On matrix models and their $q$-deformations

Abstract

Motivated by the BPS/CFT correspondence, we explore the similarities between the classical $\beta$-deformed Hermitean matrix model and the $q$-deformed matrix models associated to 3d $\mathcal{N}=2$ supersymmetric gauge theories on $D^2{\times }_q{S}^1$ and $S_b^3$ by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the $W$-algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.

arXiv comment45 pages, 2 figures; v2: typos fixed, comments added to section 4, JHEP version

References in corpus (32)

• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• SUSY Gauge Theories on Squashed Three-Spheres
• Notes on SUSY Gauge Theories on Three-Sphere
• On Geometry and Matrix Models
• Quantum Dilogarithm
• Localization techniques in quantum field theories
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Integrability and Matrix Models
• Holomorphic Blocks in Three Dimensions
• Introduction to Random Matrices - Theory and Practice
• A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
• N=2 supersymmetric theories on squashed three-sphere
• Factorisation of N = 2 theories on the squashed 3-sphere
• Partition Functions of Matrix Models as the First Special Functions of String Theory I. Finite Size Hermitean 1-Matrix Model
• Generation of Matrix Models by W-operators
• Solving Virasoro Constraints in Matrix Models
• On the complete perturbative solution of one-matrix models
• Localization on Three-Manifolds
• Ward identities and combinatorics of rainbow tensor models
• Unified description of correlators in non-Gaussian phases of Hermitean matrix model
• On (q,t)-deformation of Gaussian matrix model
• $USp(2N_c)$ SQCD${}_3$ with antisymmetric: dualities and symmetry enhancements
• Sum rules for characters from character-preservation property of matrix models
• Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
• $q$-Virasoro modular double and 3d partition functions
• Flavored surface defects in 4d N=1 SCFTs
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Surface defects in E-string compactifications and the van Diejen model
• Solving q-Virasoro constraints
• The modular properties and the integral representations of the multiple elliptic gamma functions
• Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints

Cited by in corpus (26)

• Superintegrability for ($\beta$-deformed) partition function hierarchies with $W$-representations
• Non-Abelian W-representation for GKM
• CFT approach to constraint operators for ($\beta$-deformed) hermitian one-matrix models
• Matrix model partition function by a single constraint
• Superintegrability in $\beta$-deformed Gaussian Hermitian matrix model from $W$-operators
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Hunt for 3-Schur polynomials
• Commutative families in DIM algebra, integrable many-body systems and $q,t$ matrix models
• Bilinear character correlators in superintegrable theory
• Spectral curves and $W$-representations of matrix models
• Quantization of Harer-Zagier formulas
• Two $\beta$-ensemble realization of $\beta$-deformed WLZZ models
• 3-Schurs from explicit representation of Yangian $Y({\widehat{\mathfrak{gl}}}_1)$. Levels 1-5
• W-representations of the fermionic matrix and Aristotelian tensor models
• W-representation of Rainbow tensor model
• Harer-Zagier formulas for knot matrix models
• Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
• Correlators in the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector
• Virasoro Constraint for Uglov Matrix Model
• Virasoro constraints revisited
• Higher order constraints for the ($\beta$-deformed) Hermitian matrix models
• On refined Chern-Simons and refined ABJ matrix models
• CMM formula as superintegrability property of unitary model
• Integrability and Matrix Models
• Proving superintegrability in $\beta$-deformed eigenvalue models
• $\beta$-ensembles and higher genera Catalan numbers