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

A sequence of massive scaling limits of the beta-deformed An-1 quiver matrix model that keeps the size of the matrices finite and that corresponds to the N f = 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. (c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

A sequence of massive scaling limits of the beta-deformed An-1 quiver matrix model is studied to obtain the integral representation of su(n) irregular conformal/W block. A set of relations among the mass parameters is derived in the region of maximal symmetry, which may serve as evidence for the existence of the Argyres-Douglas critical hypersurface.