Higher order loop equations for A_r and D_r quiver matrix models

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.

31 pages, 3 figures; v2: added introduction to section 2, version published in JHEP

References in corpus (27)

• 2D Gravity and Random Matrices
• Vertex Algebras and Algebraic Curves
• W-symmetry in Conformal Field Theory
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• On Geometry and Matrix Models
• Integrability and Matrix Models
• A Geometric Unification of Dualities
• Matrix Model Calculations beyond the Spherical Limit
• Higher genus correlators for the hermitian matrix model with multiple cuts
• Gravitational corrections in supersymmetric gauge theory and matrix models
• Breakdown of universality in multi-cut matrix models
• Perturbative Analysis of Gauged Matrix Models
• Conformal Matrix Models as an Alternative to Conventional Multi-Matrix Models
• Geometric Transitions and N=1 Quiver Theories
• Gorenstein Threefold Singularities with Small Resolutions via Invariant Theory for Weyl Groups
• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• Conformal Field Theory Techniques in Random Matrix models
• Gauge Invariant Matrix Model for the Â-D-Ê Closed Strings
• Holomorphic matrix models
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• Constructing Gauge Theory Geometries from Matrix Models
• Konishi anomaly approach to gravitational F-terms
• Geometric Dual and Matrix Theory for $SO/Sp$ Gauge Theories
• Intersection Theory, Integrable Hierarchies and Topological Field Theory
• Matrix Models and Gravitational Corrections
• Gravitational F-terms through anomaly equations and deformed chiral rings
• Quivers via anomaly chains

Cited by in corpus (12)

• Topological Strings and Integrable Hierarchies
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories
• Abstract loop equations, topological recursion, and applications
• Quiver Gauge Theory and Conformality at the TeV Scale
• D-brane instantons and matrix models
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Gravitational Corrections for Supersymmetric Gauge Theories with Flavors via Matrix Models
• From CFT to Ramond super-quantum curves
• Matrix model eigenvalue integrals and twist fields in the su(2)-WZW model
• Geometric Metastability, Quivers and Holography