Quantum Liouville theory versus quantized Teichmüller spaces

Abstract

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 Teichmüller 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.

Contribution to the proceedings of the 35th Ahrenshoop Symposium

References in corpus (3)

• Liouville theory revisited
• De Sitter Gravity and Liouville Theory
• Lambda<0 Quantum Gravity in 2+1 Dimensions I: Quantum States and Stringy S-Matrix

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