参考文献:1. Janik, R.: Review of AdS/CFT Integrability, Chapter III.5: L眉scher corrections, arxiv:1012.3994 2. Kazakov, V., Gromov, N.: Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability, arxiv:1012.3996 3. Bajnok, Z.: Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz, arxiv:1012.3995 4. Korchemsky, G.: Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and ${\fancyscript{N}}$ < 4 SYM, arxiv:1012.4000 5. Staudacher, M.: Review of AdS/CFT Integrability, Chapter III.1: Bethe Ans盲tze and the R-Matrix Formalism, arxiv:1012.3990 6. Ahn, C., Nepomechie, R.I.: Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix, arxiv:1012.3991 7. Vieira, P., Volin, D.: Review of AdS/CFT Integrability, Chapter III.3: The dressing factor, arxiv:1012.3992 8. Staudacher M.: The factorized S-matrix of CFT/AdS. JHEP 0505, 054 (2005) hep-th/0412188 CrossRef 9. Beisert N., Staudacher M.: Long-range PSU(2,2/4) Bethe ansaetze for gauge theory and strings. Nucl. Phys. B 727, 1 (2005) hep-th/0504190 CrossRef 10. Janik R.A.: The AdS5 脳 S5 superstring worldsheet S-matrix and crossing symmetry. Phys. Rev. D 73, 086006 (2006) hep-th/0603038 CrossRef 11. Gomez C., Hernandez R.: The magnon kinematics of the AdS/CFT correspondence. JHEP 0611, 021 (2006) hep-th/0608029 CrossRef 12. Plefka J., Spill F., Torrielli A.: On the Hopf algebra structure of the AdS/CFT S-matrix. Phys. Rev. D 74, 066008 (2006) hep-th/0608038 CrossRef 13. Eden B., Staudacher M.: Integrability and transcendentality. J. Stat. Mech. 0611, P014 (2006) hep-th/0603157 14. Beisert N., Eden B., Staudacher M.: Transcendentality and crossing. J. Stat. Mech. 0701, P021 (2007) hep-th/0610251 15. Anastasiou C., Bern Z., Dixon L.J., Kosower D.A.: Planar amplitudes in maximally supersymmetric Yang-Mills theory. Phys. Rev. Lett. 91, 251602 (2003) hep-th/0309040 CrossRef 16. Bern Z., Dixon L.J., Smirnov V.A.: Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond. Phys. Rev. D 72, 085001 (2005) hep-th/0505205 CrossRef 17. Bern Z., Czakon M., Dixon L.J., Kosower D.A., Smirnov V.A.: The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory. Phys. Rev. D 75, 085010 (2007) hep-th/0610248 CrossRef 18. Volin, D.: Minimal solution of the AdS/CFT crossing equation, arxiv:0904.4929 19. Collins J.C.: Sudakov form factors. Adv. Ser. Direct. High Energy Phys. 5, 573 (1989) hep-ph/0312336 20. Belitsky A.V., Gorsky A.S., Korchemsky G.P.: Logarithmic scaling in gauge/string correspondence. Nucl. Phys. B 748, 24 (2006) hep-th/0601112 CrossRef 21. Korchemsky G.P., Radyushkin A.V.: Loop space formalism and renormalization group for the infrared asymptotics of QCD. Phys. Lett. B 171, 459 (1986) CrossRef 22. Korchemsky G.P.: Asymptotics of the Altarelli-Parisi-Lipatov evolution kernels of Parton distributions. Mod. Phys. Lett. A 4, 1257 (1989) CrossRef 23. Korchemsky G.P., Marchesini G.: Structure function for large x and renormalization of Wilson loop. Nucl. Phys. B 406, 225 (1993) hep-ph/9210281 CrossRef 24. Kruczenski M.: A note on twist two operators in / N = 4 SYM and Wilson loops in Minkowski signature. JHEP 0212, 024 (2002) hep-th/0210115 CrossRef 25. Alday L.F., Maldacena J.M.: Gluon scattering amplitudes at