ON THE GEOMETRY OF MODULI SPACE OF VACUA IN N=2 SUPERSYMMETRIC YANG-MILLS THEORY

We consider generic properties of the moduli space of vacua in N = 2 supersymmetric Yang-Mills theory recently studied by Seiberg and Witten. We find, on general grounds, Picard-Fuchs type of differential equations expressing the existence of a flat holomorphic connection, which for one parameter (i.e. for gauge group G = SU(2)), are second order equations. In the case of coupling to gravity (as in string theory), where also ''gravitational'' dyons are present, the electric-magnetic S duality, due to quantum corrections, does not seem any longer to be directly related to Sl(2, Z) as for N = 4 supersymmetric theory.