On AGT conjecture

Abstract

In these notes we consider relation between conformal blocks and the Nekrasov partition function of certain $\mathcal{N}=2$ SYM theories proposed recently by Alday, Gaiotto and Tachikawa. We concentrate on $\mathcal{N}=2^{\ast }$ theory, which is the simplest example of AGT relation.

References added

References in corpus (11)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• 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)
• Recursion relations in CFT and N=2 SYM theory
• Recursive representation of the torus 1-point conformal block
• The Power of Nekrasov Functions
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Proving AGT relations in the large-c limit
• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
• An explicit expansion formula for the powers of the Euler Product in terms of partition hook lengths

Cited by in corpus (102)

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• Wild Quiver Gauge Theories
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• Quantum Algebraic Approach to Refined Topological Vertex
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Proving AGT conjecture as HS duality: extension to five dimensions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Instanton counting with a surface operator and the chain-saw quiver
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• M5-branes, toric diagrams and gauge theory duality
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Seiberg-Witten theory, matrix model and AGT relation
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Integrable structure, W-symmetry and AGT relation
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Towards a proof of AGT conjecture by methods of matrix models
• Notes on Ding-Iohara algebra and AGT conjecture
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Quantum Painleve-Calogero Correspondence
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Check of AGT Relation for Conformal Blocks on Sphere
• 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
• The toroidal block and the genus expansion
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• Transformations of Spherical Blocks
• A slow review of the AGT correspondence
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• Parafermionic Liouville field theory and instantons on ALE spaces
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• S-duality as a beta-deformed Fourier transform
• Coset conformal blocks and N=2 gauge theories
• Exact WKB Analysis of N = 2 Gauge Theories
• N=2 Generalized Superconformal Quiver Gauge Theory
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• BPS States in Omega Background and Integrability
• ADE Little String Theory on a Riemann Surface (and Triality)
• On AGT description of N=2 SCFT with N_f=4
• Analyticity of Nekrasov Partition Functions
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories
• Generalized matrix models and AGT correspondence at all genera
• Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state
• Exact solution for mean energy of 2d Dyson gas at beta = 1
• Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I
• Quantum Spin Systems and Supersymmetric Gauge Theories, I
• AGT, N-Burge partitions and W_N minimal models
• Seiberg-Witten curve via generalized matrix model
• Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Bands and gaps in Nekrasov partition function
• Generalized Whittaker states for instanton counting with fundamental hypermultiplets
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• On the Jeffrey-Kirwan residue of BCD-instantons
• Quantum spectral problems and isomonodromic deformations
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• q-Vertex Operator from 5D Nekrasov Function
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Resurgence, Painleve Equations and Conformal Blocks
• Recursive Method for Nekrasov partition function for classical Lie groups
• Torus Amplitudes in Minimal Liouville Gravity and Matrix Models
• Trinion Conformal Blocks from Topological strings
• Localization principle in SUSY gauge theories
• The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion
• Combinatorial approach to Mathieu and Lamé equations
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Toward the Pole
• Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models
• AGT relation in the light asymptotic limit
• Semiclassical torus blocks in the t-channel
• Norms of logarithmic primaries of Virasoro algebra
• Recursive Representations of Arbitrary Virasoro Conformal Blocks
• Virasoro blocks and quasimodular forms
• Norm of the Whittaker vector of the deformed Virasoro algebra
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• An(1) Affine Quiver Matrix Model
• Recurrence relations for toric N=1 superconformal blocks
• Analytic properties of the Virasoro modular kernel
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus
• A strange relationship between 2d CFT and 4d gauge theory
• Virasoro blocks at large exchange dimension
• Probabilistic conformal blocks for Liouville CFT on the torus
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• Painlevé/CFT correspondence on a torus