Solving N=2 SYM by Reflection Symmetry of Quantum Vacua

The recently rigorously proved nonperturbative relation $u=\pi i({\cal F}-a\partial_a{\cal F}/2)$, underlying $N=2$ SYM with gauge group $SU(2)$, implies the reflection symmetry $\overline{u(\tau)}=u(-\bar\tau)$. This symmetry is the key point to determine the moduli space of quantum vacua. 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.