Affine Algebras, Langlands Duality and Bethe Ansatz

Edward Frenkel

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arXiv · q-alg/9506003

Affine Algebras, Langlands Duality and Bethe Ansatz

Edward Frenkel

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Abstract

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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q-alg alg-geom hep-th math.AG math.QA

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BibTeX RIS

Edward Frenkel. 1999-09-23. Affine Algebras, Langlands Duality and Bethe Ansatz. https://arxiv.org/abs/q-alg/9506003

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