Anomalous dimensions of Wilson operators in the $\mathcal N=4$

A. V. Kotikov; L. N. Lipatov; A. I. Onitchenko; V. N. Velizhanin

Anomalous dimensions of Wilson operators in the $\mathcal N=4$

A. V. Kotikov ; L. N. Lipatov ; A. I. Onitchenko ; V. N. Velizhanin

Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 2, pp. 249-262 Cet article a éte moissonné depuis la source Math-Net.Ru

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Résumé

We present results for the universal anomalous dimension $\gamma_{\mathrm{un}}(j)$ of Wilson twist-2 operators in the $\mathcal N=4$ supersymmetric Yang–Mills theory in the first three orders of the perturbation theory. We obtain these expressions by extracting the most complicated terms from the corresponding anomalous dimensions in QCD. The result obtained agrees with the hypothesis of the integrability of the $\mathcal N=4$ supersymmetric Yang–Mills theory in the context of the AdS/CFT correspondence.

Mots-clés : evolution equation
Keywords: $\mathcal N=4$ supersymmetric gauge theory.

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     author = {A. V. Kotikov and L. N. Lipatov and A. I. Onitchenko and V. N. Velizhanin},
     title = {Anomalous dimensions of {Wilson} operators in the~$\mathcal N=4$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {249--262},
     year = {2007},
     volume = {150},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_150_2_a5/}
}

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A. V. Kotikov; L. N. Lipatov; A. I. Onitchenko; V. N. Velizhanin. Anomalous dimensions of Wilson operators in the $\mathcal N=4$. Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 2, pp. 249-262. http://geodesic.mathdoc.fr/item/TMF_2007_150_2_a5/

Bibliographie
Cité par

[1] V. N. Gribov, L. N. Lipatov, YaF, 15 (1972), 781; 1218; Л. Н. Липатов, ЯФ, 20 (1974), 181; G. Altarelli, G. Parisi, Nucl. Phys. B, 126 (1977), 298 ; Ю. Л. Докшицер, ЖЭТФ, 73 (1977), 1216 | DOI

[2] D. J. Gross, F. Wilczek, Phys. Rev. D, 8 (1973), 3633 ; H. Georgi, H. D. Politzer, Phys. Rev. D, 9 (1974), 416 ; E. G. Floratos, D. A. Ross, C. T. Sachrajda, Nucl. Phys. B, 129 (1977), 66 ; Erratum, 139 (1978), 545 ; 152 (1979), 493 ; A. Gonzalez-Arroyo, C. Lopez, F. J. Yndurain, Nucl. Phys. B, 153 (1979), 161 ; A. Gonzalez-Arroyo, C. Lopez, Nucl. Phys. B, 166 (1980), 429 ; G. Gurci, W. Furmanski, R. Petronzio, Nucl. Phys. B, 175 (1980), 27 ; W. Furmanski, R. Petronzio, Phys. Lett. B, 97 (1980), 437 ; E. G. Floratos, C. Kounnas, R. Lacage, Nucl. Phys. B, 192 (1981), 417 ; C. Lopes, F. J. Yndurain, Nucl. Phys. B, 171 (1980), 231 ; 183 (1981), 157 ; R. Hamberg, W. L. van Neerven, Nucl. Phys. B, 379 (1992), 143 ; R. K. Ellis, W. Vogelsang, The evolution of parton distributions beyond leading order, ; R. Mertig, W. L. van Neerven, Z. Phys. C, 70 (1996), 637 ; W. Vogelsang, Nucl. Phys. B, 475 (1996), 47 hep-ph/9602356 | DOI | DOI | DOI | DOI | DOI | DOI | DOI | DOI | DOI | DOI | DOI | DOI | DOI | DOI | DOI

[3] S. Moch, J. A. M. Vermaseren, A. Vogt, Nucl. Phys. B, 688 (2004), 101 | DOI | Zbl

[4] A. V. Kotikov, L. N. Lipatov, Nucl. Phys. B, 661 (2003), 19 ; hep-ph/0112346 | DOI | Zbl

[5] A. V. Kotikov, L. N. Lipatov, V. N. Velizhanin, Phys. Lett. B, 557 (2003), 114 | DOI | MR | Zbl

