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

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 hyperkähler 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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Published 9 May 2012