Cubic constraints for the resolvents of the ABJM matrix model and its cousins

TL;DR

This paper derives cubic and quadratic loop equations for resolvent functions in certain Chern-Simons matrix models, including ABJM and lens space models, revealing new algebraic constraints in the planar limit.

Contribution

It introduces a set of cubic constraints for resolvents in a class of Chern-Simons matrix models, extending understanding of their algebraic structure.

Findings

Derived cubic loop equations for ABJM and lens space matrix models.

Reduced cubic equations to quadratic form for specific cases n=±2.

Established algebraic constraints in the planar limit of these models.

Abstract

A set of Schwinger-Dyson equations forming constraints for at most three resolvent functions are considered for a class of Chern-Simons matter matrix models with two nodes labelled by a non-vanishing number $n$. The two cases $n=2$ and $n= -2$ label respectively the ABJM matrix model, which is the hyperbolic lift of the affine $A_1^{(1)}$ quiver matrix model, and the lens space matrix model. In the planar limit, we derive two cubic loop equations for the two planar resolvents. One of these reduces to the quadratic one when $n = \pm 2$.