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arxiv: 1005.2846 · v5 · submitted 2010-05-17 · ✦ hep-th · math-ph· math.MP· math.RT

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Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I

J. Teschner
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classification ✦ hep-th math-phmath.MPmath.RT
keywords theoryliouvillerelationcorrespondencegeometrichitchinlanglandsquantization
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We discuss the relation between Liouville theory and the Hitchin integrable system, which can be seen in two ways as a two step process involving quantization and hyperkaehler rotation. The modular duality of Liouville theory and the relation between Liouville theory and the SL(2)-WZNW-model give a new perspective on the geometric Langlands correspondence and on its relation to conformal field theory.

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