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 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 $n=\pm 2$.

23 pages; v2: a reference added

References in corpus (15)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Explicit examples of DIM constraints for network matrix models
• Exact ABJM Partition Function from TBA
• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• On Large N Solution of Gaiotto-Tomasiello Theory
• An(1) Affine Quiver Matrix Model
• Notes on Planar Resolvents of Chern-Simons-matter Matrix Models

Cited by in corpus (2)

• A slow review of the AGT correspondence
• Strong Coupling Limit of A Family of Chern-Simons-matter Theories