Selberg Integral and SU(N) AGT Conjecture

Abstract

An intriguing coincidence between the partition function of super Yang-Mills theory and correlation functions of 2d Toda system has been heavily studied recently. While the partition function of gauge theory was explored by Nekrasov, the correlation functions of Toda equation have not been completely understood. In this paper, we study the latter in the form of Dotsenko-Fateev integral and reduce it in the form of Selberg integral of several Jack polynomials. We conjecture a formula for such Selberg average which satisfies some consistency conditions and show that it reproduces the SU(N) version of AGT conjecture.

35 pages, 5 figures; v2: minor modifications; v3: typos corrected, references added

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Cited by in corpus (22)

• Gauge/Liouville Triality
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Generalized Jack polynomials and the AGT relations for the $SU(3)$ group
• 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
• β-deformed matrix model and Nekrasov partition function
• Virasoro constraint for Nekrasov instanton partition function
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Virasoro irregular conformal block and beta deformed random matrix model
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Polynomials associated with fixed points on the instanton moduli space
• Irregular conformal block, spectral curve and flow equations
• q-Vertex Operator from 5D Nekrasov Function
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• AFLT-type Selberg integrals
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Proof of 5D $A_n$ AGT conjecture at $\beta =1$
• Proof of $A_n$ AGT conjecture at $\beta =1$