NONHOLOMORPHIC TERMS IN N=2 SUSY WILSONIAN ACTIONS AND RG EQUATION

In this paper we first investigate the ansatz of one of the present authors for K(Ψ,Ψ ¯), the adimensional, modular-invariant, nonholomorphic correction to the Wilsonian effective Lagrangian of an N=2 globally supersymmetric gauge theory. The renormalization group β function of the theory crucially allows us to express K(Ψ,Ψ ¯) in a form that easily generalizes to the case in which the theory is coupled to NF hypermultiplets. K(Ψ,Ψ ¯) 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(Ψ,Ψ ¯) 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 NF=4.