Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces

Takhtajan, Leon A. and Teo, Lee-Peng (2006) Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces. Communications in Mathematical Physics, 268 (1). pp. 135-197. ISSN 0010-3616

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Official URL: http://dx.doi.org/10.1007/s00220-006-0091-4


Using Polyakov's functional integral approach and the Liouville action functional defined in [ZT87c] and [TT03a], we formulate quantum Liouville theory on a compact Riemann surface X of genus g > 1. For the partition function (X) and correlation functions with the stress-energy tensor components (Pi(=1n)(i) T(zi) Pi(l)(k=1) (T) over bar((w) over bar (k)), we describe Feynman rules in the background field formalism by expanding corresponding functional integrals around a classical solution, the hyperbolic metric on X. Extending analysis in [Tak93, Tak94, Tak96a, Tak96b], we define the regularization scheme for any choice of the global coordinate on X. For the Schottky and quasi-Fuchsian global coordinates, we rigorously prove that one- and two-point correlation functions satisfy conformal Ward identities in all orders of the perturbation theory. Obtained results are interpreted in terms of complex geometry of the projective line bundle E-C = lambda H-c/2 over the moduli space M-g where c is the central charge and lambda (H) is the Hodge line bundle, and provide the Friedan-Shenker [FS87] complex geometry approach to CFT with the first non-trivial example besides rational models.

Item Type: Article
Subjects: T Technology > T Technology (General)
Q Science > QC Physics
Divisions: Faculty of Engineering and Technology (FET)
Depositing User: Ms Suzilawati Abu Samah
Date Deposited: 13 Oct 2011 06:42
Last Modified: 03 Mar 2014 04:55
URI: http://shdl.mmu.edu.my/id/eprint/3255

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