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Advances in High Energy Physics
Volume 2011 (2011), Article ID 190587, 39 pages
http://dx.doi.org/10.1155/2011/190587
Review Article

Applications of Subleading-Color Amplitudes in N=4 SYM Theory

1Department of Physics and Astronomy, Bowdoin College, Brunswick, ME 04011, USA
2Instituto de Física Teórica, Universidade Estadual Paulista (UNESP), R. Dr. Bento T. Ferraz 271, Bl. II, 01140-070 Sao Paulo, SP, Brazil
3Theoretical Physics Group, Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02454, USA

Received 14 June 2011; Accepted 9 October 2011

Academic Editor: Anastasios Petkou

Copyright © 2011 Stephen G. Naculich et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Witten, “Perturbative gauge theory as a string theory in twistor space,” Communications in Mathematical Physics, vol. 252, no. 1-3, pp. 189–258, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. F. Cachazo, P. Svrcek, and E. Witten, “MHV vertices and tree amplitudes in gauge theory,” Journal of High Energy Physics, vol. 8, no. 9, pp. 111–131, 2004. View at Google Scholar · View at Scopus
  3. R. Britto, F. Cachazo, and B. Feng, “Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills,” Nuclear Physics B, vol. 725, no. 1-2, pp. 275–305, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. R. Britto, F. Cachazo, and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nuclear Physics B, vol. 715, no. 1-2, pp. 499–522, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct proof of the tree-level scattering amplitude recursion relation in Yang-Mills theory,” Physical Review Letters, vol. 94, no. 18, Article ID 181602, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. A. P. Hodges, “Twistor diagram recursion forall gauge-theoretic tree amplitudes,” http://arxiv.org/abs/hep-th/0503060.
  7. Z. Bern, L. J. Dixon, and V. A. Smirnov, “Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond,” Physical Review D, vol. 72, no. 8, pp. 1–27, 2005. View at Publisher · View at Google Scholar · View at Scopus
  8. A. P. Hodges, “Twistor diagrams for all tree amplitudes in gauge theory: a helicity-independent formalism,” http://arxiv.org/abs/hep-th/0512336.
  9. A. P. Hodges, “Scattering amplitudes for eight gauge fields,” http://arxiv.org/abs/hep-th/0603101.
  10. L. F. Alday and J. Maldacena, “Gluon scattering amplitudes at strong coupling,” Journal of High Energy Physics, vol. 2007, no. 6, article no. 064, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. J. M. Drummond, G. P. Korchemsky, and E. Sokatchev, “Conformal properties of four-gluon planar amplitudes and Wilson loops,” Nuclear Physics B, vol. 795, no. 1-2, pp. 385–408, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. A. Brandhuber, P. Heslop, and G. Travaglini, “MHV amplitudes in N = 4 super-Yang-Mills and Wilson Loops,” Nuclear Physics B, vol. 794, no. 1-2, pp. 231–243, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, “On planar gluon amplitudes/Wilson loops duality,” Nuclear Physics B, vol. 795, no. 1-2, pp. 52–68, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, “Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes,” Nuclear Physics B, vol. 826, no. 1, pp. 337–364, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. N. Arkani-Hamed, F. Cachazo, and J. Kaplan, “What is the simplest quantum field theory?” Journal of High Energy Physics, vol. 9, no. 16, 2010. View at Google Scholar
  16. J. M. Drummond and J. M. Henn, “All tree-level amplitudes in N=4 SYM,” Journal of High Energy Physics, vol. 4, no. 18, 2009. View at Google Scholar
  17. A. Hodges, “Eliminating spurious poles from gauge-theoretic amplitudes,” http://arxiv.org/abs/0905.1473.
  18. N. Arkani-Hamed, F. Cachazo, C. Cheung, and J. Kaplan, “A duality for the S matrix,” Journal of High Energy Physics, vol. 3, 2010. View at Google Scholar
  19. N. Arkani-Hamed, F. Cachazo, and C. Cheung, “The grassmannian origin Of dual superconformal invariance,” Journal of High Energy Physics, vol. 3, no. 36, 2010. View at Google Scholar
  20. A. Hodges, “The box integrals in momentum-twistor geometry,” http://arxiv.org/abs/1004.3323.
  21. M. Bullimore, L. Mason, and D. Skinner, “MHV diagrams in momentum twistor space,” Journal of High Energy Physics, vol. 2010, no. 12, 2010. View at Publisher · View at Google Scholar
  22. L. Mason and D. Skinner, “The complete planar S-matrix of N = 4 SYM as a Wilson loop in twistor space,” Journal of High Energy Physics, vol. 12, 2010. View at Publisher · View at Google Scholar
  23. N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, and J. Trnka, “Local integrals for planar scattering amplitudes,” http://arxiv.org/abs/1012.6032.
