Schwinger–Dyson approach to Liouville field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 519-530 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss Liouville field theory in the framework of the Schwinger–Dyson approach and derive a functional equation for the three-point structure constant. We prove the existence of a second Schwinger–Dyson equation based on the duality between the screening charge operators and obtain a second functional equation for the structure constant. We use the system of these two equations to uniquely determine the structure constant.
Keywords: Liouville field theory, conformal field theory, three-point function, Schwinger–Dyson equation.
@article{TMF_2016_187_3_a7,
     author = {P. Dutta},
     title = {Schwinger{\textendash}Dyson approach to {Liouville} field theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {519--530},
     year = {2016},
     volume = {187},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a7/}
}
TY  - JOUR
AU  - P. Dutta
TI  - Schwinger–Dyson approach to Liouville field theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 519
EP  - 530
VL  - 187
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a7/
LA  - ru
ID  - TMF_2016_187_3_a7
ER  - 
%0 Journal Article
%A P. Dutta
%T Schwinger–Dyson approach to Liouville field theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 519-530
%V 187
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a7/
%G ru
%F TMF_2016_187_3_a7
P. Dutta. Schwinger–Dyson approach to Liouville field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 519-530. http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a7/

[1] A. Polyakov, Phys. Lett. B, 103:3 (1981), 207–210 | DOI | MR

[2] T. Curtright, C. Thorn, Phys. Rev. Lett., 48:19 (1982), 1309–1313 ; E. Braaten, T. Curtright, C. Thorn, Phys. Lett. B, 118:1–3 (1982), 115–120 ; Ann. Phys., 147:2 (1983), 365–416 | DOI | MR | DOI | MR | DOI | MR | Zbl

[3] J. L. Gervais, A. Neveu, Nucl. Phys. B, 199:1 (1982), 59–76 ; 209:1 (1982), 125–145 ; 238:1 (1984), 125–141 | DOI | MR | DOI | DOI | MR

[4] E. D'Hoker, R. Jackiw, Phys. Rev. D, 26:12 (1982), 3517–3542 | DOI | MR

[5] H. J. Otto, G. Weigt, Phys. Lett. B, 159:4–6 (1985), 341–344 ; Z. Phys. C, 31:2 (1986), 219–228 | DOI | MR | DOI | MR

[6] Y. Kazama, H. Nicolai, Internat. J. Modern Phys. A, 9:5 (1994), 667–710, arXiv: hep-th/9305023 | DOI | MR | Zbl

[7] G. Jorjadze, G. Weigt, Nucl. Phys. B, 619 (2001), 232 ; arXiv: hep-th/0105306 | DOI | MR | Zbl

[8] H. Dorn, H.-J. Otto, Phys. Lett. B, 291:1–2 (1992), 39–43, arXiv: ; Nucl. Phys. B, 429:2 (1994), 375–388, arXiv: hep-th/9206053hep-th/9403141 | DOI | MR | DOI | MR | Zbl

[9] A. B. Zamolodchikov, Al. B. Zamolodchikov, Nucl. Phys. B, 477:2 (1996), 577–605, arXiv: hep-th/9506136 | DOI | MR | Zbl

[10] M. Goulian, M. Li, Phys. Rev. Lett., 66:16 (1991), 2051–2055 | DOI

[11] Vl. S. Dotsenko, V. A. Fateev, Nucl. Phys. B, 240:3 (1984), 312–348 ; 251:5–6 (1985), 691–734 | DOI | MR | DOI | MR

[12] J. Teschner, Phys. Lett. B, 363:1–2 (1995), 65–70, arXiv: hep-th/9507109 | DOI

[13] L. O'Raifeartaigh, J. M. Pawlowski, V. V. Sreedhar, Ann. Phys., 277:1 (1999), 117–143, arXiv: ; Phys. Lett. B, 481:2–4 (2000), 436–444, arXiv: hep-th/9811090hep-th/0003247 | DOI | MR | Zbl | DOI | MR | Zbl

[14] J. Teschner, Class. Quant. Grav., 18:23 (2001), R153–R222, arXiv: hep-th/0104158 | DOI | MR | Zbl

[15] J. Teschner, Internat. J. Modern Phys. A, 19:supp02 (2004), 436–458, arXiv: hep-th/0303150 | DOI | MR | Zbl

[16] Y. Nakayama, Internat. J. Modern Phys. A, 19:17–18 (2004), 2771–2930, arXiv: hep-th/0402009 | DOI | MR | Zbl

[17] G. Jorjadze, G. Weigt, Phys. Lett. B, 581:1–2 (2004), 133–140, arXiv: hep-th/0311202 | DOI | MR | Zbl

[18] P. Dutta, K. A. Meissner, H. Nicolai, Phys. Rev. D, 87:10 (2013), 105019, 11 pp., arXiv: 1303.3497 | DOI

[19] E. D'Hoker, P. S. Kurzepa, Modern Phys. Lett. A, 5:18 (1990), 1411–1421 | DOI | MR | Zbl

[20] N. Seiberg, “Notes on quantum Liouville theory and quantum gravity”, Common Trends in Mathematics and Quantum Field Theories (Kyoto, Japan, May 10–16, 1990), Progress of Theoretical Physics Supplements, 102, eds. T. Eguchi, T. Inami, T. Miwa, Yukawa Institute for Theoretical Physics, Tokyo, 1990, 319–349 | DOI | MR | Zbl

[21] K. Fujikawa, H. Suzuki, Path Integrals and Quantum Anomalies, The International Series of Monographs on Physics, 122, Oxford Sci. Publi., Oxford, 2013 | MR | Zbl

[22] J. Schnittger, TMF, 104:1 (1995), 158–191, arXiv: hep-th/9412176 | DOI | MR | Zbl