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

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

2010-05-17

arxiv.org/abs/1005.2846v5

Physics

High Energy Physics

High Energy Physics - Theory

81 pages; V2: small corrections and improvements, references added; V3: Discussion of Yang's potential moved to 5.5 and extend

Scientific paper

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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