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

J. Teschner

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arXiv · 1005.2846

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

J. Teschner

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Abstract

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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J. Teschner. 2010-05-17. Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I. https://arxiv.org/abs/1005.2846

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