Solving N=2 supersymmetric Yang-Mills theory by reflection symmetry of quantum vacua

The recently rigorously proved nonperturbative relation u=pi i(F-a partial derivative(a)F/2), underlying N=2 supersymmetry Yang-Mills theory with the gauge group SU(2): implies both the reflection symmetries (tau))over bar>)=u(-<(tau)over bar>) and u(tau+1)=-u(tau) which hold exactly. The relation also implies that tau is the inverse of the uniformizing coordinate u of the moduli space of quantum vacua M-SU(2), that is, tau:M-SU(2)-->H, where H is the upper half plane. In this context, the above quantum symmetries are the key points to determine M-SU(2). It turns out that the functions a(u) and a(D)(u), which we derive from first principles, actually coincide with the solution proposed by Seiberg and Witten. We also consider some relevant generalizations.