The Quiver Matrix Model and 2d-4d Conformal Connection

We review the quiver matrix model (the ITEP model) in the light of the recent progress on 2d-4d connection of conformal field theories, in particular, on the relation between Toda field theories and a class of quiver superconformal gauge theories. On the basis of the CFT representation of the β deformation of the model, a quantum spectral curve is introduced as 《det (χ - igs ∂φ(z))》 = 0 at finite N and for β ≠ 1. The planar loop equation in the large N limit follows with the aid of Wn constraints. Residue analysis is provided both for the curve of the matrix model with the "multi-log" potential and for the Seiberg-Witten curve in the case of SU(n) with 2n flavors, leading to the matching of the mass parameters. The isomorphism of the two curves is made manifest.