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

TL;DR

This paper explores the connection between quiver matrix models and 2d-4d conformal field theories, introducing a quantum spectral curve and demonstrating the matching of matrix model and Seiberg-Witten curves.

Contribution

It establishes a detailed link between quiver matrix models and 2d-4d conformal theories, including the derivation of a quantum spectral curve and curve matching.

Findings

Quantum spectral curve at finite N and beta ≠ 1 introduced

Residue analysis confirms curve matching for SU(n) with 2n flavors

Planar loop equations derived using W_n constraints

Abstract

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 beta deformation of the model, a quantum spectral curve is introduced as << det (x- i g_s \partial \phi(z)) >>=0 at finite N and for beta \neq 1. The planar loop equation in the large N limit follows with the aid of W_n 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.