  24. L. J. Dixon, “Scattering amplitudes: the most perfect microscopic structures in the universe,” Journal of Physics A, vol. 44, Article ID 454001, 2011. View at Google Scholar
  25. S. Catani and M. H. Seymour, “The dipole formalism for the calculation of QCD jet cross sections at next-to-leading order,” Physics Letters, Section B, vol. 378, no. 1-4, pp. 287–301, 1996. View at Publisher · View at Google Scholar · View at Scopus
  26. S. Catani, “The singular behaviour of QCD amplitudes at two-loop order,” Physics Letters, Section B, vol. 427, no. 1-2, pp. 161–171, 1998. View at Publisher · View at Google Scholar · View at Scopus
  27. G. Sterman and M. E. Tejeda-Yeomans, “Multi-loop amplitudes and resummation,” Physics Letters, Section B, vol. 552, no. 1-2, pp. 48–56, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  28. S. M. Aybat, L. J. Dixon, and G. Sterman, “The two-loop anomalous dimension matrix for soft gluon exchange,” Physical Review Letters, vol. 74, no. 7, 2006. View at Publisher · View at Google Scholar
  29. S. M. Aybat, L. J. Dixon, and G. Sterman, “Two-loop soft anomalous dimension matrix and resummation at next-to-next-to-leading poles,” Physical Review D, vol. 74, no. 7, Article ID 074004, 2006. View at Publisher · View at Google Scholar · View at Scopus
  30. T. Becher and M. Neubert, “Infrared singularities of scattering amplitudes in perturbative QCD,” Physical Review Letters, vol. 102, no. 16, Article ID 162001, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. E. Gardi and L. Magnea, “Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes,” Journal of High Energy Physics, vol. 2009, no. 3, 2009. View at Publisher · View at Google Scholar
  32. L. J. Dixon, “Matter dependence of the three-loop soft-anomalous-dimension matrix,” Physical Review D, vol. 79, no. 9, 2009. View at Publisher · View at Google Scholar
  33. T. Becher and M. Neubert, “On the structure of infrared singularities of gauge-theory amplitudes,” Journal of High Energy Physics, vol. 6, 2009. View at Publisher · View at Google Scholar
  34. M. B. Green, J. H. Schwarz, and L. Brink, “N = 4 Yang-Mills and N = 8 supergravity as limits of string theories,” Nuclear Physics, Section B, vol. 198, no. 3, pp. 474–492, 1982. View at Google Scholar · View at Scopus
  35. F. A. Berends, W. T. Giele, and H. Kuijf, “On relations between multi-gluon and multi-graviton scattering,” Physics Letters B, vol. 211, no. 1-2, pp. 91–94, 1988. View at Publisher · View at Google Scholar · View at Scopus
  36. Z. Bern, L. Dixon, D. C. Dunbar, M. Perelstein, and J. S. Rozowsky, “On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences,” Nuclear Physics B, vol. 530, no. 1-2, pp. 401–456, 1998. View at Publisher · View at Google Scholar · View at Scopus
  37. Z. Bern, L. Dixon, M. Perelstein, and J. S. Rozowsky, “Multi-leg one-loop gravity amplitudes from gauge theory,” Nuclear Physics B, vol. 546, no. 1-2, pp. 423–479, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  38. N. E. J. Bjerrum-Bohr, D. C. Dunbar, and H. Ita, “Similarities of gauge and gravity amplitudes,” http://arxiv.org/abs/hep-th/0608007. View at Publisher · View at Google Scholar
  39. S. G. Naculich, H. Nastase, and H. J. Schnitzer, “Two-loop graviton scattering relation and IR behavior in N = 8 supergravity,” Nuclear Physics B, vol. 805, no. 1-2, pp. 40–58, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  40. Z. Bern, J. J. M. Carrasco, and H. Johansson, “New relations for gauge-theory amplitudes,” Physical Review D, vol. 78, no. 8, Article ID 085011, 2008. View at Publisher · View at Google Scholar · View at Scopus
  41. S. G. Naculich, H. Nastase, and H. J. Schnitzer, “Subleading-color contributions to gluon-gluon scattering in N = 4 SYM theory and relations to N = 8 supergravity,” Journal of High Energy Physics, vol. 11, 2008. View at Publisher · View at Google Scholar
  42. Z. Bern, J. J. M. Carrasco, and H. Johansson, “Perturbative quantum gravity as a double copy of gauge theory,” Physical Review Letters, vol. 105, no. 6, Article ID 061602, 2010. View at Publisher · View at Google Scholar · View at Scopus
  43. Z. Bern, T. Dennen, Y.-T. Huang, and M. Kiermaier, “Gravity as the square of gauge theory,” Physical Review D, vol. 82, no. 6, 2010. View at Publisher · View at Google Scholar