strong couplin. JHEP 0706, 064 (2007) arxiv:0705.0303 CrossRef 26. Sieg, C.: Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory, arxiv:1012.3984 27. Tseytlin, A.: Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5 脳 S5 string solutions, arxiv:1012.3986 28. McLoughlin, T.: Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5 脳 S5, arxiv:1012.3987 29. Gubser S.S., Klebanov I.R., Polyakov A.M.: A semi-classical limit of the gauge/string correspondence. Nucl. Phys. B 636, 99 (2002) hep-th/0204051 CrossRef 30. Frolov S., Tseytlin A.A.: Semiclassical quantization of rotating superstring in AdS5 脳 S5. JHEP 0206, 007 (2002) hep-th/0204226 CrossRef 31. Roiban R., Tirziu A., Tseytlin A.A.: Two-loop world-sheet corrections in AdS5 脳 S5 superstring. JHEP 0707, 056 (2007) arxiv:0704.3638 CrossRef 32. Roiban R., Tseytlin A.A.: Strong-coupling expansion of cusp anomaly from quantum superstring. JHEP 0711, 016 (2007) arxiv:0709.0681 CrossRef 33. Beccaria, M., Dunne, G.V., Forini, V., Pawellek, M., Tseytlin, A.A.: Exact computation of one-loop correction to energy of spinning folded string in AdS5 脳 S5, arxiv:1001.4018 34. Kotikov A.V., Lipatov L.N.: On the highest transcendentality in ${\fancyscript{N} =}$ 4 SUSY. Nucl. Phys. B 769, 217 (2007) hep-th/0611204 CrossRef 35. Alday L.F., Arutyunov G., Benna M.K., Eden B., Klebanov I.R.: On the strong coupling scaling dimension of high spin operators. JHEP 0704, 082 (2007) hep-th/0702028 CrossRef 36. Kostov I., Serban D., Volin D.: Strong coupling limit of Bethe ansatz equations. Nucl. Phys. B 789, 413 (2008) hep-th/0703031 CrossRef 37. Beccaria M., De Angelis G.F., Forini V.: The scaling function at strong coupling from the quantum string Bethe equations. JHEP 0704, 066 (2007) hep-th/0703131 CrossRef 38. Basso B., Korchemsky G.P., Kotanski J.: Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling. Phys. Rev. Lett. 100, 091601 (2008) arxiv:0708.3933 CrossRef 39. Casteill P.Y., Kristjansen C.: The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz. Nucl. Phys. B 785, 1 (2007) arxiv:0705.0890 CrossRef 40. Kostov I., Serban D., Volin D.: Functional BES equation. JHEP 0808, 101 (2008) arxiv:0801.2542 CrossRef 41. Basso B., Korchemsky G.P.: Nonperturbative scales in AdS/CFT. J. Phys. A 42, 254005 (2009) arxiv:0901.4945 CrossRef 42. Belitsky A.V., Gorsky A.S., Korchemsky G.P.: Gauge/string duality for QCD conformal operators. Nucl. Phys. B 667, 3 (2003) hep-th/0304028 CrossRef 43. Belitsky A.V., Korchemsky G.P., Pasechnik R.S.: Fine structure of anomalous dimensions in ${\fancyscript{N} =}$ 4 super Yang-Mills theory. Nucl. Phys. B 809, 244 (2009) arxiv:0806.3657 CrossRef 44. Korchemsky G.P.: Quasiclassical QCD pomeron. Nucl. Phys. B 462, 333 (1996) hep-th/9508025 CrossRef 45. Freyhult L., Rej A., Staudacher M.: A generalized scaling function for AdS/CFT. J. Stat. Mech. 0807, P07015 (2008) arxiv:0712.2743 CrossRef 46. Feverati G., Fioravanti D., Grinza P., Rossi M.: On the finite size corrections of anti-ferromagnetic anomalous dimensions in ${\fancyscript{N} =}$ 4 SYM. JHEP 0605, 068 (2006) hep-th/0602189 CrossRef 47. Feverati G., Fioravanti D., Grinza P., Rossi M.: Hubbard鈥檚 adventures