Twist-2 at five loops: Wrapping corrections without wrapping computations

Journal of High Energy Physics

Volumn 2014, Issue 6, 2014, Pages

  Velizhanin, V N ^a,b  

^a Institut für Mathematik Institut für Physik IRIS Adlershof   (Germany)

^b PETERSBURG NUCLEAR PHYSICS INSTITUTE   (Russian Federation)

Author keywords

AdS CFT Correspondence; Integrable Field Theories; Renormalization Group; Supersymmetric gauge theory

Indexed keywords

EID: 84904326415     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP06(2014)108     Document Type: Article

References (86)

1. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [ hep-th/9711200 ].
2. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [ hep-th/9802109 ].
3. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [ hep-th/9802150 ].
4. D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N =4 super Yang-Mills, JHEP 04 (2002) 013 [ hep-th/0202021 ].
5. J.A. Minahan and K. Zarembo, The Bethe ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [ hep-th/0212208 ].
6. L.N. Lipatov, High-energy asymptotics of multicolor QCD and exactly solvable lattice models, hep-th/9311037.
7. L.N. Lipatov, Asymptotic behavior of multicolor QCD at high energies in connection with exactly solvable spin models, JETP Lett. 59 (1994) 596.
8. L.D. Faddeev and G.P. Korchemsky, High-energy QCD as a completely integrable model, Phys. Lett. B 342 (1995) 311 [ hep-th/9404173 ].
9. V.M. Braun, S.E. Derkachov and A.N. Manashov, Integrability of three particle evolution equations in QCD, Phys. Rev. Lett. 81 (1998) 2020 [ hep-ph/9805225 ].
10. 5 superstring, Phys. Rev. D 69 (2004) 046002 [ hep-th/0305116 ].
11. N. Beisert, C. Kristjansen and M. Staudacher, The Dilatation operator of conformal N = 4 super Yang-Mills theory, Nucl. Phys. B 664 (2003) 131 [ hep-th/0303060 ]. (Pubitemid 36860529)
12. N. Beisert and M. Staudacher, The N = 4 SYM integrable super spin chain, Nucl. Phys. B 670 (2003) 439 [ hep-th/0307042 ]. (Pubitemid 37223521)
13. N. Beisert, The complete one loop dilatation operator of N = 4 super Yang-Mills theory, Nucl. Phys. B 676 (2004) 3 [ hep-th/0307015 ]. (Pubitemid 37501390)
14. N. Beisert, The SU(2|3) dynamic spin chain, Nucl. Phys. B 682 (2004) 487 [ hep-th/0310252 ]. (Pubitemid 38236273)
15. D. Serban and M. Staudacher, Planar N = 4 gauge theory and the Inozemtsev long range spin chain, JHEP 06 (2004) 001 [ hep-th/0401057 ].
16. V.A. Kazakov, A. Marshakov, J.A. Minahan and K. Zarembo, Classical/quantum integrability in AdS/CFT, JHEP 05 (2004) 024 [ hep-th/0402207 ].
17. N. Beisert, V. Dippel and M. Staudacher, A novel long range spin chain and planar N = 4 super Yang-Mills, JHEP 07 (2004) 075 [ hep-th/0405001 ].
18. G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [ hep-th/0406256 ].
19. M. Staudacher, The factorized S-matrix of CFT/AdS, JHEP 05 (2005) 054 [ hep-th/0412188 ]. (Pubitemid 40919909)
20. N. Beisert and M. Staudacher, Long-range PSU (2, 2|4) Bethe ansatze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [ hep-th/0504190 ]. (Pubitemid 41430761)
21. N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [ hep-th/0511082 ].
22. 5 superstring worldsheet S-matrix and crossing symmetry, Phys. Rev. D 73 (2006) 086006 [ hep-th/0603038 ].
23. R. Hernandez and E. Lopez, Quantum corrections to the string Bethe ansatz, JHEP 07 (2006) 004 [ hep-th/0603204 ]. (Pubitemid 44406231)
24. 5 string S-matrix, Phys. Lett. B 639 (2006) 378 [ hep-th/0604043 ]. (Pubitemid 44080444)
25. 5 strings, JHEP 11 (2006) 070 [ hep-th/0609044 ].
26. B. Eden and M. Staudacher, Integrability and transcendentality, J. Stat. Mech. 0611 (2006) P11014 [ hep-th/0603157 ].
27. Z. Bern, M. Czakon, L.J. Dixon, D.A. Kosower and V.A. Smirnov, The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 75 (2007) 085010 [ hep-th/0610248 ].
28. N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 0701 (2007) P01021 [ hep-th/0610251 ].
29. S. Schäfer-Nameki, M. Zamaklar and K. Zarembo, How accurate is the quantum string Bethe ansatz?, JHEP 12 (2006) 020 [ hep-th/0610250 ].
