Selberg integral and \(\mathrm{SU}(N)\) AGT conjecture

DOI10.1007/JHEP12(2011)106zbMath1306.81134arXiv1110.5255OpenAlexW2078435937WikidataQ123355358 ScholiaQ123355358MaRDI QIDQ2261219

Hong Zhang, Yutaka Matsuo

Publication date: 6 March 2015

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5255

zbMATH Keywords

duality in gauge field theoriesconformal and W symmetry

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Supersymmetric field theories in quantum mechanics (81T60) Yang-Mills and other gauge theories in quantum field theory (81T13) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

Towards \(\mathcal{R}\)-matrix construction of Khovanov-Rozansky polynomials I. Primary \(T\)-deformation of HOMFLY, Irregular conformal block, spectral curve and flow equations, Virasoro irregular conformal block and beta deformed random matrix model, Line operators in theories of class \( \mathcal{S} \), quantized moduli space of flat connections, and Toda field theory, Towards the proof of AGT relations with the help of the generalized Jack polynomials, 2d-4d connection between \(q\)-Virasoro/\(W\) block at root of unity limit and instanton partition function on ALE space, AFLT-type Selberg integrals, Spherical Hecke algebra in the Nekrasov-Shatashvili limit, Notes on 3-point functions of \(A_{N-1}\) Toda theory and AGT-W relation for \(\operatorname{SU}(N)\) quiver, Large \(N\) limit of \(\beta\)-ensembles and deformed Seiberg-Witten relations, Virasoro constraint for Nekrasov instanton partition function, \(\beta\)-deformed matrix model and Nekrasov partition function

Cites Work

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• A direct proof of AGT conjecture at {\(\beta\)} = 1
• Correlation functions in conformal Toda field theory. II
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Correlation functions in conformal Toda field theory. I
• Conformal blocks in Virasoro and W theories: Duality and the Calogero-Sutherland model
• Brezin-Gross-Witten model as ``pure gauge limit of Selberg integrals
• AGT conjecture and integrable structure of conformal field theory for \(c=1\)
• A Selberg integral for the Lie algebra \(A_n\)
• Method of generating q-expansion coefficients for conformal block and \({\mathcal N}=2\) Nekrasov function by \(\beta \)-deformed matrix model
• Conformal blocks and generalized Selberg integrals
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Proving AGT conjecture as HS duality: Extension to five dimensions
• Collective field theory, Calogero-Sutherland model and generalized matrix models
• The Selberg-Jack symmetric functions
• Two- and three-point functions in Liouville theory
• Some combinatorial properties of Jack symmetric functions
• Matrix models, topological strings, and supersymmetric gauge theories
• Excited states of the Calogero-Sutherland model and singular vectors of the \(W_N\) algebra
• Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials
• Conformal bootstrap in Liouville field theory
• On AGT relation in the case of \(U(3)\)
• Integrable structure, W-symmetry and AGT relation
• Liouville correlation functions from four-dimensional gauge theories
• A LECTURE ON THE LIOUVILLE VERTEX OPERATORS (REVIEW)
• CONFORMAL BLOCKS AS DOTSENKO–FATEEV INTEGRAL DISCRIMINANTS
• Liouville theory revisited
• Boundary Liouville field theory: boundary three-point function