QCD-like properties of anomalous dimensions in the $\mathcal N=4$ supersymmetric Yang–Mills theory

M. Beccaria; V. Forini

QCD-like properties of anomalous dimensions in the $\mathcal N=4$ supersymmetric Yang–Mills theory

M. Beccaria ; V. Forini

Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 353-363 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Résumé

We show how closed formulas for the anomalous dimensions of two classes of operators in the $\mathcal N=4$ supersymmetric Yang–Mills theory can be derived either based on numerical investigation or based on QCD-inspired assumptions. We consider the case of twist-$3$ "gauge" operators for which we completely prove the reciprocity.

Keywords: integrable quantum field theory, Bethe ansatz.

@article{TMF_2009_159_3_a2,
     author = {M. Beccaria and V. Forini},
     title = {QCD-like properties of anomalous dimensions in the~$\mathcal N=4$ supersymmetric {Yang{\textendash}Mills} theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {353--363},
     year = {2009},
     volume = {159},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a2/}
}

TY  - JOUR
AU  - M. Beccaria
AU  - V. Forini
TI  - QCD-like properties of anomalous dimensions in the $\mathcal N=4$ supersymmetric Yang–Mills theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 353
EP  - 363
VL  - 159
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a2/
LA  - ru
ID  - TMF_2009_159_3_a2
ER  -

%0 Journal Article
%A M. Beccaria
%A V. Forini
%T QCD-like properties of anomalous dimensions in the $\mathcal N=4$ supersymmetric Yang–Mills theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 353-363
%V 159
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a2/
%G ru
%F TMF_2009_159_3_a2

M. Beccaria; V. Forini. QCD-like properties of anomalous dimensions in the $\mathcal N=4$ supersymmetric Yang–Mills theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 353-363. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a2/

Bibliographie
Cité par

[1] J. M. Maldacena, Adv. Theor. Math. Phys., 2:2 (1998), 231–252 ; ; Internat. J. Theoret. Phys., 38:4 (1999), 1113–1133 ; S. S. Gubser, I. R. Klebanov, A. M. Polyakov, Phys. Lett. B, 428:1–2 (1998), 105–114 ; ; E. Witten, Adv. Theor. Math. Phys., 2:2 (1998), 253–291 ; ; V. A. Kazakov, A. Marshakov, J. A. Minahan, K. Zarembo, JHEP, 05 (2004), 024 ; arXiv: hep-th/9711200 arXiv: hep-th/9802109 arXiv: hep-th/9802150 arXiv: hep-th/0402207 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR

[2] I. Bena, J. Polchinski, R. Roiban, Phys. Rev. D, 69:4 (2004), 046002 ; arXiv: hep-th/0305116 | DOI | MR

[3] N. Beisert, C. Kristjansen, M. Staudacher, Nucl. Phys. B, 664:1–2 (2003), 131–184 ; ; N. Beisert, Phys. Rep., 405:1–3 (2005), 1–202 ; arXiv: hep-th/0303060 arXiv: hep-th/0407277 | DOI | MR | Zbl | DOI | MR

[4] N. Beisert, M. Staudacher, Nucl. Phys. B, 670:3 (2003), 439–463 ; arXiv: hep-th/0307042 | DOI | MR | Zbl

[5] N. Beisert, M. Staudacher, Nucl. Phys. B, 727:1–2 (2005), 1–62 ; arXiv: hep-th/0504190 | DOI | MR | Zbl

[6] M. Beccaria, V. Forini, JHEP, 11 (2007), 031 ; arXiv: 0710.0217 | DOI | MR | Zbl

[7] G. Ferretti, R. Heise, K. Zarembo, Phys. Rev. D, 70:7 (2004), 074024 ; arXiv: hep-th/0404187 | DOI

[8] N. Beisert, G. Ferretti, R. Heise, K. Zarembo, Nucl. Phys. B, 717:1–2 (2005), 137–189 ; arXiv: hep-th/0412029 | DOI | MR | Zbl

[9] A. Rej, M. Staudacher, S. Zieme, J. Stat. Mech., 08 (2007), 08006 ; arXiv: hep-th/0702151 | DOI

[10] A. V. Belitsky, S. É. Derkachov, G. P. Korchemsky, A. N. Manashov, Phys. Rev. D, 70:4 (2004), 045021 ; ; A. V. Belitsky, V. M. Braun, A. S. Gorsky, G. P. Korchemsky, Internat. J. Modern Phys. A, 19:28 (2004), 4715–4788 ; ; A. V. Belitsky, S. É. Derkachov, G. P. Korchemsky, A. N. Manashov, Nucl. Phys. B, 722:1–2 (2005), 191–221 ; arXiv: hep-th/0311104 arXiv: hep-th/0407232 arXiv: hep-th/0503137 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl

[11] L. N. Lipatov, Pisma v ZhETF, 59:9 (1994), 571–574 ; ; L. D. Faddeev, G. P. Korchemsky, Phys. Lett. B, 342:1–4 (1995), 311–322 ; ; G. P. Korchemsky, Nucl. Phys. B, 443:1–2 (1995), 255–301 ; ; V. M. Braun, S. É. Derkachov, A. N. Manashov, Phys. Rev. Lett., 81:10 (1998), 2020–2023 ; arXiv: hep-th/9311037 arXiv: hep-th/9404173 arXiv: hep-ph/9501232 arXiv: hep-ph/9805225 | DOI | MR | DOI | DOI

[12] A. V. Belitsky, S. É. Derkachov, G. P. Korchemsky, A. N. Manashov, Nucl. Phys. B, 708:1–3 (2005), 115–193 ; arXiv: hep-th/0409120 | DOI | MR | Zbl

[13] A. V. Belitsky, G. P. Korchemsky, D. Müller, Phys. Rev. Lett., 94:15 (2005), 151603 ; arXiv: hep-th/0412054 | DOI | MR

[14] A. V. Belitsky, G. P. Korchemsky, D. Müller, Nucl. Phys. B, 735:1–3 (2006), 17–83 ; arXiv: hep-th/0509121 | DOI | MR | Zbl

[15] P. Di Vecchia, A. Tanzini, J. Geom. Phys., 54:1 (2005), 116–130 ; arXiv: hep-th/0405262 | DOI | MR | Zbl

[16] Yu. L. Dokshitzer, YaF, 71:4, 660–674 | DOI | MR

[17] L. J. Dixon, Gluon scattering in $N=4$ super-Yang–Mills theory from weak to strong coupling, arXiv: hep-th/0803.2475

[18] A. V. Kotikov, L. N. Lipatov, A. I. Onishchenko, V. N. Velizhanin, Phys. Lett. B, 595:1–4 (2004), 521–529 ; 632:5–6 (2006), 754–756 ; ; A. V. Kotikov, L. N. Lipatov, DGLAP and BFKL evolution equations in the $N=4$ supersymmetric gauge theory, ; Nucl. Phys. B, 661:1–2 (2003), 19–61 ; 685:1–3 (2004), 405–407 ; arXiv: hep-th/0404092 arXiv: hep-ph/0112346 arXiv: hep-ph/0208220 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | Zbl | DOI

[19] S. Moch, J. A. M. Vermaseren, A. Vogt, Nucl. Phys. B, 688:1–2 (2004), 101–134 ; ; A. Vogt, S. Moch, J. A. M. Vermaseren, Nucl. Phys. B, 691:1–2 (2004), 129–181 ; arXiv:hep-ph/0403192 arXiv: hep-ph/0404111 | DOI | MR | Zbl | DOI | Zbl

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

[21] Z. Bern, L. J. Dixon, V. A. Smirnov, Phys. Rev. D, 72:8 (2005), 085001 ; arXiv: hep-th/0505205 | DOI | MR

[22] A. V. Kotikov, L. N. Lipatov, A. Rej, M. Staudacher, V. N. Velizhanin, J. Stat. Mech., 10 (2007), 10003 ; arXiv: 0704.3586 | DOI

[23] M. Beccaria, JHEP, 06 (2007), 044 ; arXiv: 0704.3570 | DOI | MR

[24] M. Beccaria, JHEP, 06 (2007), 054 ; arXiv: 0705.0663 | DOI | MR

[25] M. Beccaria, Yu. L. Dokshitzer, G. Marchesini, Phys. Lett. B, 652:4 (2007), 194–202 ; arXiv: 0705.2639 | DOI | MR | Zbl

[26] M. Beccaria, JHEP, 09 (2007), 023 ; arXiv: 0707.1574 | DOI | MR

[27] A. V. Belitsky, J. Henn, C. Jarczak, D. Müller, E. Sokatchev, Phys. Rev. D, 77:4 (2008), 045029 ; arXiv: 0707.2936 | DOI | MR

[28] M. Beccaria, F. Catino, JHEP, 01 (2008), 067 ; arXiv: 0710.1991 | DOI | MR

[29] G. Altarelli, Phys. Rep., 81:1 (1982), 1–129 | DOI

[30] A. D. Martin, Acta Phys. Polon. B, 39:9 (2008), 2025–2062 ; arXiv: 0802.0161 | MR

[31] L. N. Lipatov, YaF, 23 (1976), 642–656

[32] C. Gómez, J. Gunnesson, R. Hernández, JHEP, 09 (2008), 060 ; arXiv: 0807.2339 | DOI

