Quantum Liouville theory versus quantized Teichmüller spaces
نویسندگان
چکیده
منابع مشابه
On the Relation between Quantum Liouville Theory and the Quantized Teichmüller Spaces
— We review both the construction of conformal blocks in quantum Liouville theory and the quantization of Teichmüller spaces as developed by Kashaev, Checkov and Fock. In both cases one assigns to a Riemann surface a Hilbert space acted on by a representation of the mapping class group. According to a conjecture of H. Verlinde, the two are equivalent. We describe some key steps in the verificat...
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We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincaré accessory parameters. This provides the semiclassical four point vertex functio...
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We describe in elementary geometrical terms Teichmüller spaces of decorated and holed surfaces. We construct explicit global coordinates on them as well as on the spaces of measured laminations with compact and closed support respectively and show explicitly that the latter spaces are asymptotically isomorphic to the former. We discuss briefly quantisation of Teichmüller spaces and some other a...
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Quantum Liouville theory is annualized in terms of the infinite dimensional representations of Uqsl(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 Uqsl(2,C). We furthe...
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We survey explicit coordinate descriptions for two (A and X) versions of Teichmüller and lamination spaces for open 2D surfaces, and extend them to the more general setup of surfaces with distinguished collections of points on the boundary. Main features, such as mapping class group action, Poisson and symplectic structures and others, are described in these terms. The lamination spaces are int...
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ژورنال
عنوان ژورنال: Fortschritte der Physik
سال: 2003
ISSN: 0015-8208,1521-3978
DOI: 10.1002/prop.200310109