Quantum Liouville theory versus quantized Teichmüller spaces

Details Quantum Liouville theory versus quantized Teichmüller spaces Quantum Liouville theory versus quantized Teichmüller spaces

2002-12-19

arxiv.org/abs/hep-th/0212243v1

Fortsch.Phys. 51 (2003) 865-872

Physics

High Energy Physics

High Energy Physics - Theory

Contribution to the proceedings of the 35th Ahrenshoop Symposium

Scientific paper

This note announces the proof of a conjecture of H. Verlinde, according to which the spaces of Liouville conformal blocks and the Hilbert spaces from the quantization of the Teichm\"uller spaces of Riemann surfaces carry equivalent representations of the mapping class group. This provides a basis for the geometrical interpretation of quantum Liouville theory in its relation to quantized spaces of Riemann surfaces.

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