Geodesic
The BRST-invariant effective action of shadows, conformal fields, and the AdS/CFT correspondence
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 495-514 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the completely symmetric, arbitrary-spin, massless and massive fields propagating in anti-de Sitter space. Using the de Donder-type gauge for such fields, we obtain a Lagrangian invariant under the global BRST transformations. We use this Lagrangian to calculate the vacuum partition function and the effective action. We show that the effective action calculated for the nonnormalizable solution of the field equations of motion with the Dirichlet boundary value problem coincides with the BRST-invariant effective action of a shadow. In the case of massless fields, the logarithmic divergence of the effective action results in a simple expression for the BRST-invariant Lagrangian of an arbitrary-spin conformal field. We show that the Nakanishi–Lautrup fields appearing in the BRST-invariant action of conformal fields can be interpreted geometrically as the boundary values of massless fields in anti-de Sitter space.
Keywords: BRST symmetry, conformal field, AdS/CFT-correspondence. 
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     author = {R. R. Metsaev},
     title = {The~BRST-invariant effective action of shadows, conformal fields, and {the~AdS/CFT} correspondence},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {495--514},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_181_3_a6/}
}
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R. R. Metsaev. The BRST-invariant effective action of shadows, conformal fields, and the AdS/CFT correspondence. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 495-514. http://geodesic.mathdoc.fr/item/TMF_2014_181_3_a6/

[1] A. A. Slavnov, TMF, 10:2 (1972), 153–161 ; J. C. Taylor, Nucl. Phys. B, 33:2 (1971), 436–444 | DOI | DOI | MR

[2] C. Becchi, A. Rouet, R. Stora, Ann. Phys., 98:2 (1976), 287–321 ; И. В. Тютин, Калибровочная инвариантность в теории поля и статистической физике в операторном формализме, Препринт No 35, ФИАН, М., 1975, arXiv: 0812.0580 | DOI | MR

[3] D. Z. Freedman, S. D. Mathur, A. Matusis, L. Rastelli, Nucl. Phys. B, 546:1–2 (1999), 96–118, arXiv: hep-th/9804058 | DOI | MR | Zbl

[4] H. Liu, A. A. Tseytlin, Nucl. Phys. B, 533:1–3 (1998), 88–108, arXiv: hep-th/9804083 | DOI | MR | Zbl

[5] W. Mück, K. S. Viswanathan, Phys. Rev. D, 58:10 (1998), 106006, 7 pp., arXiv: ; A. Polishchuk, JHEP, 07 (1999), 007, 13 pp., arXiv: hep-th/9805145hep-th/9905048 | DOI | MR | DOI

[6] R. R. Metsaev, Phys. Rev. D, 83:10 (2011), 106004, 28 pp., arXiv: 1011.4261 | DOI | MR

[7] R. R. Metsaev, Phys. Rev. D, 81:10 (2010), 106002, 29 pp., arXiv: 0907.4678 | DOI | MR

[8] R. R. Metsaev, Phys. Rev. D, 85:12 (2012), 126011, 20 pp., arXiv: 1110.3749 | DOI

[9] V. K. Dobrev, Nucl. Phys. B, 553:3 (1999), 559–582, arXiv: ; N. Aizawa, V. K. Dobrev, Intertwining operator realization of anti de Sitter holography, arXiv: hep-th/98121941406.2129 | DOI | MR | Zbl | MR

[10] R. R. Metsaev, Nucl. Phys. B, 563:1–2 (1999), 295–348, arXiv: hep-th/9906217 | DOI | MR | Zbl

[11] R. R. Metsaev, Phys. Lett. B, 636:3–4 (2006), 227–233, arXiv: hep-th/0512330 | DOI | MR | Zbl

[12] R. R. Metsaev, Phys. Rev. D, 78:10 (2008), 106010, 31 pp., arXiv: 0805.3472 | DOI | MR

[13] R. K. Gupta, S. Lal, JHEP, 07 (2012), 071, 16 pp., arXiv: 1205.1130 | DOI | MR

[14] A. A. Tseytlin, Nucl. Phys. B, 877:2 (2013), 598–631, arXiv: 1309.0785 | DOI | MR | Zbl

[15] R. R. Metsaev, Phys. Lett. B, 671:1 (2009), 128–134, arXiv: 0808.3945 | DOI | MR

