Analytic result for the two-loop six-point NMHV amplitude in N = 4 super Yang-Mills theory

Journal of High Energy Physics

Volumn 2012, Issue 1, 2012, Pages

  Dixon, Lance J ^a   Drummond, James M ^b,c   Henn, Johannes M ^d,e  

^a SLAC NATIONAL ACCELERATOR LABORATORY   (United States)

^b CERN   (Switzerland)

^c UNIVERSITÉ DE SAVOIE   (France)

^d HUMBOLDT UNIVERSITY   (Germany)

^e INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

Conformal and W Symmetry; Supersymmetric gauge theory

Indexed keywords

EID: 84857344943     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP01(2012)024     Document Type: Article

References (84)

1. J. Drummond, J. Henn, V. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [?SPIRE].
2. 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] [?SPIRE].
3. J. Drummond, G. Korchemsky and E. Sokatchev, Conformalproperties offour-gluonplanar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [arXiv:0707.0243] [?SPIRE].
4. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, On planar gluon amplitudes/Wilson loops duality, Nucl. Phys. B 795 (2008) 52 [arXiv:0709.2368] [?SPIRE].
5. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys. B 826 (2010) 337 [arXiv:0712.1223] [?SPIRE].
6. L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [?SPIRE].
7. L.F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [arXiv:0710.1060] [?SPIRE].
8. A. Brandhuber, P. Heslop and G. Travaglini, MHV amplitudes ina;? = 4 super Yang-Mills and Wilson loops, Nucl. Phys. B 794 (2008) 231 [arXiv:0707.1153] [?SPIRE].
9. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, The hexagon Wilson loop and the BDS ansatzfor the six-gluon amplitude, Phys. Lett. B 662 (2008) 456 [arXiv:0712.4138] [?SPIRE].
10. Z. Bern et al., The two-loop six-gluon MHV amplitude in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 78 (2008) 045007 [arXiv:0803.1465] [?SPIRE].
11. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHVamplitude, Nucl. Phys. B 815 (2009) 142 [arXiv:0803.1466] [?SPIRE].
12. Z. Bern, L.J. Dixon and V.A. Smirnov, Iteration ofplanar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D 72 (2005) 085001 [hep-th/0505205] [?SPIRE].
13. J. Bartels, L. Lipatov and A. Sabio Vera, BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes, Phys. Rev. D 80 (2009) 045002 [arXiv:0802.2065] [?SPIRE].
14. V. Del Duca, C. Duhr and V.A. Smirnov, An analytic result for the two-loop hexagon Wilson Loop inΛÍ = 4 SYM, JHEP 03 (2010) 099 [arXiv:0911.5332] [?SPIRE].
15. V. Del Duca, C. Duhr and V.A. Smirnov, The two-loop hexagon Wilson loop ina;? = 4 SYM, JHEP 05 (2010) 084 [arXiv:1003.1702] [?SPIRE].
16. A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical polylogarithms for amplitudes and Wilson loops, Phys. Rev. Lett. 105 (2010) 151605 [arXiv:1006.5703] [?SPIRE].
17. K.T. Chen, Iteratedpath integrals, Bull. Amer. Math. Soc. 83 (1977) 831.
18. F. Brown, Multiple zeta values and periods of moduli spaces M, Ann. Sci. Ecole Norm. Sup. 4 (2009) 42 371 [math/0606419].
19. A.B. Goncharov, A simple construction of Grassmannian polylogarithms, arXiv:0908.2238 .
20. J.M. Drummond and J.M. Henn, Simple loop integrals and amplitudes ina;? = 4 SYM, JHEP 05 (2011) 105 [arXiv:1008.2965] [?SPIRE].
21. L.F. Alday, J.M. Henn, J. Plefka and T. Schuster, Scattering into the fifth dimension of ?=4 super Yang-Mills, JHEP 01 (2010) 077 [arXiv:0908.0684] [?SPIRE].
22. L.J. Dixon, J.M. Drummond and J.M. Henn, Bootstrapping the three-loop hexagon JHEP 11 (2011) 023 [arXiv:1108.4461] [?SPIRE].
23. L.F. Alday, D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, An operatorproduct expansion forpolygonal null Wilson loops, JHEP 04 (2011) 088 [arXiv:1006.2788] [?SPIRE].
24. D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, Bootstrapping null polygon Wilson loops, JHEP 03 (2011) 092 [arXiv:1010.5009] [?SPIRE].
