Affine Algebras, Langlands Duality and Bethe Ansatz

Details Affine Algebras, Langlands Duality and Bethe Ansatz Affine Algebras, Langlands Duality and Bethe Ansatz

1995-06-05

arxiv.org/abs/q-alg/9506003v3

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, Latex

Scientific paper

We review various aspects of representation theory of affine algebras at the critical level, geometric Langlands correspondence, and Bethe ansatz in the Gaudin models. Geometric Langlands correspondence relates D-modules on the moduli space of G-bundles on a complex curve X and flat G^L-bundles on X. Beilinson and Drinfeld construct it by applying a localization functor to representations of affine algebras of critical level. We show that in genus zero the corresponding D-modules are closely related to the diagonalization problem in the Gaudin model associated to G. This allows us to give a new interpretation of the Bethe ansatz and Sklyanin's separation of variables in the Gaudin model in terms of Langlands correspondence.

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