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 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.
Citation
J. Teschner. "Quantization of the Hitchin moduli spaces, Liouville theory and the geometric Langlands correspondence I." Adv. Theor. Math. Phys. 15 (2) 471 - 564, April 2011.