Superintegrability as the hidden origin of Nekrasov calculus

Abstract

Once famous and a little mysterious, AGT relations between Nekrasov functions and conformal blocks are now understood as the Hubbard-Stratanovich duality in the Dijkgraaf-Vafa (DV) phase of a peculiar Dotsenko-Fateev multi-logarithmic matrix model. However, it largely remains a collection of somewhat technical tricks, lacking a clear and generalizable conceptual interpretation. Our new claim is that the Nekrasov functions emerge in matrix models as a straightforward implication of superintegrability, factorization of peculiar matrix model averages. Recently, we demonstrated that, in the Gaussian Hermitian model, the factorization property can be extended from averages of single characters to their bilinear combinations. In this paper, we claim that this is true also for multi-logarithmic matrix models, where factorized are just the point-split products of two characters. It is this enhanced superintegrability that is responsible for existence of the Nekrasov functions and the AGT relations. This property can be generalized both to multi-matrix models, thus leading to AGT relations for multi-point conformal blocks, and to DV phases of other non-Gaussian models.

17 pages

References in corpus (8)

• 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)
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Superintegrability for ($\beta$-deformed) partition function hierarchies with $W$-representations
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• New Insights into Superintegrability from Unitary Matrix Models

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