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Spectral Duality Between Heisenberg Chain and Gaudin Model

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In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL k Heisenberg chain is dual to the special reduced k + 2-points gl N Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.

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Authors and Affiliations

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

    Andrei Mironov

  2. ITEP, Moscow, Russia

    Andrei Mironov, Alexei Morozov, Boris Runov, Yegor Zenkevich & Andrei Zotov

  3. MIPT, Dolgoprudniy, Moscow, Russia

    Boris Runov

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

    Yegor Zenkevich

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  1. Andrei Mironov
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  2. Alexei Morozov
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  4. Yegor Zenkevich
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Mironov, A., Morozov, A., Runov, B. et al. Spectral Duality Between Heisenberg Chain and Gaudin Model. Lett Math Phys 103, 299–329 (2013). https://doi.org/10.1007/s11005-012-0595-0

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