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When N = 2 gauge theories are compactified on $S^4$, the large $N_c$ limitthen selects a unique vacuum of the theory determined by saddle-pointequations, which remains determined even in the flat-theory limit. We show thatexactly the same equations can be reproduced purely from Seiberg-Witten theory,describing a vacuum where magnetically charged particles become massless, andcorresponding to a specific degenerating limit of the Seiberg-Witten spectralcurve 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 coupledwith $2N_f$ massive fundamental flavors. We show that the theory exhibits aquantum phase transition where the critical point describes a particularArgyres-Douglas point of the Riemann surface.

Large $N_c$ from Seiberg-Witten Curve and Localization