Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model

Abstract

A sequence of massive scaling limits of the $\beta$-deformed $A_{n-1}$ quiver matrix model that keeps the size of the matrices finite and that corresponds to the $N_f=2n\to 2n-1,2n-2$ limits on the number of flavors at 4d $su(n)$ $\mathcal{N}=2$ 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.

arXiv comment12 pages, 3 figures; v2: published version

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