On the relation between quantum Liouville theory and the quantized Teichm"uller spaces

Details On the relation between quantum Liouville theory and the quantized Teichm"uller spaces On the relation between quantum Liouville theory and the quantized Teichm"uller spaces

2003-03-17

arxiv.org/abs/hep-th/0303149v2

Int.J.Mod.Phys.A19S2:459-477,2004

Physics

High Energy Physics

High Energy Physics - Theory

Contribution to the proceedings of the 6th International Conference on CFTs and Integrable Models, Chernogolovka, Russia, Sept

Scientific paper

10.1142/S0217751X04020579

We review both the construction of conformal blocks in quantum Liouville theory and the quantization of Teichm\"uller spaces as developed by Kashaev, Checkov and Fock. In both cases one assigns to a Riemann surface a Hilbert space acted on by a representation of the mapping class group. According to a conjecture of H. Verlinde, the two are equivalent. We describe some key steps in the verification of this conjecture.

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