Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-11-22
Nucl.Phys. B492 (1997) 717-742
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, Latex file, no figures
Scientific paper
10.1016/S0550-3213(97)00073-4
Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this Liouville theory are factorized into `classical' vertex operators and those which are constructed from the finite dimensional representations of $U_qsl(2,C)$. We further show explicitly that fusion rules in this model also enjoys such a factorization. Upon the conjecture that the Liouville action effectively decouples into the classical Liouville action and that of a quantum theory, correlation functions and transition amplitudes are discussed, especially an intimate relation between our model and geometric quantization of the moduli space of Riemann surfaces is suggested. The most important result is that our Liouville theory is in the strong coupling region, i.e., the central charge c_L satisfies $1
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