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

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 labeled by a nonvanishing number [Formula: see text]. The two cases [Formula: see text] and [Formula: see text] label, respectively, the ABJM matrix model, which is the hyperbolic lift of the affine [Formula: see text] 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 [Formula: see text].