in ${\fancyscript{N} =}$ 4 SYM-land? Some non-perturbative considerations on finite length operators. J. Stat. Mech. 0702, P001 (2007) hep-th/0611186 48. Fioravanti D., Rossi M.: On the commuting charges for the highest dimension SU(2) operator in planar ${\fancyscript{N} =}$ 4 SYM. JHEP 0708, 089 (2007) arxiv:0706.3936 CrossRef 49. Bombardelli, D., Fioravanti, D., Rossi, M.: Non-linear integral equations in ${\fancyscript{N}=}$ 4 SYM, arxiv:0711.2934 50. Bombardelli D., Fioravanti D., Rossi M.: Large spin corrections in ${\fancyscript{N} =}$ 4 SYM sl(2): still a linear integral equation. Nucl. Phys. B 810, 460 (2009) arxiv:0802.0027 CrossRef 51. Freyhult L., Zieme S.: The virtual scaling function of AdS/CFT. Phys. Rev. D 79, 105009 (2009) arxiv:0901.2749 CrossRef 52. Fioravanti, D., Grinza, P., Rossi, M.: On the logarithmic powers of / sl(2) SYM4, arxiv:0911.2425 53. Kotikov A.V., Lipatov L.N.: DGLAP and BFKL evolution equations in the / N聽=聽4 supersymmetric gauge theory. Nucl. Phys. B 661, 19 (2003) hep-ph/0208220 54. Georgi H., Politzer H.D.: Electroproduction scaling in an asymptotically free theory of strong interactions. Phys. Rev. D 9, 416 (1974) CrossRef 55. Gross D.J., Wilczek F.: Asymptotically free gauge theories. 1. Phys. Rev. D 8, 3633 (1973) CrossRef 56. Dolan F.A., Osborn H.: Conformal four point functions and the operator product expansion. Nucl. Phys. B 599, 459 (2001) hep-th/0011040 CrossRef 57. Kotikov A.V., Lipatov L.N., Velizhanin V.N.: Anomalous dimensions of Wilson operators in / N = 4 SYM theory. Phys. Lett. B 557, 114 (2003) hep-ph/0301021 CrossRef 58. Kotikov A.V., Lipatov L.N., Onishchenko A.I., Velizhanin V.N.: Three-loop universal anomalous dimension of the Wilson operators in ${\fancyscript{N} =}$ 4 SUSY Yang-Mills model. Phys. Lett. B 595, 521 (2004) hep-th/0404092 CrossRef 59. Moch S., Vermaseren J.A.M., Vogt A.: The three-loop splitting functions in QCD: the non-singlet case. Nucl. Phys. B 688, 101 (2004) hep-ph/0403192 CrossRef 60. Vermaseren J.: Harmonic sums, Mellin transforms and integrals. Int. J. Mod. Phys. A 14, 2037 (1999) hep-ph/9806280 CrossRef 61. Beccaria M.: Anomalous dimensions at twist-3 in the sl(2) sector of ${\fancyscript{N} =}$ 4 SYM. JHEP 0706, 044 (2007) arxiv:0704.3570 CrossRef 62. Kotikov A.V., Lipatov L.N., Rej A., Staudacher M., Velizhanin V.N.: Dressing and Wrapping. J. Stat. Mech. 0710, P10003 (2007) arxiv:0704.3586 CrossRef 63. Beccaria M., Dokshitzer Y.L., Marchesini G.: Twist 3 of the sl(2) sector of ${\fancyscript{N} =}$ 4 SYM and reciprocity respecting evolution. Phys. Lett. B 652, 194 (2007) arxiv:0705.2639 CrossRef 64. Beccaria M., Forini V., Lukowski T., Zieme S.: Twist-three at five loops, Bethe Ansatz and wrapping. JHEP 0903, 129 (2009) arxiv:0901.4864 CrossRef 65. Lukowski, T., Rej, A., Velizhanin, V.N.: Five-Loop Anomalous Dimension of Twist-Two Operators, arxiv:0912.1624 66. Beccaria M., Catino F.: Sum rules for higher twist sl(2) operators in ${\fancyscript{N} =}$ 4 SYM. JHEP 0806, 103 (2008) arxiv:0804.3711 CrossRef 67. Derkachov S.E., Korchemsky G.P., Manashov A.N.: Evolution equations for quark gluon distributions in multi-color QCD and open spin