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Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability

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Abstract

We review recent applications of the integrable discrete Hirota dynamics (Y-system) in the context of calculation of the planar AdS/CFT spectrum. We start from the description of solution of Hirota equations by the Bäcklund method where the requirement of analyticity results in the nested Bethe ansatz equations. Then, we discuss applications of the Hirota dynamics for the analysis of the asymptotic limit of long operators in the AdS/CFT Y-system.

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Authors and Affiliations

  1. Department of Mathematics, King’s College London, London, WC2R 2LS, UK

    Nikolay Gromov

  2. St. Petersburg INP, St. Petersburg, Russia

    Nikolay Gromov

  3. Ecole Normale Superieure, Laboratoire de Physique Théorique, 75231, Paris Cedex 5, France

    Vladimir Kazakov

  4. l’Université Paris-VI, Paris, France

    Vladimir Kazakov

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  1. Nikolay Gromov
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  2. Vladimir Kazakov
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Correspondence to Nikolay Gromov.

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Gromov, N., Kazakov, V. Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability. Lett Math Phys 99, 321–347 (2012). https://doi.org/10.1007/s11005-011-0513-x

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  • DOI: https://doi.org/10.1007/s11005-011-0513-x

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