[6] L. N. Lipatov, YaF, 23 (1976), 642; V. S. Fadin, E. A. Kuraev, L. N. Lipatov, Phys. Lett. B, 60 (1975), 50 ; Е. А. Кураев, Л. Н. Липатов, В. С. Фадин, ЖЭТФ, 71 (1976), 840; 72 (1977), 377 ; И. И. Балицкий, Л. Н. Липатов, ЯФ, 28 (1978), 1597; Письма в ЖЭТФ, 30 (1979), 383 | DOI | MR

[7] V. S. Fadin, L. N. Lipatov, Phys. Lett. B, 429 (1998), 127 | DOI

[8] A. V. Kotikov, L. N. Lipatov, Nucl. Phys. B, 582 (2000), 19 | DOI

[9] A. V. Kotikov, L. N. Lipatov, A. I. Onishchenko, V. N. Velizhanin, Phys. Lett. B, 595 (2004), 521 | DOI | MR | Zbl

[10] G. Arutyunov, B. Eden, A. C. Petkou, E. Sokatchev, Nucl. Phys. B, 620 (2002), 380 ; B. Eden, C. Jarczak, E. Sokatchev, Y. S. Stanev, Nucl. Phys. B, 722 (2005), 119 ; ; B. Eden, Nucl. Phys. B, 738 (2006), 409 ; hep-th/0501077 hep-th/0501234 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[11] N. Beisert, C. Kristjansen, M. Staudacher, Nucl. Phys. B, 664 (2003), 131 | DOI | MR | Zbl

[12] B. Eden, C. Jarczak, E. Sokatchev, Nucl. Phys. B, 712 (2005), 157 ; hep-th/0409009 | DOI | MR | Zbl

[13] M. Staudacher, JHEP, 05 (2005), 054 ; hep-th/0412188 | DOI | MR

[14] B. Eden, M. Staudacher, J. Stat. Mech., 11 (2006), 014 ; hep-th/0603157

[15] J. Maldacena, Adv. Theor. Math. Phys., 2 (1998), 231 | DOI | MR | Zbl

[16] A. P. Bukhvostov, E. A. Kuraev, L. N. Lipatov, G. V. Frolov, Pisma v ZhETF, 41 (1985), 77

[17] L. N. Lipatov, “Evolution equations in QCD”, Perspectives in hadronic physics, Proc. ICTP Conf. (Trieste, Italy, 1997), eds. S. Boffi, C. Cio Degli Atti, M. Giannini, World Scientific, Singapore, 1998, 413

[18] L. N. Lipatov, “Effective action for high energy processes in QCD”, Very high multiplicity physics, Proc. Int. Workshop (Dubna, 2000), eds. J. Manjavidze, A. Sissakian, JINR, Dubna, 2000, 159; Nucl. Phys. B. Proc. Suppl., 99 (2001), 175 | DOI

[19] V. M. Braun, S. E. Derkachov, A. N. Manashov, Phys. Rev. Lett., 81 (1998), 2020 ; A. V. Belitsky, Phys. Lett. B, 453 (1999), 59 | DOI | DOI

[20] G. Ferretti, R. Heise, K. Zarembo, Phys. Rev. D, 70 (2004), 074024 ; N. Beisert, G. Ferretti, R. Heise, K. Zarembo, Nucl. Phys. B, 717 (2005), 137 ; hep-th/0412029 | DOI | DOI | MR | Zbl

[21] J. A. Minahan, K. Zarembo, JHEP, 03 (2003), 013 | DOI | MR

[22] N. Beisert, M. Staudacher, Nucl. Phys. B, 670 (2003), 439 | DOI | MR | Zbl

[23] L. N. Lipatov, Pisma v ZhETF, 59 (1994), 571; L. N. Lipatov, High energy asymptotics of multi–colour QCD and exactly solvable lattice models, ; L. D. Faddeev, G. P. Korchemsky, Phys. Lett. B, 342 (1995), 311 hep-th/9311037 | DOI | MR

[24] L. Brink, J. H. Schwarz, J. Scherk, Nucl. Phys. B, 121 (1977), 77 | DOI | MR

[25] A. V. Belitsky, D. M. Muller, A. Schafer, Phys. Lett. B, 450 (1999), 126 ; A. V. Belitsky, D. Müller, Nucl. Phys. B. Proc. Suppl., 79 (1999), 576 ; ; Phys. Rev. D, 65 (2002), 054037 hep-ph/9905211 | DOI | MR | Zbl | DOI | DOI

