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Spectral dualities in XXZ spin chains and five dimensional gauge theories

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Abstract

Motivated by recent progress in the study of supersymmetric gauge theories we propose a very compact formulation of spectral duality between XXZ spin chains. The action of the quantum duality is given by the Fourier transform in the spectral parameter. We investigate the duality in various limits and, in particular, prove it for q → 1, i.e. when it reduces to the XXX/Gaudin duality. We also show that the universal difference operators are given by the normal ordering of the classical spectral curves.

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Authors and Affiliations

  1. Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia

    A. Mironov, A. Morozov, B. Runov, Y. Zenkevich & A. Zotov

  2. Theory Department, Lebedev Physics Institute, Moscow, Russia

    A. Mironov

  3. Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia

    Y. Zenkevich

  4. Moscow Institute of Physics and Technology (MIPT), Dolgoprudniy, Moscow, Russia

    B. Runov & A. Zotov

  5. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

    A. Zotov

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  1. A. Mironov
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  2. A. Morozov
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  4. Y. Zenkevich
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  5. A. Zotov
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Correspondence to Y. Zenkevich.

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ArXiv ePrint: 1307.1502

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Mironov, A., Morozov, A., Runov, B. et al. Spectral dualities in XXZ spin chains and five dimensional gauge theories. J. High Energ. Phys. 2013, 34 (2013). https://doi.org/10.1007/JHEP12(2013)034

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