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

TL;DR

This paper derives integral representations of irregular conformal blocks for $su(n)$ from a scaled $A_{n-1}$ quiver matrix model, revealing relations among mass parameters and potential critical phenomena in $ ext{N}=2$ SUSY gauge theories.

Contribution

It introduces a novel scaling limit of the $A_{n-1}$ quiver matrix model to obtain $su(n)$ irregular conformal blocks and explores mass relations indicating Argyres-Douglas critical points.

Findings

Integral representation of $su(n)$ irregular conformal blocks derived.

Relations among mass parameters suggest existence of Argyres-Douglas critical hypersurface.

Deformation of integration paths enables matrix model extension with log potentials.

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 $N_{f} =2n \rightarrow 2n-1, 2n-2$ limits on the number of flavors at 4d $su(n)$ ${\cal N} = 2$ 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.