25. D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, Pulling the straps ofpolygons, JHEP 12 (2011) 011 [arXiv:1102.0062] [?SPIRE].
26. C. Anastasiou, A. Brandhuber, P. Heslop, V.V. Khoze, B. Spence and G. Travaglini, Two-loop polygon Wilson loops inM=4 SYM, JHEP 05 (2009) 115 [arXiv:0902.2245] [?SPIRE].
27. A. Brandhuber, P. Heslop, V.V. Khoze and G. Travaglini, Simplicity of polygon Wilson loops inN=4 SYM, JHEP 01 (2010) 050 [arXiv:0910.4898] [INSPIRE].
28. C. Vergu, Higher point MHV amplitudes inN=4 supersymmetric Yang-Mills theory, Phys. Rev. D 79 (2009) 125005 [arXiv:0903.3526] [INSPIRE].
29. N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Local integrals for planar scattering amplitudes, arXiv:1012.6032 [INSPIRE].
30. S. Caron-Huot, Superconformal symmetry and two-loop amplitudes in planarN = 4 super Yang-Mills, arXiv:1105.5606 [INSPIRE].
31. A. Sever and P. Vieira, Multichannel conformal blocks for polygon Wilson loops, arXiv:1105.5748 [INSPIRE].
32. V. Del Duca, C. Duhr and V.A. Smirnov, A two-loop octagon Wilson loop inN=4 SYM, JHEP 09 (2010) 015 [arXiv:1006.4127] [INSPIRE].
33. P. Heslop and V.V. Khoze, Analytic results for MHV Wilson loops, JHEP 11 (2010) 035 [arXiv: 1007.1805] [INSPIRE].
34. L.F. Alday, Some analytic results for two-loop scattering amplitudes, JHEP 07 (2011) 080 [arXiv:1009.1110] [INSPIRE].
35. P. Heslop and V.V. Khoze, Wilson loops @ 3-loops in special kinematics, JHEP 11 (2011) 152 [arXiv:1109.0058] [INSPIRE].
36. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes inN = 4 super-Yang-Mills theory, Nucl. Phys. B 828 (2010) 317 [arXiv: 0807.1095] [INSPIRE].
37. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
38. Z. Bern, V. Del Duca, L.J. Dixon and D.A. Kosower, All non-maximally-helicity-violating one-loop seven-gluon amplitudes inN = 4 super-Yang-Mills theory, Phys. Rev. D 71 (2005) 045006 [hep-th/0410224] [INSPIRE].
39. Y.-t. Huang, N = 4 SYM NMHV loop amplitude in superspace, Phys. Lett. B 631 (2005) 177 [hep-th/0507117] [INSPIRE].
40. K. Risager, S.J. Bidder and W.B. Perkins, One-loop nMHVamplitudes involving gluinos and scalars inN = 4 gauge theory, JHEP 10 (2005) 003 [hep-th/0507170] [INSPIRE].
41. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Generalized unitarity forN = 4 super-amplitudes, arXiv:0808.0491 [INSPIRE].
42. D. Kosower, R. Roiban and C. Vergu, The six-point NMHV amplitude in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 83 (2011) 065018 [arXiv:1009.1376] [INSPIRE].
43. J. Drummond and J. Henn, All tree-level amplitudes inN = 4 SYM, JHEP 04 (2009) 018 [arXiv: 0808. 2475] [INSPIRE].
44. N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A duality for the S matrix, JHEP 03 (2010) 020 [arXiv:0907.5418] [INSPIRE].
45. L. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and Grassmannians, JHEP 11 (2009) 045 [arXiv:0909.0250] [INSPIRE].
46. N. Arkani-Hamed, F. Cachazo and C. Cheung, The Grassmannian origin of dual superconformalinvariance, JHEP 03 (2010) 036 [arXiv:0909.0483] [INSPIRE].
47. G. Korchemsky and E. Sokatchev, Superconformal invariants for scattering amplitudes in N =4 SYMtheory, Nucl. Phys. B 839 (2010) 377 [arXiv:1002.4625] [INSPIRE].
48. J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry ofscattering amplitudes in N =4 super Yang-Mills theory, JHEP 05 (2009) 046 [arXiv:0902.2987] [INSPIRE].
49. G. Korchemsky and E. Sokatchev, Symmetries and analytic properties of scattering amplitudes inN=4 SYMtheory, Nucl. Phys. B 832 (2010) 1 [arXiv:0906.1737] [INSPIRE].
50. L. Mason and D. Skinner, The complete planar S-matrix ofN=4 SYM as a Wilson loop in twistor space, JHEP 12 (2010) 018 [arXiv:1009.2225] [INSPIRE].
51. S. Caron-Huot, Notes on the scattering amplitude/Wilson loop duality, JHEP 07 (2011) 058 [arXiv:1010.1167] [INSPIRE].
52. B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: Part I, arXiv:1103.3714 [INSPIRE].
