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Quantum Liouville theory versus quantized Teichm\"uller spaces
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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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Cited by 1 Pith paper
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Anyon Condensation in Virasoro TQFT: Wormhole Factorization
Condensing a diagonal anyon in Virasoro TQFT factorizes wormhole partition functions and produces Liouville CFT on the two boundary surfaces.
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