[33] A. V. Belitsky, A. S. Gorsky, G. P. Korchemsky, Nucl. Phys. B, 667:1–2 (2003), 3–54 ; arXiv: hep-th/0304028 | DOI | MR | Zbl

[34] G. P. Korchemsky, G. Marchesini, Nucl. Phys. B, 406:1–2 (1993), 225–258 ; arXiv: hep-ph/9210281 | DOI

[35] A. V. Belitsky, A. S. Gorsky, G. P. Korchemsky, Nucl. Phys. B, 748:1–2 (2006), 24–59 ; arXiv: hep-th/0601112 | DOI | MR | Zbl

[36] B. Basso, G. P. Korchemsky, J. Kotański, Phys. Rev. Lett., 100:9 (2008), 091601 ; arXiv: 0708.3933 | DOI | MR | Zbl

[37] M. K. Benna, S. Benvenuti, I. R. Klebanov, A. Scardicchio, Phys. Rev. Lett., 98:13 (2007), 131603 ; ; L. F. Alday, G. Arutyunov, B. Eden, M. K. Benna I. R. Klebanov, JHEP, 04 (2007), 082 ; ; M. Beccaria, G. F. De Angelis, V. Forini, JHEP, 04 (2007), 066 ; ; I. Kostov, D. Serban, D. Volin, Nucl. Phys. B, 789:3 (2008), 413–451 ; ; P. Y. Casteill, C. Kristjansen, Nucl. Phys. B, 785:1–2 (2007), 1–18 ; ; I. Kostov, D. Serban, D. Volin, JHEP, 08 (2008), 101 ; arXiv: hep-th/0611135 arXiv: hep-th/0702028 arXiv: hep-th/0703131 arXiv: hep-th/0703031 arXiv: 0705.0890 arXiv: 0801.2542 | DOI | DOI | MR | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR

[38] L. Freyhult, A. Rej, M. Staudacher, J. Stat. Mech., 07 (2008), 07015 ; ; B. Basso, G. P. Korchemsky, Nucl. Phys. B, 807:3 (2009), 397–423 ; ; D. Fioravanti, P. Grinza, M. Rossi, The generalised scaling function: a systematic study, arXiv: 0712.2743 arXiv: 0805.4194 arXiv: 0808.1886 | DOI | MR | DOI | MR | Zbl | MR | MR

[39] M. Kruczenski, A. A. Tseytlin, Phys. Rev. D, 77:12 (2008), 126005 ; arXiv: 0802.2039 | DOI | MR | MR

[40] B. Eden, M. Staudacher, J. Stat. Mech., 11 (2006), 11014 ; arXiv: hep-th/0603157 | DOI

[41] N. Beisert, B. Eden, M. Staudacher, J. Stat. Mech., 01 (2007), 01021 ; arXiv: hep-th/0610251 | DOI

[42] Yu. L. Dokshitzer, Talk at the Workshop “Future Physics at HERA” (DESY, Hamburg, 1995–1996), unpublished; Y. L. Dokshitzer, V. A. Khoze, S. I. Troyan, Phys. Rev. D, 53:1 (1996), 89–119 ; ; Yu. L. Dokshitzer, G. Marchesini, G. P. Salam, Phys. Lett. B, 634:5–6 (2006), 504–507 ; arXiv: hep-ph/9506425 arXiv: hep-ph/0511302 | DOI | DOI | MR

[43] E. Laenen, L. Magnea, G. Stavenga, Phys. Lett. B, 669:2 (2008), 173–179 ; arXiv: 0807.4412 | DOI

[44] B. Basso, G. P. Korchemsky, Nucl. Phys. B, 775:1–2 (2007), 1–30 ; arXiv: hep-th/0612247 | DOI | MR | Zbl

[45] M. Beccaria, V. Forini, JHEP, 06 (2008), 077 ; arXiv: 0803.3768 | DOI | MR

[46] A. V. Belitsky, Phys. Lett. B, 650:1 (2007), 72–80 ; arXiv: hep-th/0703058 | DOI | MR

[47] A. V. Belitsky, Nucl. Phys. B, 803:1–2 (2008), 171–193 ; arXiv: 0803.2035 | DOI | MR | Zbl

[48] M. Beccaria, V. Forini, A. Tirziu, A. A. Tseytlin, Structure of large spin expansion of anomalous dimensions at strong coupling, arXiv: 0809.5234 | MR

[49] N. Beisert, M. Bianchi, J. F. Morales, H. Samtleben, JHEP, 07 (2004), 058 ; arXiv: hep-th/0405057 | DOI | MR

[50] R. Mertig, W. L. van Neerven, Z. Phys. C, 70:4 (1996), 637–653 ; arXiv: hep-ph/9506451 | DOI

Parcourir par

Geodesic

Parcourir par