A solvable 3d quantum gravity model is defined by summing Virasoro TQFT copies over all topologies, shown to be dual to a 2d CFT ensemble and to exhibit semiclassical features such as cured negative density of states and Hawking-Page transition in the large-c limit.
Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I
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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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A solvable model of 3d quantum gravity
A solvable 3d quantum gravity model is defined by summing Virasoro TQFT copies over all topologies, shown to be dual to a 2d CFT ensemble and to exhibit semiclassical features such as cured negative density of states and Hawking-Page transition in the large-c limit.