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Gaudin model, Bethe Ansatz and critical level

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Abstract

We propose a new method of diagonalization oif hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on the Wakimoto modules over affine algebras at the critical level. We construct eigenvectors of these hamiltonians by restricting certain invariant functionals on tensoproducts of Wakimoto modules. This gives explicit formulas for the eigenvectors via bosonic correlation functions. Analogues of the Bethe Ansatz equations naturally appear as equations on the existence of singular vectors in Wakimoto modules. We use this construction to explain the connection between Gaudin's model and correlation functios of WZNW models.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, Kosygina st 2, 117940, Moscow, Russia

    Boris Feigin

  2. Department of Mathematics, Harvard University, 02138, Cambridge, MA, USA

    Edward Frenkel

  3. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Nikolai Reshetikhin

Authors
  1. Boris Feigin
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  2. Edward Frenkel
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  3. Nikolai Reshetikhin
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Communicated by A. Jaffe

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Feigin, B., Frenkel, E. & Reshetikhin, N. Gaudin model, Bethe Ansatz and critical level. Commun.Math. Phys. 166, 27–62 (1994). https://doi.org/10.1007/BF02099300

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  • DOI: https://doi.org/10.1007/BF02099300

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