On AGT relation in the case of U(3)

Abstract

We consider the AGT relation, expressing conformal blocks for the Virasoro and W-algebras in terms of Nekrasov's special functions, in the simplest case of the 4-point functions for the first non-trivial W_3 algebra. The standard set of Nekrasov functions is sufficient only if additional null-vector restriction is imposed on a half of the external $W$-primaries and this is just the case when the conformal blocks are fully dictated by W-symmetry and do not depend on a particular model. Explicit checks confirm that the AGT relation survives in this restricted case, as expected.

30 pages

References in corpus (57)

• 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
• N=2 dualities
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Integrability and Seiberg-Witten Exact Solution
• On Geometry and Matrix Models
• Hurwitz numbers and intersections on moduli spaces of curves
• Quantum integrability and supersymmetric vacua
• An Algorithm for the Microscopic Evaluation of the Coefficients of the Seiberg-Witten Prepotential
• Integrability and Seiberg-Witten Theory: Curves and Periods
• Complete Set of Cut-and-Join Operators in Hurwitz-Kontsevich Theory
• Asymptotically free N=2 theories and irregular conformal blocks
• Correlation functions in conformal Toda field theory I
• Partition Functions of Matrix Models as the First Special Functions of String Theory I. Finite Size Hermitean 1-Matrix Model
• Perturbative Analysis of Gauged Matrix Models
• Generalized Kazakov-Migdal-Kontsevich Model: group theory aspects
• Integrable Structures in Supersymmetric Gauge and String Theory
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• RG Equations from Whitham Hierarchy
• On Correlation Functions for Non-critical Strings with c<1 but d>1
• Instantons and Merons in Matrix Models
• Prepotential and the Seiberg-Witten Theory
• N=2 Supersymmetric QCD and Integrable Spin Chains: Rational Case N_f < 2N_c
• Matrix models vs. Seiberg-Witten/Whitham theories
• The Power of Nekrasov Functions
• Multiscale N=2 SUSY field theories, integrable systems and their stringy/brane origin -- I
• On Combinatorial Expansions of Conformal Blocks
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• Complex Curve of the Two Matrix Model and its Tau-function
• Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation
• Complex Matrix Models and Statistics of Branched Coverings of 2D Surfaces
• SUSY field theories, integrable systems and their stringy/brane origin -- II
• Unitary Integrals and Related Matrix Models
• Generalized Hirota Equations and Representation Theory. I. The case of $SL(2)$ and $S{L}_q(2)$"
• Virasoro constraints for Kontsevich-Hurwitz partition function
• Calculating Gluino-Condensate Prepotential
• Null vectors, 3-point and 4-point functions in conformal field theory
• Matrix Models vs. Matrix Integrals
• Gluino-Condensate (CIV-DV) Prepotential from its Whitham-Time Derivatives
• Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case
• Complex Geometry of Matrix Models
• Insights and Puzzles from Branes: 4d SUSY Yang-Mills from 6d Models
• KP hierarchy for Hodge integrals
• On a c-number quantum $\tau$-function
• On the property of Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential
• Higher dimensional uniformisation and W-geometry
• Geometric Dual and Matrix Theory for $SO/Sp$ Gauge Theories
• $q$--Hypergeometric Functions in the Formalism of Free Fields
• Supersymmetric SO(N)/Sp(N) Gauge Theory from Matrix Model:Exact Mesonic Vacua
• Generalized Yukawa couplings and Matrix Models
• Finite W_3 Transformations in a Multi-time Approach
• $c=r_g$ Theories of $W_G$-Gravity: The Set of Observables as a Model of Simply Laced $G$

Cited by in corpus (191)

