MODULAR INVARIANCE AND STRUCTURE OF THE EXACT WILSONIAN ACTION OF N=2SUPERSYMMETRIC YANG-MILLS THEORY

We construct modular invariants on M(SU(2)), the moduli space of quant um vacua of N = 2 supersymmetric Yang-mills theory with gauge group SU (2). We also introduce the nonchiral function K(A,(A) over bar) = 2 al pha pi e(phi SW-phi/2), when e(phi SW) is the Seiberg-Witten metric. e (phi) is the Poincare metric on M(SU(2)), and alpha is a regularizatio n scheme-dependent constant. It turns out that K(A,(A) over bar) has a ll the expected properties of the next to leading term in the Wilsonia n effective action S[A,(A) over bar] whose modular properties are cons idered in the framework of the dimensional regularization.