Nonholomorphic terms in N=2 supersymmetric Wilsonian actions and the renormalization group equation

In this paper we first investigate the ansatz of one of the present authors for K(Psi,<(Psi)over bar>), the adimensional, modular-invariant, nonholomorphic correction to the Wilsonian effective Lagrangian of an N=2 globally supersymmetric gauge theory. The renormalization group beta function of the theory crucially allows us to express K(Psi<(Psi)over bar>) in a form that easily generalizes to the case in which the theory is coupled to N-F hypermultiplets. K(Psi<(Psi)over bar>) satisfies an equation which should be viewed as a fully nonperturbative ''nonchiral superconformal Ward identity.'' We also determine its renormalization group equation. Furthermore, as a first step towards checking the validity of this ansatz, we compute the contribution to K(Psi,<(Psi)over bar>) from multi-instanton configurations of winding number k=1 and k=2. As a by-product of our analysis we check a nonrenormalization theorem for N-F=4. [S0556-2821(97)07520-6].