53. B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: PartII, arXiv:1103.4353 [INSPIRE].
54. A. Belitsky, G. Korchemsky and E. Sokatchev, Are scattering amplitudes dual to super Wilson loops?, Nucl. Phys. B 855 (2012) 333 [arXiv:1103.3008] [INSPIRE].
55. A. Sever, P. Vieira and T. Wang, OPEfor super loops, JHEP 11 (2011) 051 [arXiv:1108.1575] [INSPIRE].
56. J.M. Henn, S. Moch and S.G. Naculich, Form factors and scattering amplitudes inN=4 SYMin dimensional and massive regularizations, arXiv:1109.5057 [INSPIRE].
57. N. Arkani-Hamed, J.L. Bourjaily F. Cachazo, S. Caron-Huot and J. Trnka, The all-loop integrand for scattering amplitudes in planar N = 4 SYM, JHEP 01 (2011) 041 [arXiv: 1008. 2958] [INSPIRE].
58. J.M. Drummond, J.M. Henn and J. Trnka, New differential equations for on-shell loop integrals, JHEP 04 (2011) 083 [arXiv:1010.3679] [INSPIRE].
59. L.J. Dixon, J.M. Drummond and J.M. Henn, The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes inN = 4 SYM, JHEP 06 (2011) 100 [arXiv :1104. 2787] [INSPIRE].
60. V. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett. B 214 (1988) 215 [INSPIRE].
61. G. Georgiou, E. Glover and V.V. Khoze, Non-MHV tree amplitudes in gauge theory, JHEP 07 (2004) 048 [hep-th/0407027] [INSPIRE].
62. N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
63. A. Hodges, Eliminating spurious polesfrom gauge-theoretic amplitudes, arXiv:0905.1473 [INSPIRE].
64. M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [INSPIRE].
65. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [?SPIRE].
66. D.A. Kosower and P. Uwer, One loop splitting amplitudes in gauge theory, Nucl. Phys. B 563 (1999) 477 [hep-ph/9903515] [?SPIRE].
67. V. Del Duca, C. Duhr and V.A. Smirnov, The massless hexagon integral inD = 6 dimensions, Phys. Lett. B 703 (2011) 363 [arXiv:1104.2781] [?SPIRE].
68. A. Kotikov, L. Lipatov, A. Onishchenko and V. Velizhanin, Three loop universal anomalous dimension of the Wilson operators in? = 4 SUSY Yang-Mills model, Phys. Lett. B 595 (2004) 521 [Erratum ibid. B 632 (2006) 754-756] [hep-th/0404092] [?SPIRE].
69. S. Caron-Huot, private communication.
70. E. Remiddi and J. Vermaseren, Harmonic polylogarithms
71. Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [?SPIRE].
72. T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [?SPIRE].
73. T. Gehrmann and E. Remiddi, Numerical evaluation ofharmonic p olylog arithms, Comput. Phys. Commun. 141 (2001) 296 [hep-ph/0107173] [?SPIRE].
74. J.M. Henn, S.G. Naculich, H.J. Schnitzer and M. Spradlin, More loops and legs in Higgs-regulated?=4 SYMamplitudes, JHEP 08 (2010) 002 [arXiv:1004.5381] [?SPIRE].
75. I. Korchemskaya and G. Korchemsky, On lightlike Wilson loops, Phys. Lett. B 287 (1992) 169 [?SPIRE].
76. J.M. Henn, S.G. Naculich, H.J. Schnitzer and M. Spradlin, Higgs-regularized three-loop four-gluon amplitude ina;?=4 SYM: exponentiation and Regge limits, JHEP 04 (2010) 038 [arXiv :1001.1358] [?SPIRE].
77. J.M. Henn, Scattering amplitudes on the Coulomb branch ofa;? = 4 super Yang-Mills, Nucl. Phys. Proc. Suppl. 205-206 (2010) 193 [arXiv:1005.2902] [?SPIRE].
78. M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Commun. 175 (2006) 559 [hep-ph/0511200] [?SPIRE].
79. M. Czakon, MBasymptotics.m, http://projects.hepforge.org/mbtools/.
80. D. Kosower, barnesroutines.m, http://projects.hepforge.org/mbtools/.
81. T. Gehrmann and E. Remiddi, Two loop master integrals for γ?3 jets: the planar topologies, Nucl. Phys. B 601 (2001) 248 [hep-ph/0008287] [?SPIRE].
82. T. Gehrmann and E. Remiddi, Two loop master integrals for γ?3 jets: the nonplanar topologies, Nucl. Phys. B 601 (2001) 287 [hep-ph/0101124] [?SPIRE].
83. D. Mâtre, HPL, a Mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun. 174 (2006) 222, package can be downloaded at http://krone.physik.unizh.ch/-maitreda/HPL/ [hep-ph/0507152] [?SPIRE].
84. V. Smirnov, Feynman integral calculus, Springer Verlag, Heidelberg Germany (2006).