chains. Nucl. Phys. B 566, 203 (2000) hep-ph/9909539 CrossRef 68. Belitsky A.V., Korchemsky G.P., Mueller D.: Towards Baxter equation in supersymmetric Yang-Mills theories. Nucl. Phys. B 768, 116 (2007) hep-th/0605291 CrossRef 69. Belitsky A.V.: Long-range SL(2) Baxter equation in ${\fancyscript{N} =}$ 4 super-Yang-Mills theory. Phys. Lett. B 643, 354 (2006) hep-th/0609068 CrossRef 70. Belitsky A.V.: Baxter equation beyond wrapping. Phys. Lett. B 677, 93 (2009) arxiv:0902.3198 CrossRef 71. Kotikov A.V., Rej A., Zieme S.: Analytic three-loop Solutions for ${\fancyscript{N} =}$ 4 SYM Twist Operators. Nucl. Phys. B 813, 460 (2009) arxiv:0810.0691 CrossRef 72. Beccaria, M., Belitsky, A.V., Kotikov, A.V., Zieme, S.: Analytic solution of the multiloop Baxter equation, arxiv:0908.0520 73. Kuraev E., Lipatov L., Fadin V.S.: The Pomeranchuk singularity in nonabelian gauge theories. Sov. Phys. JETP 45, 199 (1977) 74. Balitsky I., Lipatov L.: The Pomeranchuk singularity in quantum chromodynamics. Sov. J. Nucl. Phys. 28, 822 (1978) 75. Bajnok Z., Janik R.A., Lukowski T.: Four loop twist two, BFKL, wrapping and strings. Nucl. Phys. B 816, 376 (2009) arxiv:0811.4448 CrossRef 76. Beccaria M., Forini V.: Four loop reciprocity of twist two operators in ${\fancyscript{N} =}$ 4 SYM. JHEP 0903, 111 (2009) arxiv:0901.1256 CrossRef 77. Dokshitzer Y.L., Marchesini G., Salam G.P.: Revisiting parton evolution and the large-x limit. Phys. Lett. B 634, 504 (2006) hep-ph/0511302 CrossRef 78. Basso B., Korchemsky G.P.: Anomalous dimensions of high-spin operators beyond the leading order. Nucl. Phys. B 775, 1 (2007) hep-th/0612247 CrossRef 79. Dokshitzer Y.L., Marchesini G.: ${\fancyscript{N} =}$ 4 SUSY Yang-Mills: three loops made simple(r). Phys. Lett. B 646, 189 (2007) hep-th/0612248 CrossRef 80. Beccaria, M., Forini, V., Macorini, G.: Generalized Gribov-Lipatov reciprocity and AdS/CFT, arxiv:1002.2363 81. Braun V.M., Korchemsky G.P., Mueller D.: The uses of conformal symmetry in QCD. Prog. Part. Nucl. Phys. 51, 311 (2003) hep-ph/0306057 CrossRef 82. Beccaria M., Forini V.: Reciprocity of gauge operators in ${\fancyscript{N} =}$ 4 SYM. JHEP 0806, 077 (2008) arxiv:0803.3768 CrossRef 83. Gribov V.N., Lipatov L.N.: e+ e- pair annihilation and deep inelastic e p scattering in perturbation theory. Sov. J. Nucl. Phys. 15, 675 (1972) 84. Vogt A., Moch S., Vermaseren J.A.M.: The three-loop splitting functions in QCD: The singlet case. Nucl. Phys. B 691, 129 (2004) hep-ph/0404111 CrossRef 85. Beccaria M.: Universality of three gaugino anomalous dimensions in ${\fancyscript{N} =}$ 4 SYM. JHEP 0706, 054 (2007) arxiv:0705.0663 CrossRef 86. Beccaria M.: Three loop anomalous dimensions of twist-3 gauge operators in ${\fancyscript{N}}$ = 4 SYM. JHEP 0709, 023 (2007) arxiv:0707.1574 CrossRef 87. Giombi, S., Ricci, R., Roiban, R., Tseytlin, A.A., Vergu, C.: Quantum / AdS 5 脳 / S 5 superstring in the AdS light-cone gauge, arxiv:0912.5105 88. Klose, T.: Review of AdS/CFT Integrability, Chapter IV.3: ${\fancyscript{N} =\, }$ 6 Chern-Simons and Strings on AdS4 脳 CP3, arxiv:1012.3999 89. Benna M.K., Benvenuti S., Klebanov I.R., Scardicchio A.: A test of the AdS/CFT correspondence