTENDED SUPERSPACE, HIGHER DERIVATIVES AND SL(2,Z) DUALITY

We consider the low-energy effective action for the Coulomb phase of a n N = 2 supersymmetric gauge theory with a rank one gauge group. The N = 2 superspace formalism is naturally invariant under an SL(2,Z) grou p of duality transformations, regardless of the form of the action. Th e leading and next to leading terms in the long distance expansion of the action are given by the holomorphic prepotential and a real analyt ic function respectively. The latter is shown to be modular invariant with respect to SL(2,Z).