  When N = 2 gauge theories are compactified on $S^4$, the large $N_c$ limit
then selects a unique vacuum of the theory determined by saddle-point
equations, which remains determined even in the flat-theory limit. We show that
exactly the same equations can be reproduced purely from Seiberg-Witten theory,
describing a vacuum where magnetically charged particles become massless, and
corresponding to a specific degenerating limit of the Seiberg-Witten spectral
curve where $2N_c-2$ branch points join pairwise giving $a_{Dn}=0$,
$n=1,...,N_c-1$. We consider the specific case of N = 2 $SU(N_c)$ SQCD coupled
with $2N_f$ massive fundamental flavors. We show that the theory exhibits a
quantum phase transition where the critical point describes a particular
Argyres-Douglas point of the Riemann surface.
