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

Text (Quantum liouville theory in the background field formalism I. Compact Riemann surfaces)
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## Abstract

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 |
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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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