[26] A. I. Onishchenko, V. N. Velizhanin, JHEP, 02 (2004), 036 | DOI | MR

[27] W. Siegel, Phys. Lett. B, 84 (1979), 193 | DOI | MR

[28] J. Fleischer, A. V. Kotikov, O. L. Veretin, Nucl. Phys. B, 547 (1999), 343 ; Acta Phys. Polon. B, 29 (1998), 2611 | DOI

[29] D. I. Kazakov, A. V. Kotikov, Nucl. Phys. B, 307 (1988), 721 ; Erratum, 345 (1990), 299 ; Phys. Lett. B, 291 (1992), 171 | DOI | DOI | DOI

[30] A. V. Kotikov, V. N. Velizhanin, Analytic continuation of the Mellin moments of deep inelastic structure functions, hep-ph/0501274

[31] A. V. Kotikov, YaF, 57 (1994), 142

[32] The Small x Collaboration (B. Andersson, et al.), Eur. Phys. J. C, 25 (2002), 77 ; hep-ph/0204115 | DOI

[33] H1 Collaboration (C. Adloff et al.), Eur. Phys. J. C, 21 (2001), 33 ; ; ZEUS Collaboration (S. Chekanov et al.), Eur. Phys. J. C, 21 (2001), 443 ; hep-ex/0012053 hep-ex/0105090 | DOI | DOI

[34] D. Berenstein, J. M. Maldacena, H. Nastase, JHEP, 04 (2002), 013 | DOI | MR

[35] K. Konishi, Phys. Lett. B, 135 (1984), 439 | DOI

[36] N. Beisert, Nucl. Phys. B, 682 (2004), 487 | DOI | MR | Zbl

[37] G. Arutyunov, S. Frolov, J. Russo, A. A. Tseytlin, Nucl. Phys. B, 671 (2003), 3 ; G. Arutyunov, J. Russo, A. A. Tseytlin, Phys. Rev. D, 69 (2004), 086009 ; G. Arutyunov, M. Staudacher, JHEP, 03 (2004), 004 ; V. A. Kazakov, A. Marshakov, J. A. Minahan, K. Zarembo, JHEP, 05 (2004), 024 ; G. Arutyunov, S. Frolov, M. Staudacher, JHEP, 10 (2004), 016 ; V. A. Kazakov, K. Zarembo, JHEP, 10 (2004), 060 ; S. Frolov, A. A. Tseytlin, JHEP, 07 (2003), 016 ; Nucl. Phys. B, 668 (2003), 77 ; Phys. Lett. B, 570 (2003), 96 ; S. Frolov, I. Y. Park, A. A. Tseytlin, Phys. Rev. D, 71 (2005), 026006 ; N. Beisert, J. A. Minahan, M. Staudacher, K. Zarembo, JHEP, 09 (2003), 010 ; N. Beisert, S. Frolov, M. Staudacher, A. A. Tseytlin, JHEP, 10 (2003), 037 | DOI | MR | Zbl | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl | DOI | DOI | MR | DOI | MR

[38] S. S. Gubser, I. R. Klebanov, A. M. Polyakov, Nucl. Phys. B, 636 (2002), 99 | DOI | MR | Zbl

[39] M. Kruczenski, JHEP, 12 (2002), 024 ; Yu. Makeenko, JHEP, 01 (2003), 007 ; ; M. Axenides, E. Floratos, A. Kehagias, Nucl. Phys. B, 662 (2003), 170 ; hep-th/0210256 hep-th/0210091 | DOI | MR | DOI | MR | DOI | MR | Zbl

[40] S. Frolov, A. A. Tseytlin, JHEP, 06 (2002), 007 | DOI | MR

[41] J. Polchinski, M. J. Strassler, JHEP, 05 (2003), 012 | DOI | MR

[42] A. V. Kotikov, L. N. Lipatov, A. I. Onishchenko, V. N. Velizhanin, Phys. Lett. B, 632 (2006), 754 | DOI | MR | Zbl

[43] R. C. Brower, J. Polchinski, M. J. Strassler, C.-I. Tan, The Pomeron and gauge/string duality, hep-th/0603115 | MR

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