  44. N. E.J. Bjerrum-Bohr, P. H. Damgaard, B. Feng, and T. Søndergaard, “Gravity and Yang-Mills amplitude relations,” Physical Review D, vol. 82, no. 10, 2010. View at Publisher · View at Google Scholar
  45. N. E. J. Bjerrum-Bohr, P. H. Damgaard, B. Feng, and T. Søndergaard, “Proof of gravity and Yang-Mills amplitude relations,” Journal of High Energy Physics, no. 9, p. 067, 18, 2010. View at Google Scholar
  46. N. E. J. Bjerrum-Bohr, P. H. Damgaard, T. Søndergaard, and P. Vanhove, “The momentum kernel of gauge and gravity theories,” Journal of High Energy Physics, vol. 1, 2011. View at Google Scholar · View at Zentralblatt MATH
  47. R. Kleiss and H. Kuijf, “Multigluon cross sections and 5-jet production at hadron colliders,” Nuclear Physics, Section B, vol. 312, no. 3, pp. 616–644, 1989. View at Google Scholar · View at Scopus
  48. E. W. N. Glover, C. Oleari, and M. E. Tejeda-Yeomans, “Two-loop QCD corrections to gluon-gluon scatteringstar sign,” Nuclear Physics B, vol. 605, no. 1–3, pp. 467–485, 2001. View at Publisher · View at Google Scholar · View at Scopus
  49. S. G. Naculich and H. J. Schnitzer, “IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM theory,” Journal of High Energy Physics, vol. 10, 2009. View at Publisher · View at Google Scholar
  50. Z. Bern, J. J.M. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, “Manifest ultraviolet behavior for the three-loop four-point amplitude of N=8 supergravity,” Physical Review D, vol. 78, no. 10, 2008. View at Publisher · View at Google Scholar
  51. A. Armoni, “Anomalous dimensions from a spinning D5-brane,” Journal of High Energy Physics, vol. 11, 2006. View at Publisher · View at Google Scholar · View at Scopus
  52. L. F. Alday and J. Maldacena, “Comments on operators with large spin,” Journal of High Energy Physics, vol. 11, 2007. View at Publisher · View at Google Scholar
  53. M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory. Vol. 1, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1987.
  54. Z. Bern, J. S. Rozowsky, and B. Yan, “Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills,” Physics Letters, Section B, vol. 401, no. 3-4, pp. 273–282, 1997. View at Publisher · View at Google Scholar · View at Scopus
  55. V. A. Smirnov, “Analytical result for dimensionally regularized massless on-shell double box,” Physics Letters, Section B, vol. 460, no. 3-4, pp. 397–404, 1999. View at Publisher · View at Google Scholar · View at Scopus
  56. J. B. Tausk, “Non-planar massless two-loop Feynman diagrams with four on-shell legs,” Physics Letters, Section B, vol. 469, no. 1–4, pp. 225–234, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  57. Z. Bern and D. A. Kosower, “Color decomposition of one-loop amplitudes in gauge theories,” Nuclear Physics B, vol. 362, no. 1-2, pp. 389–448, 1991. View at Publisher · View at Google Scholar · View at Scopus
  58. A. Brandhuber, P. Heslop, A. Nasti, B. Spence, and G. Travaglini, “Four-point amplitudes in N = 8 supergravity and Wilson loops,” Nuclear Physics B, vol. 807, no. 1-2, pp. 290–314, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  59. Z. Bern, A. De Freitas, and L. Dixon, “Two-loop helicity amplitudes for gluon-gluon scattering in QCD and supersymmetric Yang-Mills theory,” Journal of High Energy Physics, vol. 3, pp. 287–343, 2002. View at Google Scholar · View at Scopus
  60. C. Anastasiou, L. Dixon, Z. Bern, and D. A. Kosower, “Planar amplitudes in Maximally supersymmetric Yang-Mills theory,” Physical Review Letters, vol. 91, no. 25, pp. 2516021–2516024, 2003. View at Google Scholar · View at Scopus
  61. D. Vaman and Y. P. Yao, “Constraints and generalized gauge transformations on tree-level gluon and graviton amplitudes,” Journal of High Energy Physics, vol. 11, 2010. View at Publisher · View at Google Scholar · View at Scopus
  62. Z. Bern, L. J. Dixon, and R. Roiban, “Is N = 8 supergravity ultraviolet finite?” Physics Letters, Section B, vol. 644, no. 4, pp. 265–271, 2007. View at Publisher · View at Google Scholar · View at Scopus
  63. H. Kawai, D. C. Lewellen, and S. H. H. Tye, “A relation between tree amplitudes of closed and open strings,” Nuclear Physics, Section B, vol. 269, no. 1, pp. 1–23, 1986. View at Google Scholar · View at Scopus