using high-spin operators. Phys. Rev. Lett. 98, 131603 (2007) hep-th/0611135 CrossRef 90. Belitsky A.V.: Strong coupling expansion of Baxter equation in ${\fancyscript{N} =\, }$ 4 SYM. Phys. Lett. B 659, 732 (2008) arxiv:0710.2294 CrossRef 91. Kotikov A.V., Lipatov L.N.: Eden-Staudacher and Beisert-Eden-Staudacher equations in the ${\fancyscript{N} = }$ 4 supersymmetric gauge theory. Theor. Math. Phys. 155, 606 (2008) CrossRef 92. Eden, B.: The BES equation and its strong coupling limit. In: Talk at 12th Itzykson meeting, Saclay, Paris 93. Volin, D.: Quantum integrability and functional equations, arxiv:1003.4725 94. Beccaria M., Forini V., Tirziu A., Tseytlin A.A.: Structure of large spin expansion of anomalous dimensions at strong coupling. Nucl. Phys. B 812, 144 (2009) arxiv:0809.5234 CrossRef 95. Basso, B.: Exciting the GKP string at any coupling, arxiv:1010.5237 96. Freyhult, L., Rej, A., Zieme, S.: From weak coupling to spinning strings, arxiv:0911. 2458 97. Rej A., Staudacher M., Zieme S.: Nesting and dressing. J. Stat. Mech. 0708, P08006 (2007) hep-th/0702151 CrossRef 98. Kotanski J.: Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory. Acta Phys. Polon. B 39, 3127 (2008) arxiv:0811.2667 99. Alday L.F., Maldacena J.M.: Comments on operators with large spin. JHEP 0711, 019 (2007) arxiv:0708.0672 CrossRef 100. Basso B., Korchemsky G.P.: Embedding nonlinear O(6) sigma model into ${\fancyscript{N} = }$ 4 super-Yang-Mills theory. Nucl. Phys. B 807, 397 (2009) arxiv:0805.4194 CrossRef 101. Bajnok Z., Balog J., Basso B., Korchemsky G.P., Palla L.: Scaling function in AdS/CFT from the O(6) sigma model. Nucl. Phys. B 811, 438 (2009) arxiv:0809.4952 CrossRef 102. Giombi, S., Ricci, R., Roiban, R., Tseytlin, A.A., Vergu, C.: Generalized scaling function from light-cone gauge AdS5 脳 S5 superstring, arxiv:1002.0018 103. Fioravanti, D., Grinza, P., Rossi, M.: The generalised scaling function: a note, arxiv:0805.4407 104. Buccheri, F., Fioravanti, D.: The integrable O(6) model and the correspondence: checks and predictions, arxiv:0805.4410 105. Gromov, N.: Generalized Scaling Function at Strong Coupling. JHEP 0811, 085 (2008). arxiv:0805.4615 106. Beccaria M.: The generalized scaling function of AdS/CFT and semiclassical string theory. JHEP 0807, 082 (2008) arxiv:0806.3704 CrossRef 107. Fioravanti, D., Grinza, P., Rossi, M.: The generalised scaling function: a systematic study, arxiv:0808.1886 108. Volin, D.: The 2-loop generalized scaling function from the BES/FRS equation, arxiv:0812.4407
作者单位:Lisa Freyhult (1)
1. Division for Theoretical Physics, Department of Physics and Astronomy, Uppsala University, Box 516, 751 20, Uppsala, Sweden
ISSN:1573-0530
文摘
We review the computation of the anomalous dimension of twist operators in the planar limit of ${\mathcal{N}=4}$ SYM using the asymptotic Bethe ansatz and demonstrate how this quantity is obtained at weak, strong and intermediate values of the coupling constant. The anomalous dimension of twist operators in the limit of large Lorentz spin played a major role in the construction as well as in many tests of the asymptotic Bethe equations; this aspect of the story is emphasized.