• Gauge Theories and Macdonald Polynomials
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• On non-conformal limit of the AGT relations
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Affine SL(2) conformal blocks from 4d gauge theories
• Para-Liouville/Toda central charges from M5-branes
• On AGT conjecture
• A & B model approaches to surface operators and Toda theories
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• W-symmetry, topological vertex and affine Yangian
• Hitchin systems, N=2 gauge theories and W-gravity
• Proving AGT conjecture as HS duality: extension to five dimensions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• Superpolynomials for toric knots from evolution induced by cut-and-join operators
• Instanton counting with a surface operator and the chain-saw quiver
• A direct proof of AGT conjecture at beta = 1
• Ding-Iohara-Miki symmetry of network matrix models
• Explicit examples of DIM constraints for network matrix models
• Penner Type Matrix Model and Seiberg-Witten Theory
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Instanton moduli spaces and bases in coset conformal field theory
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Vertices, Vortices & Interacting Surface Operators
• Integrable structure, W-symmetry and AGT relation
• Proving AGT relations in the large-c limit
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Matrix models for $\beta$-ensembles from Nekrasov partition functions
• Liouville/Toda central charges from M5-branes
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Instantons and 2d Superconformal field theory
• Matrix Models for Random Partitions
• 3d TQFT from 6d SCFT
• An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories
• The matrix model version of AGT conjecture and CIV-DV prepotential
• On AGT Conjecture for Pure Super Yang-Mills and W-algebra
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• N=2 gauge theories and degenerate fields of Toda theory
• Towards a proof of AGT conjecture by methods of matrix models
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Modular anomaly equation, heat kernel and S-duality in N=2 theories
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Exploring ${\mathcal{W}}_{\infty }$ in the quadratic basis
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• On colored HOMFLY polynomials for twist knots
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Anomaly in RTT relation for DIM algebra and network matrix models
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• Check of AGT Relation for Conformal Blocks on Sphere
• Gauge Theory Wilson Loops and Conformal Toda Field Theory
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble
• Spectral dualities in XXZ spin chains and five dimensional gauge theories
• W_3 irregular states and isolated N=2 superconformal field theories
• Hitchin Equation, Singularity, and N=2 Superconformal Field Theories
• Decomposing Nekrasov Decomposition
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• A slow review of the AGT correspondence
• Whittaker pairs for the Virasoro algebra and the Gaiotto - BMT states
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• Equations on knot polynomials and 3d/5d duality
• A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems
• S-duality as a beta-deformed Fourier transform
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
• AGT, Burge pairs and minimal models
• N=2 Generalized Superconformal Quiver Gauge Theory
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• On elementary proof of AGT relations from six dimensions
• Selberg Integral and SU(N) AGT Conjecture
• Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model
• On genus expansion of superpolynomials
• Isomonodromic $\tau$-functions and $W_N$ conformal blocks
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• Torus HOMFLY as the Hall-Littlewood Polynomials
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• On AGT description of N=2 SCFT with N_f=4
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Conformal blocks of W_N Minimal Models and AGT correspondence
• Liouville theory, N=2 gauge theories and accessory parameters
• Generalized matrix models and AGT correspondence at all genera
• Matrix model from N = 2 orbifold partition function
• Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• On AGT-W Conjecture and q-Deformed W-Algebra
• On determinant representation and integrability of Nekrasov functions
• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• Higgsed network calculus
• Exact solution for mean energy of 2d Dyson gas at beta = 1
• R-matrix-valued Lax pairs and long-range spin chains
• S-duality as Fourier transform for arbitrary ${\epsilon }_1,{\epsilon }_2$
• S-Duality and Modular Transformation as a non-perturbative deformation of the ordinary pq-duality
• Compactification on the Ω-background and the AGT correspondence
• W(1+infinity) algebra as a symmetry behind AGT relation
• AGT, N-Burge partitions and W_N minimal models
• Factorization of differential expansion for antiparallel double-braid knots
• Seiberg-Witten curve via generalized matrix model
• β-deformed matrix model and Nekrasov partition function
• From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality
• Complete solution to Gaussian tensor model and its integrable properties
• Virasoro constraint for Nekrasov instanton partition function
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• On modular transformations of non-degenerate toric conformal blocks
• Seiberg-Witten curves and double-elliptic integrable systems
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• Coset conformal field theory and instanton counting on C^2/Z_p
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• W-algebras and surface operators in N=2 gauge theories
• Generalized Whittaker states for instanton counting with fundamental hypermultiplets
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Superintegrability as the hidden origin of Nekrasov calculus
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• On the six-dimensional origin of the AGT correspondence
• N=1 superconformal blocks with Ramond fields from AGT correspondence
• Mixed network calculus
• (de)Tails of Toda CFT
• Perspectives of differential expansion
• Cauchy formula and the character ring
• Comment on integrability in Dijkgraaf-Vafa beta-ensembles
• Classical limit of irregular blocks and Mathieu functions
• On Factorization of Generalized Macdonald Polynomials
• Orthogonal Polynomials in Mathematical Physics
• Polynomials associated with fixed points on the instanton moduli space
• A Macdonald refined topological vertex
• Challenges of beta-deformation
• Matching branches of non-perturbative conformal block at its singularity divisor
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories
• Beta-ensembles for toric orbifold partition function
• q-Painleve equation from Virasoro constraints
• q-Vertex Operator from 5D Nekrasov Function
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• Higher AGT Correspondences, W-algebras, and Higher Quantum Geometric Langlands Duality from M-Theory
• Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation
• Higher rank isomonodromic deformations and W-algebras
• The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• On the status of DELL systems
• On Hamiltonians for Kerov functions
• Check-Operators and Quantum Spectral Curves
• Rigid Fuchsian systems in 2-dimensional conformal field theories
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• On generalized Macdonald polynomials
• On solutions of the Fuji-Suzuki-Tsuda system
• Pentad and triangular structures behind the Racah matrices
• Faces of matrix models
• Analytic properties of the Virasoro modular kernel
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• An(1) Affine Quiver Matrix Model
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Quantum spectral curve for (q,t)-matrix model
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• MacMahon KZ equation for Ding-Iohara-Miki algebra
• A strange relationship between 2d CFT and 4d gauge theory
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• Note on refined topological vertex, Jack polynomials and instanton counting
• SQCD, Superconducting Gaps and Cyclic RG Flows
• Quasi-Hopf twist and elliptic Nekrasov factor
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Discrete Painleve equation, Miwa variables, and string equation in 5d matrix models
• A-D hypersurface of $su(n)$ $\mathcal{N}=2$ supersymmetric gauge theory with $N_f=2n-2$ flavors
• On a path integral representation of the Nekrasov instanton partition function and its Nekrasov--Shatashvili limit
• Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model
• AGT basis in SCFT for c=3/2 and Uglov Polynomials
• Diamond of triads
• Coloured refined topological vertices and parafermion conformal field theories
• Symmetric deformed 2D/3D Hurwitz-Kontsevich model and affine Yangian of gl(1)
• A note on W symmetry of N=2 gauge theory
• The $SU(r{)}_2$ string functions as $q$-diagrams
• 5D AGT conjecture for circular quivers
• AGT correspondence, (q-)Painlevè equations and matrix models