Towards a proof of AGT conjecture by methods of matrix models

Abstract

A matrix model approach to proof of the AGT relation is briefly reviewed. It starts from the substitution of conformal blocks by the Dotsenko-Fateev beta-ensemble averages and Nekrasov functions by a double deformation of the exponentiated Seiberg-Witten prepotential in beta \neq 1 and g_s \neq 0 directions. Establishing the equality of these two quantities is a typical matrix model problem, and it presumably can be ascertained by investigation of integrability properties and developing an associated Harer-Zagier technique for evaluation of the exact resolvent.

25 pages

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Cited by in corpus (43)

• Proving AGT conjecture as HS duality: extension to five dimensions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• On KP-integrable Hurwitz functions
• Ding-Iohara-Miki symmetry of network matrix models
• A direct proof of AGT conjecture at beta = 1
• Explicit examples of DIM constraints for network matrix models
• M5-branes, toric diagrams and gauge theory duality
• On the complete perturbative solution of one-matrix models
• Character expansion for HOMFLY polynomials. I. Integrability and difference equations
• Spectral Duality in Integrable Systems from AGT Conjecture
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux
• Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble
• Decomposing Nekrasov Decomposition
• A slow review of the AGT correspondence
• Parafermionic Liouville field theory and instantons on ALE spaces
• Equations on knot polynomials and 3d/5d duality
• S-duality as a beta-deformed Fourier transform
• Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• On elementary proof of AGT relations from six dimensions
• S-duality as Fourier transform for arbitrary ${\epsilon }_1,{\epsilon }_2$
• W(1+infinity) algebra as a symmetry behind AGT relation
• AGT, N-Burge partitions and W_N minimal models
• Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
• Superintegrability as the hidden origin of Nekrasov calculus
• Confinement and Mayer cluster expansions
• Comment on integrability in Dijkgraaf-Vafa beta-ensembles
• On Factorization of Generalized Macdonald Polynomials
• Quantization of Harer-Zagier formulas
• Challenges of beta-deformation
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• q-Vertex Operator from 5D Nekrasov Function
• Superintegrability of matrix Student's distribution
• Trinion Conformal Blocks from Topological strings
• Faces of matrix models
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
• Geometric transitions, double scaling limits and gauge theories
• On a path integral representation of the Nekrasov instanton partition function and its Nekrasov--Shatashvili limit
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