  64. S. Weinberg, “Infrared photons and gravitons,” Physical Review, vol. 140, no. 2B, pp. B516–B524, 1965. View at Publisher · View at Google Scholar · View at Scopus
  65. S. G. Naculich and H. J. Schnitzer, “Eikonal methods applied to gravitational scattering amplitudes,” Journal of High Energy Physics, vol. 1105, no. 087, 2011. View at Google Scholar
  66. H. Elvang and D. Z. Freedman, “Note on graviton MHV amplitudes,” Journal of High Energy Physics, vol. 5, 2008. View at Publisher · View at Google Scholar · View at Scopus
  67. S. Ananth and S. Theisen, “KLT relations from the Einstein-Hilbert Lagrangian,” Physics Letters, Section B, vol. 652, no. 2-3, pp. 128–134, 2007. View at Publisher · View at Google Scholar · View at Scopus
  68. B. Feng and S. He, “KLT and new relations for N = 8 SUGRA and N = 4 SYM,” Journal of High Energy Physics, vol. 2010, no. 9, 2010. View at Publisher · View at Google Scholar
  69. Z. Bern, L. Dixon, D. C. Dunbar, and D. A. Kosower, “One-loop n-point gauge theory amplitudes, unitarity and collinear limits,” Nuclear Physics B, vol. 425, no. 1-2, pp. 217–260, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  70. Z. Bern, L. Dixon, D. C. Dunbar, and D. A. Kosower, “One-loop self-dual and N = 4 super Yang-Mills,” Physics Letters, Section B, vol. 394, no. 1-2, pp. 105–115, 1997. View at Publisher · View at Google Scholar · View at Scopus
  71. N. E. J. Bjerrum-Bohr, P. H. Damgaard, B. Feng, and T. Søndergaard, “New identities among gauge theory amplitudes,” Physics Letters, Section B, vol. 691, no. 5, pp. 268–273, 2010. View at Publisher · View at Google Scholar · View at Scopus
  72. B. Feng, S. He, R. Huang, and Y. Jia, “Note on new KLT relations,” Journal of High Energy Physics, vol. 10, 2010. View at Publisher · View at Google Scholar
  73. S. H. H. Tye and Y. Zhang, “Dual identities inside the gluon and the graviton scattering amplitudes,” Journal of High Energy Physics, vol. 2010, no. 6, 2010. View at Publisher · View at Google Scholar · View at Scopus
  74. H. Elvang and M. Kiermaier, “Stringy KLT relations, global symmetries, and E7(7)-violation,” Journal of High Energy Physics, vol. 10, 2010. View at Publisher · View at Google Scholar · View at Scopus
  75. H. Nastase and H. J. Schnitzer, “On KLT and SYM-supergravity relations from 5-point 1-loop amplitudes,” Journal of High Energy Physics, vol. 1, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  76. Z. Bern and D. A. Kosower, “The computation of loop amplitudes in gauge theories,” Nuclear Physics B, vol. 379, no. 3, pp. 451–561, 1992. View at Publisher · View at Google Scholar · View at Scopus
  77. D. C. Dunbar and P. S. Norridge, “Infinities within graviton scattering amplitudes,” Classical and Quantum Gravity, vol. 14, no. 2, pp. 351–365, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  78. S. J. Parke and T. R. Taylor, “Amplitude for n-Gluon scattering,” Physical Review Letters, vol. 56, no. 23, pp. 2459–2460, 1986. View at Publisher · View at Google Scholar · View at Scopus
  79. L. Mason and D. Skinner, “Amplitudes at weak coupling as polytopes in AdS5,” Journal of Physics A, vol. 44, no. 13, 2011. View at Publisher · View at Google Scholar
  80. H. Nastase and H. J. Schnitzer, “Twistor and polytope interpretations for subleading color one-loop amplitudes,” Nuclear Physics B, vol. 855, p. 901, 2012. View at Google Scholar
  81. Z. Bern, L. Dixon, D. C. Dunbar, and D. A. Kosower, “Fusing gauge theory tree amplitudes into loop amplitudes,” Nuclear Physics B, vol. 435, no. 1-2, pp. 59–101, 1995. View at Publisher · View at Google Scholar · View at Scopus
  82. V. P. Nair, “A current algebra for some gauge theory amplitudes,” Physics Letters B, vol. 214, no. 2, pp. 215–218, 1988. View at Publisher · View at Google Scholar · View at Scopus
  83. F. A. Berends and W. T. Giele, “Recursive calculations for processes with n gluons,” Nuclear Physics, Section B, vol. 306, no. 4, pp. 759–808, 1988. View at Google Scholar · View at Scopus
  84. D. A. Kosower, R. Roiban, and C. Vergu, “The six-point NMHV amplitude in maximally supersymmetric Yang-Mills theory,” Physical Review D, vol. 83, 2011. View at Google Scholar
  85. J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, “Generalized unitarity for N=4 super-amplitudes,” http://arxiv.org/abs/0808.0491.