Conformal Turaev-Viro theory is a triangulation-based dual to Virasoro TQFT whose partition function equals the modular S-transform of |Z_Vir|^2.
Quantization of moduli spaces of flat connections and Liouville theory
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We review known results on the relations between conformal field theory, the quantization of moduli spaces of flat PSL(2,R)-connections on Riemann surfaces, and the quantum Teichmueller theory.
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Conformal Turaev-Viro Theory
Conformal Turaev-Viro theory is a triangulation-based dual to Virasoro TQFT whose partition function equals the modular S-transform of |Z_Vir|^2.