On AGT Conjecture for Pure Super Yang-Mills and W-algebra

Abstract

Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal blocks associated with the conformal algebra. Likewise, a counterpart in pure super Yang-Mills theory exists in conformal field theory. We propose a simple relation between the Shapovalov matrix of the W_3-algebra and the Nekrasov partition function of N=2 SU(3) Yang-Mills theory.

22 pages

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• 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
• 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
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• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• The ABCDEFG of Instantons and W-algebras
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Instantons and 2d Superconformal field theory
• 3d TQFT from 6d SCFT
• Tao Probing the End of the World
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial
• Towards a proof of AGT conjecture by methods of matrix models
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• W_3 irregular states and isolated N=2 superconformal field theories
• A slow review of the AGT correspondence
• Whittaker pairs for the Virasoro algebra and the Gaiotto - BMT states
• A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• N=2 Generalized Superconformal Quiver Gauge Theory
• Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• Matrix model from N = 2 orbifold partition function
• Generalized matrix models and AGT correspondence at all genera
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• Exact solution for mean energy of 2d Dyson gas at beta = 1
• Compactification on the Ω-background and the AGT correspondence
• Generalized Whittaker states for instanton counting with fundamental hypermultiplets
• Modular and duality properties of surface operators in N=2* gauge theories
• On the six-dimensional origin of the AGT correspondence
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• Beta-ensembles for toric orbifold partition function
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Surface operators in 5d gauge theories and duality relations
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• A strange relationship between 2d CFT and 4d gauge theory
• Deformed planar topological open string amplitudes on Seiberg-Witten curve
• A note on W symmetry of N=2 gauge theory
• Chiral rings for surface operators in 4d and 5d SQCD
• The $SU(r{)}_2$ string functions as $q$-diagrams