NONPERTURBATIVE RELATIONS IN N=2 SUSY YANG-MILLS AND WDVV EQUATION

We find the nonperturbative relation between <trφ2>, <trφ3> the prepotential F and <φi> in N = 2 supersymmetric Yang-Mills theory (SYM) with gauge group SU(3). Nonlinear differential equations for F including the Witten-Dijkgraaf-Verlinde-Verlinde equation are obtained, indicating that N = 2 SYM theories are essentially topological field theories which should be seen as the low-energy limit of some topological string theory. Furthermore, we construct relevant modular invariant quantities, derive canonical relations between the periods, and find the β function in terms of the moduli. In doing this we discuss the uniformization problem for the quantum moduli space.