Geodesic
From amplitudes to form factors in the $\mathcal{N}=4$ SYM theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 1, pp. 32-48
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss the latest progress in understanding the infrared behavior of inclusive cross sections and the form factors for the so-called half-BPS operators in the $\mathcal{N}=4$ SYM theory. In both cases, we observe the exponentiation of the infrared divergences while the finite parts do not have such a simple behavior. We show how the infrared divergences cancel in inclusive cross sections when the emission of soft and collinear quanta is taken into account. We calculate the finite parts of the form factors in the two-loop approximation. They are rather complicated and are expressed in terms of generalized polylogarithms of several variables. But the principle of maximal transcendentality is nevertheless still satisfied.
Keywords: $\mathcal N=4$ maximally supersymmetric Yang–Mills theory, form factor, $\mathcal N=1$ superspace, infrared-finite observable, maximally helicity-violating amplitude. 
@article{TMF_2011_169_1_a3,
     author = {L. V. Bork and D. I. Kazakov and G. S. Vartanov},
     title = {From amplitudes to form factors in the~$\mathcal{N}=4$ {SYM} theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {32--48},
     year = {2011},
     volume = {169},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_169_1_a3/}
}
TY  - JOUR
AU  - L. V. Bork
AU  - D. I. Kazakov
AU  - G. S. Vartanov
TI  - From amplitudes to form factors in the $\mathcal{N}=4$ SYM theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 32
EP  - 48
VL  - 169
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_169_1_a3/
LA  - ru
ID  - TMF_2011_169_1_a3
ER  - 
%0 Journal Article
%A L. V. Bork
%A D. I. Kazakov
%A G. S. Vartanov
%T From amplitudes to form factors in the $\mathcal{N}=4$ SYM theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 32-48
%V 169
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2011_169_1_a3/
%G ru
%F TMF_2011_169_1_a3
L. V. Bork; D. I. Kazakov; G. S. Vartanov. From amplitudes to form factors in the $\mathcal{N}=4$ SYM theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 1, pp. 32-48. http://geodesic.mathdoc.fr/item/TMF_2011_169_1_a3/

[1] N. Beisert, On Yangian symmetry in planar $\mathcal N=4$ SYM, arXiv: 1004.5423

[2] J. M. Drummond, J. Henn, V. A. Smirnov, E. Sokatchev, JHEP, 01 (2007), 064, 15 pp., arXiv: hep-th/0607160 | DOI | MR

[3] L. F. Alday, J. M. Maldacena, JHEP, 06 (2007), 064, 26 pp., arXiv: 0705.0303 | DOI | MR

[4] J. M. Drummond, G. P. Korchemsky, E. Sokatchev, Nucl. Phys. B, 795:1–2 (2008), 385–408, arXiv: 0707.0243 | DOI | MR | Zbl

[5] L. F. Alday, J. Maldacena, A. Sever, P. Vieira, J. Phys. A, 43:48 (2010), 485401, 57 pp. | DOI | MR | Zbl

[6] Z. Bern, L. J. Dixon, V. A. Smirnov, Phys. Rev. D, 72:8 (2005), 085001, 27 pp., arXiv: hep-th/0505205 | DOI | MR

[7] S. V. Ivanov, G. P. Korchemskii, A. V. Radyushkin, YaF, 44 (1986), 230–240 | MR

[8] L. Magnea, G. F. Sterman, Phys. Rev. D, 42:12 (1990), 4222–4227 | DOI

[9] L. F. Alday, R. Roiban, Phys. Rept., 468:5 (2008), 153–211, arXiv: 0807.1889 | DOI | MR

[10] T. Kinoshita, J. Math. Phys., 3:4 (1962), 650–677 ; T. D. Lee, M. Nauenberg, Phys. Rev. B, 133 (1964), 1549 | DOI | Zbl | DOI | MR

[11] C. L. Basham, L. S. Brown, S. D. Ellis, S. T. Love, Phys. Rev. Lett., 41:23 (1978), 1585–1588 | DOI

[12] D. M. Hofman, J. Maldacena, JHEP, 05 (2008), 012, 60 pp., arXiv: 0803.1467 | DOI

[13] L. V. Bork, D. I. Kazakov, G. S. Vartanov, A. V. Zhiboedov, Phys. Lett. B, 681:3 (2009), 296–303, arXiv: ; Phys. Rev. D, 81:10 (2010), 105028, 29 pp., arXiv: 0908.03870911.1617 | DOI | MR | DOI

[14] L. V. Bork, D. I. Kazakov, G. S. Vartanov, A. V. Zhiboedov, Problemy sovremennoi teoreticheskoi i matematicheskoi fiziki. Kalibrovochnye teorii i superstruny, Sbornik statei. K 70-letiyu so dnya rozhdeniya akademika Andreya Alekseevicha Slavnova, Tr. MIAN, 272, MAIK, M., 2011, 46–53 | MR

[15] W. L. van Neerven, Z. Phys. C, 30:4 (1986), 595–598 | DOI

[16] J. Maldacena, A. Zhiboedov, JHEP, 11 (2010), 104, 42 pp., arXiv: 1009.1139 | DOI | MR

[17] L. V. Bork, D. I. Kazakov, G. S. Vartanov, JHEP, 02 (2011), 063, 35 pp., arXiv: 1011.2440 | DOI | MR

[18] A. Brandhuber, B. Spence, G. Travaglini, G. Yang, JHEP, 01 (2011), 134, 22 pp., arXiv: 1011.1899 | DOI | Zbl

[19] G. Altarelli, G. Parisi, Nucl. Phys. B, 126:2 (1977), 298–318 | DOI

[20] V. N. Gribov, L. N. Lipatov, YaF, 15:4 (1972), 781–807

[21] A. V. Kotikov, L. N. Lipatov, Nucl. Phys. B, 769:3 (2007), 217–255, arXiv: hep-th/0611204 | DOI | MR | Zbl