30. A.V. Kotikov, L.N. Lipatov, A. Rej, M. Staudacher and V.N. Velizhanin, Dressing and wrapping, J. Stat. Mech. 0710 (2007) P10003 [ arXiv:0704.3586 ].
31. J. Ambjørn, R.A. Janik and C. Kristjansen, Wrapping interactions and a new source of corrections to the spin-chain/string duality, Nucl. Phys. B 736 (2006) 288 [ hep-th/0510171 ]. (Pubitemid 43092731)
32. M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states, Commun. Math. Phys. 104 (1986) 177.
33. M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 2. Scattering states, Commun. Math. Phys. 105 (1986) 153.
34. Z. Bajnok and R.A. Janik, Four-loop perturbative Konishi from strings and finite size effects for multiparticle states, Nucl. Phys. B 807 (2009) 625 [ arXiv:0807.0399 ].
35. Z. Bajnok, R.A. Janik and T. Lukowski, Four loop twist two, BFKL, wrapping and strings, Nucl. Phys. B 816 (2009) 376 [ arXiv:0811.4448 ].
36. Z. Bajnok, A. Hegedus, R.A. Janik and T. Lukowski, Five loop Konishi from AdS/CFT, Nucl. Phys. B 827 (2010) 426 [ arXiv:0906.4062 ].
37. T. Lukowski, A. Rej and V.N. Velizhanin, Five-loop anomalous dimension of twist-two operators, Nucl. Phys. B 831 (2010) 105 [ arXiv:0912.1624 ].
38. F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Wrapping at four loops in N = 4 SYM, Phys. Lett. B 666 (2008) 100 [ arXiv:0712.3522 ].
39. F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Anomalous dimension with wrapping at four loops in N = 4 SYM, Nucl. Phys. B 805 (2008) 231 [ arXiv:0806.2095 ].
40. C. Sieg and A. Torrielli, Wrapping interactions and the genus expansion of the 2-point function of composite operators, Nucl. Phys. B 723 (2005) 3 [ hep-th/0505071 ]. (Pubitemid 41110221)
41. V.N. Velizhanin, The four-loop anomalous dimension of the Konishi operator in N = 4 supersymmetric Yang-Mills theory, JETP Lett. 89 (2009) 6 [ arXiv:0808.3832 ].
42. V.N. Velizhanin, Leading transcedentality contributions to the four-loop universal anomalous dimension in N = 4 SYM, Phys. Lett. B 676 (2009) 112 [ arXiv:0811.0607 ].
43. L.N. Lipatov, Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian Gauge Theories, Sov. J. Nucl. Phys. 23 (1976) 338.
44. E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk singularity in nonabelian gauge theories, Sov. Phys. JETP 45 (1977) 199.
45. I.I. Balitsky and L.N. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822.
46. M. Beccaria, V. Forini, T. Lukowski and S. Zieme, Twist-three at five loops, Bethe Ansatz and wrapping, JHEP 03 (2009) 129 [ arXiv:0901.4864 ].
47. V.N. Velizhanin, Six-loop anomalous dimension of twist-three operators in N = 4 SYM, JHEP 11 (2010) 129 [ arXiv:1003.4717 ].
48. A.B. Zamolodchikov, Thermodynamic Bethe ansatz in relativistic models. Scaling three state Potts and Lee-Yang models, Nucl. Phys. B 342 (1990) 695.
49. A.B. Zamolodchikov, On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories, Phys. Lett. B 253 (1991) 391.
50. N. Gromov, V. Kazakov and P. Vieira, Exact spectrum of anomalous dimensions of planar N =4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 103(2009) 131601 [ arXiv:0901.3753 ].
51. N. Gromov, V. Kazakov, A. Kozak and P. Vieira, Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory: TBA and excited states, Lett. Math. Phys. 91 (2010) 265 [ arXiv:0902.4458 ].
52. N. Gromov, V. Kazakov and P. Vieira, Exact spectrum of planar N = 4 supersymmetric Yang-Mills theory: Konishi dimension at any coupling, Phys. Rev. Lett. 104 (2010) 211601 [ arXiv:0906.4240 ].
53. D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal, J. Phys. A 42 (2009) 375401 [ arXiv:0902.3930 ].
54. G. Arutyunov, S. Frolov and R. Suzuki, Exploring the mirror TBA, JHEP 05 (2010) 031 [ arXiv:0911.2224 ].
55. 5 mirror model, JHEP 05 (2009) 068 [ arXiv:0903.0141 ].
56. G. Arutyunov, S. Frolov and R. Suzuki, Five-loop Konishi from the mirror TBA, JHEP 04 (2010) 069 [ arXiv:1002.1711 ].
57. J. Balog and A. Hegedus, 5-loop Konishi from linearized TBA and the XXX magnet, JHEP 06 (2010) 080 [ arXiv:1002.4142 ].
58. J. Balog and A. Hegedus, The Bajnok-Janik formula and wrapping corrections, JHEP 09 (2010) 107 [ arXiv:1003.4303 ].
59. Z. Bajnok and O. el Deeb, 6-loop anomalous dimension of a single impurity operator from AdS/CFT and multiple zeta values, JHEP 01 (2011) 054 [ arXiv:1010.5606 ].
60. V.G. Gorshkov, V.N. Gribov, L.N. Lipatov and G.V. Frolov, Doubly logarithmic asymptotic behavior in quantum electrodynamics, Sov. J. Nucl. Phys. 6 (1968) 95.
61. V.G. Gorshkov, V.N. Gribov, L.N. Lipatov and G.V. Frolov, Backward electron-positron scattering at high-energies, Sov. J. Nucl. Phys. 6 (1968) 262.
62. V.G. Gorshkov, V.N. Gribov, L.N. Lipatov and G.V. Frolov, Double logarithmic asymptotics of quantum electrodynamics, Phys. Lett. 22 (1966) 671.
63. R. Kirschner and L.N. Lipatov, Double logarithmic asymptotics of quark scattering amplitudes with flavor exchange, Phys. Rev. D 26 (1982) 1202.
64. R. Kirschner and L. Lipatov, Doubly logarithmic asymptotic of the quark scattering amplitude with nonvacuum exchange in the t channel, Sov. Phys. JETP 56 (1982) 266.
65. R. Kirschner and L. Lipatov, Double logarithmic asymptotics and Regge singularities of quark amplitudes with flavor exchange, Nucl. Phys. B 213 (1983) 122.
66. V.N. Velizhanin, Double-logs, Gribov-Lipatov reciprocity and wrapping, JHEP 08 (2011) 092 [ arXiv:1104.4100 ].
67. J.A.M. Vermaseren, Harmonic sums, Mellin transforms and integrals, Int. J. Mod. Phys. A 14 (1999) 2037 [ hep-ph/9806280 ].
68. A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL equations in the N = 4 supersymmetric gauge theory, Nucl. Phys. B 661 (2003) 19 [Erratum ibid. B 685 (2004) 405] [ hep-ph/0208220 ].
69. A.V. Kotikov, L.N. Lipatov and V.N. Velizhanin, Anomalous dimensions of Wilson operators in N = 4 SYM theory, Phys. Lett. B 557 (2003) 114 [ hep-ph/0301021 ].
70. A.V. Kotikov, L.N. Lipatov, A.I. Onishchenko and V.N. Velizhanin, Three loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model, Phys. Lett. B 595 (2004) 521 [Erratum ibid. B 632 (2006) 754] [ hep-th/0404092 ].
71. Y. Dokshitzer, G. Marchesini and G.P. Salam, Revisiting parton evolution and the large-x limit, Phys. Lett. B 634 (2006) 504 [ hep-ph/0511302 ]. (Pubitemid 43343621)
72. Y. Dokshitzer and G. Marchesini, N = 4 SUSY Yang-Mills: three loops made simple(r), Phys. Lett. B 646 (2007) 189 [ hep-th/0612248 ].
73. V.N. Velizhanin, Three loop anomalous dimension of the non-singlet transversity operator in QCD, Nucl. Phys. B 864 (2012) 113 [ arXiv:1203.1022 ].
74. A.K. Lenstra, H.W. Lenstra and L. Lovasz, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982) 515.
75. M. Beccaria, A.V. Belitsky, A.V. Kotikov and S. Zieme, Analytic solution of the multiloop Baxter equation, Nucl. Phys. B 827 (2010) 565 [ arXiv:0908.0520 ].
76. V.S. Fadin and L.N. Lipatov, BFKL Pomeron in the next-to-leading approximation, Phys. Lett. B 429 (1998) 127 [ hep-ph/9802290 ].
77. A.V. Kotikov and L.N. Lipatov, NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories, Nucl. Phys. B 582 (2000) 19 [ hep-ph/0004008 ].
78. E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [ hep-ph/9905237 ].
79. J.A.M. Vermaseren, New features of FORM, math-ph/0010025.
80. M. de Leeuw and T. Lukowski, Twist operators in N = 4 beta-deformed theory, JHEP 04 (2011) 084 [ arXiv:1012.3725 ].
81. V.N. Velizhanin, The non-planar contribution to the four-loop universal anomalous dimension in N = 4 supersymmetric Yang-Mills theory, JETP Lett. 89 (2009) 593 [ arXiv:0902.4646 ].
82. V.N. Velizhanin, The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: First moments in N = 4 SYM and non-singlet QCD, Nucl. Phys. B 846 (2011) 137 [ arXiv:1008.2752 ].
83. Z. Bajnok and R.A. Janik, Six and seven loop Konishi from Lüscher corrections, JHEP 11 (2012) 002 [ arXiv:1209.0791 ].
84. S. Leurent, D. Serban and D. Volin, Six-loop Konishi anomalous dimension from the Y-system, Phys. Rev. Lett. 109 (2012) 241601 [ arXiv:1209.0749 ].
85. S. Leurent and D. Volin, Multiple zeta functions and double wrapping in planar N = 4 SYM, Nucl. Phys. B 875 (2013) 757 [ arXiv:1302.1135 ].
86. B. Basso, An exact slope for AdS/CFT, arXiv:1109.3154.