Explicit examples of DIM constraints for network matrix models

Abstract

Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple for what we call balanced networks. Then, the Ward identities (known under the names of Virasoro/W-constraints or loop equations or regularity condition for qq-characters) are also promoted to the DIM level, where they all become corollaries of a single identity.

46 pages

References in corpus (27)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Refined Topological Vertex
• Notes on SUSY Gauge Theories on Three-Sphere
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Correlation functions in conformal Toda field theory II
• Ding-Iohara-Miki symmetry of network matrix models
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Fiber-Base Duality and Global Symmetry Enhancement
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Notes on Ding-Iohara algebra and AGT conjecture
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Kernel function and quantum algebras
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• ADE Little String Theory on a Riemann Surface (and Triality)
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state
• Quantum toroidal gl(1) and Bethe ansatz
• W(1+infinity) algebra as a symmetry behind AGT relation
• Virasoro constraint for Nekrasov instanton partition function
• On spectrum of ILW hierarchy in conformal field theory II: coset CFT's
• Seiberg-Witten curves and double-elliptic integrable systems
• Representations of quantum toroidal $g{l}_n$
• Logarithmic potential beta-ensembles and Feynman graphs
• Polynomials associated with fixed points on the instanton moduli space

Cited by in corpus (81)

• Webs of W-algebras
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• Quiver Yangian and Supersymmetric Quantum Mechanics
• On (q,t)-deformation of Gaussian matrix model
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Anomaly in RTT relation for DIM algebra and network matrix models
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Sum rules for characters from character-preservation property of matrix models
• Quiver elliptic W-algebras
• A slow review of the AGT correspondence
• Holomorphic blocks and the 5d AGT correspondence
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• $\mathcal{W}$-algebra Modules, Free Fields, and Gukov-Witten Defects
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• A Note on Quiver Quantum Toroidal Algebra
• Higgsed network calculus
• On determinant representation and integrability of Nekrasov functions
• $q$-Virasoro modular double and 3d partition functions
• Refined geometric transition and $qq$-characters
• Factorization of differential expansion for antiparallel double-braid knots
• The MacMahon R-matrix
• A note on the algebraic engineering of 4D $\mathcal{N}=2$ super Yang-Mills theories
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
• 3d Mirror Symmetry from S-duality
• An analogue of Schur functions for the plane partitions
• Fiber-base duality from the algebraic perspective
• Mixed network calculus
• Rectangular superpolynomials for the figure-eight knot
• Commutative families in DIM algebra, integrable many-body systems and $q,t$ matrix models
• On Factorization of Generalized Macdonald Polynomials
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• Orthogonal Polynomials in Mathematical Physics
• On complete solution of the quantum Dell system
• q-Painleve equation from Virasoro constraints
• A non-torus link from topological vertex
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• Bootstrapping the $S^5$ partition function
• Can tangle calculus be applicable to hyperpolynomials?
• Gauge origami and quiver W-algebras
• Simple Representations of BPS Algebras: the case of $Y({\widehat{\mathfrak{gl}}}_2)$
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• Correlators in the supereigenvalue model in the Ramond sector
• On Hamiltonians for Kerov functions
• Check-Operators and Quantum Spectral Curves
• Modular properties of 6d (DELL) systems
• On generalized Macdonald polynomials
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• Polynomial representations of classical Lie algebras and flag varieties
• Shifted quantum groups and matter multiplets in supersymmetric gauge theories
• On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians
• Irreducible representations of simple Lie algebras by differential operators
• Wall-Crossing Effects on Quiver BPS Algebras
• Exact correlators in the Gaussian Hermitian matrix model
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• Algorithms for representations of quiver Yangian algebras
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Engineering 3D $\mathcal{N}=2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Seiberg-Witten period relations in Omega background
• Towards the theory of Yangians
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Supersymmetric polynomials and algebro-combinatorial duality
• Hopf superpolynomial from topological vertices
• The Grassmannian VOA
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Tunnels Under Geometries (or Instantons Know Their Algebras)
• Vogel's universality and the classification problem for Jacobi identities
• Interrelations between dualities in classical integrable systems and classical-classical version of quantum-classical duality
• Diamond of triads
• Tau-functions beyond the group elements
• CMM formula as superintegrability property of unitary model
• Twisted Baker-Akhiezer function from determinants
• Free field realization of the Ding-Iohara algebra at general levels
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture
• Large N limit of spectral duality in classical integrable systems
• Intertwining operator and integrable hierarchies from topological strings