S-duality as a beta-deformed Fourier transform

Abstract

An attempt is made to formulate Gaiotto's S-duality relations in an explicit quantitative form. Formally the problem is that of evaluation of the Racah coefficients for the Virasoro algebra, and we approach it with the help of the matrix model representation of the AGT-related conformal blocks and Nekrasov functions. In the Seiberg-Witten limit, this S-duality reduces to the Legendre transformation. In the simplest case, its lifting to the level of Nekrasov functions is just the Fourier transform, while corrections are related to the beta-deformation. We calculate them with the help of the matrix model approach and observe that they vanish for beta=1. Explicit evaluation of the same corrections from the U_q(sl(2)) infinite-dimensional representation formulas due to B.Ponsot and J.Teshner remains an open problem.

21 pages

References in corpus (17)

• 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)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Instantons and Merons in Matrix Models
• The Power of Nekrasov Functions
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation
• Symplectic invariants, Virasoro constraints and Givental decomposition
• Instanton counting via affine Lie algebras I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectors
• Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Nekrasov prepotential with fundamental matter from the quantum spin chain
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Some properties of the Alday-Maldacena minimum
• Seiberg-Witten curve via generalized matrix model