[16] R. R. Metsaev, Phys. Lett. B, 682:4–5 (2010), 455–461, arXiv: 0907.2207 | DOI | MR

[17] C. Fronsdal, Phys. Rev. D, 20:4 (1979), 848–856 | DOI | MR

[18] I. L. Buchbinder, A. Pashnev, M. Tsulaia, Phys. Lett. B, 523:3–4 (2001), 338–346, arXiv: hep-th/0109067 | DOI | MR | Zbl

[19] Yu. M. Zinoviev, “On massive high spin particles in (A)d”, arXiv: hep-th/0108192

[20] V. E. Lopatin, M. A. Vasiliev, Modern Phys. Lett. A, 3:3 (1988), 257–270 ; Yu. M. Zinoviev, Nucl. Phys. B, 808:1 (2009), 185–204, arXiv: ; D. S. Ponomarev, M. A. Vasiliev, Nucl. Phys. B, 839:3 (2010), 466–498, arXiv: 0808.17781001.0062 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl

[21] I. L. Buchbinder, V. A. Krykhtin, P. M. Lavrov, Nucl. Phys. B, 762:3 (2007), 344–376, arXiv: hep-th/0608005 | DOI | MR | Zbl

[22] K. B. Alkalaev, M. Grigoriev, Nucl. Phys. B, 835:1–2 (2010), 197–220, arXiv: 0910.2690 | DOI | MR | Zbl

[23] K. Alkalaev, M. Grigoriev, Nucl. Phys. B, 853:3 (2011), 663–687, arXiv: 1105.6111 | DOI | MR | Zbl

[24] M. Grigoriev, A. Waldron, Nucl. Phys. B, 853:2 (2011), 291–326, arXiv: 1104.4994 | DOI | MR | Zbl

[25] N. Boulanger, S. Leclercq, P. Sundell, JHEP, 08 (2008), 056, 33 pp., arXiv: 0805.2764 | DOI | MR

[26] R. R. Metsaev, Phys. Lett. B, 720:1–3 (2013), 237–243, arXiv: 1205.3131 | DOI | MR

[27] M. Henneaux, G. L. Gomez, R. Rahman, JHEP, 08 (2012), 093, 44 pp., arXiv: ; 01 (2014), 087, 44 pp., arXiv: 1206.10481310.5152 | DOI | MR | DOI

[28] M. Taronna, JHEP, 04 (2012), 029, 75 pp., arXiv: 1107.5843 | DOI | MR

[29] P. Dempster, M. Tsulaia, Nucl. Phys. B, 865:2 (2012), 353–375, arXiv: 1203.5597 | DOI | MR | Zbl

[30] I. L. Buchbinder, P. Dempster, M. Tsulaia, Nucl. Phys. B, 877:2 (2013), 260–289, arXiv: 1308.5539 | DOI | MR | Zbl

[31] I. A. Batalin, K. Bering, P. M. Lavrov, I. V. Tyutin, A systematic study of finite field dependent BRST-BV transformations in $Sp(2)$ extended field-antifield formalism, arXiv: 1406.4695 | MR

[32] G. E. Arutyunov, S. A. Frolov, Nucl. Phys. B, 544:3 (1999), 576–589, arXiv: hep-th/9806216 | DOI | MR | Zbl

[33] V. E. Didenko, E. D. Skvortsov, JHEP, 04 (2013), 158, 27 pp., arXiv: 1210.7963 | DOI | MR

[34] I. Y. Aref'eva, I. V. Volovich, On large $N$ conformal theories, field theories in anti-De Sitter space and singletons, arXiv: hep-th/9803028

[35] X. Bekaert, M. Grigoriev, Nucl. Phys. B, 876:2 (2013), 667–714, arXiv: 1305.0162 | DOI | MR | Zbl

[36] M. A. Vasiliev, J. Phys. A, 46:21 (2013), 214013, 47 pp., arXiv: 1203.5554 | DOI | MR | Zbl

[37] E. S. Fradkin, A. A. Tseytlin, Phys. Rep., 119:4–5 (1985), 233–362 | DOI | MR

[38] R. R. Metsaev, Nucl. Phys. B, 885 (2014), 734–771, arXiv: 1404.3712 | DOI | MR | Zbl