An(1) Affine Quiver Matrix Model

TL;DR

This paper introduces the affine quiver matrix model based on extended Cartan matrices, analyzing its Schwinger-Dyson equations and planar limits, and derives loop equations and constraints for specific cases.

Contribution

It extends matrix model analysis to affine quivers using Cartan matrices, deriving new loop equations and constraints for different affine types.

Findings

Derived finite N Schwinger-Dyson equations and planar limits.

Established cubic planar loop equations for n=1 models.

Formulated quadratic, cubic, and quartic constraints for n=2 models.

Abstract

We introduce An(1) (n=1,2,...) affine quiver matrix model by simply adopting the extended Cartan matrices as incidence matrices and study its finite N Schwinger-Dyson equations as well as their planar limit. In the case of n=1, we extend our analysis to derive the cubic planar loop equation for one-parameter family of models labelled by alpha: alpha=1 and alpha=2 correspond to the non-affine A2 case and the affine A1(1) case respectively. In the case of n=2, we derive three sets of constraint equations for the resolvents which are quadratic, cubic and quartic respectively.