An(1) Affine Quiver Matrix Model

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.

20 pages

References in corpus (29)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Solutions Of Four-Dimensional Field Theories Via M Theory
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
• The Coulomb Phase of N=2 Supersymmetric QCD
• On AGT relation in the case of U(3)
• Instanton counting on blowup. I. 4-dimensional pure gauge theory
• On the Quantum Moduli Space of Vacua of $N=2$ Supersymmetric $SU(N_c)$ Gauge Theories
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On non-conformal limit of the AGT relations
• Conformal Matrix Models as an Alternative to Conventional Multi-Matrix Models
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• On AGT conjecture
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Proving AGT conjecture as HS duality: extension to five dimensions
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• A direct proof of AGT conjecture at beta = 1
• The Power of Nekrasov Functions
• Matrix model version of AGT conjecture and generalized Selberg integrals
• On Combinatorial Expansions of Conformal Blocks
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Gauge Invariant Matrix Model for the Â-D-Ê Closed Strings
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• W(1+infinity) algebra as a symmetry behind AGT relation
• Matrix Models at Finite N

Cited by in corpus (6)

• Generalized Jack polynomials and the AGT relations for the $SU(3)$ group
• A slow review of the AGT correspondence
• β-deformed matrix model and Nekrasov partition function
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins