Construction of irregular conformal/W block and flavor mass relations of N=2 SUSY gauge theory from the An−1 quiver matrix model

Abstract

A sequence of massive scaling limits of the β-deformed An−1 quiver matrix model that keeps the size of the matrices finite and that corresponds to the Nf=2n→2n−1,2n−2 limits on the number of flavors at 4d su(n) N=2 SUSY gauge theory side is carried out to provide us with the integral representation of su(n) irregular conformal/W block. The original paths are naturally deformed into those in the complex plane, permitting us to convert into an su(n) extension of the unitary matrix model of GWW type with a set of log potentials for all species of eigenvalues. Looking at the region in the parameter space that enjoys the maximal symmetry of the model, we derive a set of relations among the mass parameters which may serve as evidence for the existence of the Argyres-Douglas critical hypersurface.