Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces
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 compon...
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| Format: | Article |
| Language: | English |
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SPRINGER
2006
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| Online Access: | http://shdl.mmu.edu.my/3255/ http://shdl.mmu.edu.my/3255/1/1294.pdf |
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| author | Takhtajan, Leon A. Teo, Lee-Peng |
| author_facet | Takhtajan, Leon A. Teo, Lee-Peng |
| author_sort | Takhtajan, Leon A. |
| building | MMU Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:10:03Z |
| format | Article |
| id | mmu-3255 |
| institution | Multimedia University |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:10:03Z |
| publishDate | 2006 |
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| spelling | mmu-32552014-03-03T04:55:15Z http://shdl.mmu.edu.my/3255/ Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces Takhtajan, Leon A. Teo, Lee-Peng T Technology (General) QC Physics 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. SPRINGER 2006-11 Article NonPeerReviewed text en http://shdl.mmu.edu.my/3255/1/1294.pdf 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 http://dx.doi.org/10.1007/s00220-006-0091-4 doi:10.1007/s00220-006-0091-4 doi:10.1007/s00220-006-0091-4 |
| spellingShingle | T Technology (General) QC Physics Takhtajan, Leon A. Teo, Lee-Peng Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces |
| title | Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces |
| title_full | Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces |
| title_fullStr | Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces |
| title_full_unstemmed | Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces |
| title_short | Quantum Liouville Theory in the Background Field Formalism I. Compact Riemann Surfaces |
| title_sort | quantum liouville theory in the background field formalism i. compact riemann surfaces |
| topic | T Technology (General) QC Physics |
| url | http://shdl.mmu.edu.my/3255/ http://shdl.mmu.edu.my/3255/ http://shdl.mmu.edu.my/3255/ http://shdl.mmu.edu.my/3255/1/1294.pdf |