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.

12 pages, 3 figures; v2: published version

References in corpus (9)

• On AGT relation in the case of U(3)
• Asymptotically free N=2 theories and irregular conformal blocks
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• Wilson loops in unitary matrix models at finite $N$
• Multiple phases and meromorphic deformations of unitary matrix models
• Multiple phases in a generalized Gross-Witten-Wadia matrix model
• Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
• Phases of unitary matrix models and lattice QCD2