Higher order loop equations for A_r and D_r quiver matrix models

TL;DR

This paper derives higher order loop equations for A_r and D_r quiver matrix models using free boson techniques, revealing their connection to Casimir algebras and Calabi-Yau geometries at large N.

Contribution

It explicitly computes higher order loop equations for A_r and D_r quiver models and links them to Casimir algebras and geometric deformations.

Findings

Higher order loop equations are derived for A_r and D_r models.

Loop equations relate to Casimir algebras.

At large N, equations connect to Calabi-Yau geometry deformations.

Abstract

We use free boson techniques to investigate A-D-E-quiver matrix models. Certain higher spin fields in the free boson formulation give rise to higher order loop equations valid at finite N. These fields form a special kind of W-algebra, called Casimir algebra. We compute explicitly the loop equations for A_r and D_r quiver models and check that at large N they are related to a deformation of the corresponding singular Calabi-Yau geometry.