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arxiv: hep-th/0303149 · v2 · submitted 2003-03-17 · ✦ hep-th · math.QA

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

J. Teschner
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classification ✦ hep-th math.QA
keywords conjectureliouvillequantumspacesteichmtheoryulleraccording
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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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