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A 5d/3d duality from relativistic integrable system

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Abstract

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Ω deformation. In the limit proposed by Nekrasov and Shatashvili, the supersymmetric vacua become isolated and are identified with the eigenstates of a quantum integrable system. The effective twisted superpotentials are the Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show that they match on-shell by deriving the Bethe ansatz equation from the saddle point of the five-dimensional partition function. We also show that the Chern-Simons terms match and extend our proposal to the elliptic quiver generalizations.

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Authors and Affiliations

  1. Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei, 10617, Taiwan

    Heng-Yu Chen

  2. Department of Physics, University of Cincinnati, Cincinnati, OH, 45221, U.S.A.

    Heng-Yu Chen

  3. Department of Physics and Astronomy, University of Kentucky, Lexington, KY, 40506, U.S.A.

    Heng-Yu Chen

  4. Department of Physics, Swansea University, Swansea, SA2 8PP, U.K.

    Timothy J. Hollowood

  5. DAMTP, University of Cambridge, Cambridge, CB3 0WA, U.K.

    Peng Zhao

Authors
  1. Heng-Yu Chen
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  2. Timothy J. Hollowood
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  3. Peng Zhao
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Correspondence to Peng Zhao.

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ArXiv ePrint: 1205.4230

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Chen, HY., Hollowood, T.J. & Zhao, P. A 5d/3d duality from relativistic integrable system. J. High Energ. Phys. 2012, 139 (2012). https://doi.org/10.1007/JHEP07(2012)139

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