Large Nc from Seiberg–Witten curve and localization

When N=2 gauge theories are compactified on S4, the large Nc 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 2Nc−2 branch points join pairwise giving aDn=0, n=1,…,Nc−1. We consider the specific case of N=2 SU(Nc) SQCD coupled with 2Nf 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