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S-duality as a β-deformed Fourier transform

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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 β = 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.

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Authors and Affiliations

  1. ITEP, Bol.Cheremuchinskaya, 25, Moscow, Russia

    D. Galakhov, A. Mironov & A. Morozov

  2. Rutgers University, Piscataway, NJ, U.S.A.

    D. Galakhov

  3. Theory Department, Lebedev Physics Institute, Leninsky prospekt, 53, Moscow, Russia

    A. Mironov

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  1. D. Galakhov
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  2. A. Mironov
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  3. A. Morozov
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Correspondence to A. Mironov.

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Galakhov, D., Mironov, A. & Morozov, A. S-duality as a β-deformed Fourier transform. J. High Energ. Phys. 2012, 67 (2012). https://doi.org/10.1007/JHEP08(2012)067

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  • DOI: https://doi.org/10.1007/JHEP08(2012)067

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