Integrable structure, W-symmetry and AGT relation

Abstract

In these notes we consider integrable structure of the conformal field theory with the algebra of symmetries $\mathcal{A}=W_n\otimes H$, where $W_n$ is $W-$algebra and $H$ is Heisenberg algebra. We found the system of commuting Integrals of Motion with relatively simple properties. In particular, this system has very simple spectrum and the matrix elements of special primary operators between its eigenstates have nice factorized form coinciding exactly with the contribution of the bifundamental multiplet to the Nekrasov partition function for U(n) gauge theories.

References in corpus (13)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Correlation functions in conformal Toda field theory I
• Correlation functions in conformal Toda field theory II
• The Power of Nekrasov Functions
• A direct proof of AGT conjecture at beta = 1
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Instantons on ALE spaces and Super Liouville Conformal Field Theories
• Instantons and 2d Superconformal field theory
• Notes on Ding-Iohara algebra and AGT conjecture
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory

Cited by in corpus (50)

• Irregular singularities in Liouville theory
• Ding-Iohara-Miki symmetry of network matrix models
• M5-branes, toric diagrams and gauge theory duality
• Instanton moduli spaces and bases in coset conformal field theory
• Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• W_3 irregular states and isolated N=2 superconformal field theories
• A slow review of the AGT correspondence
• On spectrum of ILW hierarchy in conformal field theory
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
• Selberg Integral and SU(N) AGT Conjecture
• The large central charge limit of conformal blocks
• Isomonodromic $\tau$-functions and $W_N$ conformal blocks
• Conformal blocks of W_N Minimal Models and AGT correspondence
• Liouville reflection operator, affine Yangian and Bethe ansatz
• Liouville theory, N=2 gauge theories and accessory parameters
• SH${}^c$ Realization of Minimal Model CFT: Triality, Poset and Burge Condition
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• On AGT-W Conjecture and q-Deformed W-Algebra
• AGT, N-Burge partitions and W_N minimal models
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• Virasoro constraint for Nekrasov instanton partition function
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Yangian associated with 2D $\mathcal{N}=1$ SCFT
• Free fermions, W-algebras and isomonodromic deformations
• Classical limit of irregular blocks and Mathieu functions
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Polynomials associated with fixed points on the instanton moduli space
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• q-Vertex Operator from 5D Nekrasov Function
• Trinion Conformal Blocks from Topological strings
• Higher rank isomonodromic deformations and W-algebras
• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
• Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations
• Recurrence relations for the ${\mathcal{W}}_3$ conformal blocks and $\mathcal{N}=2$ SYM partition functions
• AFLT-type Selberg integrals
• Twist-field representations of W-algebras, exact conformal blocks and character identities
• On solutions of the Fuji-Suzuki-Tsuda system
• Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• From topological strings to minimal models
• Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation
• AGT basis in SCFT for c=3/2 and Uglov Polynomials
• Deformed SW curve and the null vector decoupling equation in Toda field theory
• The light asymptotic limit of conformal blocks in Toda field theory
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture
• Direct Sum Structure of the Super Virasoro Algebra and a Fermion Algebra Arising from the Quantum Toroidal ${\mathfrak{gl}}_2$