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Five-point amplitudes in N=4 super-Yang-Mills theory and N=8 supergravity

John Joseph M. Carrasco1,* and Henrik Johansson2,†

  • 1Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305-4060, USA
  • 2Institut de Physique Théorique, CEA-Saclay, F–91191 Gif-sur-Yvette cedex, France

  • *jjmc@stanford.edu
  • †henrik.johansson@cea.fr
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Phys. Rev. D 85, 025006 – Published 13 January, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.025006

Abstract

We present the complete integrands of five-point superamplitudes in N=4 super-Yang-Mills theory and N=8 supergravity, at one and two loops, for four-dimensional external states and D-dimensional internal kinematics. For N=4 super-Yang-Mills theory we give the amplitudes for general gauge group—including all nonplanar contributions. The results are constructed using integral diagrams that manifestly satisfy the conjectured duality between color and kinematics, providing additional nontrivial evidence in favor of the duality for multipoint and multiloop amplitudes. We determine the ultraviolet poles by integrating the amplitudes in the dimensions where logarithmic divergences first occur. We introduce new kinematic prefactors which offer a convenient decomposition of the external state structure of the nonplanar five-point amplitudes in the maximally supersymmetric theories to all loop orders.

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References (60)

  1. J. M. Drummond, J. Henn, V. A. Smirnov, and E. Sokatchev, J. High Energy Phys. 01 (2007) 064; Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower, and V. A. Smirnov, Phys. Rev. D 75, 085010 (2007).
  2. J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, Nucl. Phys. B828, 317 (2010); A. Brandhuber, P. Heslop, and G. Travaglini, Phys. Rev. D 78, 125005 (2008).
  3. E. Witten, Commun. Math. Phys. 252, 189 (2004).
  4. N. Arkani-Hamed, F. Cachazo, C. Cheung, and J. Kaplan, J. High Energy Phys. 03 (2010) 020; L. J. Mason and D. Skinner, 11 (2009) 045; N. Arkani-Hamed, F. Cachazo, and C. Cheung, 03 (2010) 036.
  5. Z. Bern, J. J. M. Carrasco, and H. Johansson, Phys. Rev. D 78, 085011 (2008).
  6. Z. Bern, J. J. M. Carrasco, and H. Johansson, Phys. Rev. Lett. 105, 061602 (2010).
  7. N. E. J. Bjerrum-Bohr, P. H. Damgaard, and P. Vanhove, Phys. Rev. Lett. 103, 161602 (2009); S. Stieberger, arXiv:0907.2211.
  8. B. Feng, R. Huang, and Y. Jia, Phys. Lett. B 695, 350 (2011); Y. X. Chen, Y. J. Du, and B. Feng, J. High Energy Phys. 02 (2011) 112.
  9. Z. Bern, J. J. M. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban (unpublished).
  10. Z. Bern, T. Dennen, Y. t. Huang, and M. Kiermaier, Phys. Rev. D 82, 065003 (2010).
  11. H. Kawai, D. C. Lewellen, and S. H. H. Tye, Nucl. Phys. B269, 1 (1986); Z. Bern, Living Rev. Relativity 5, 5 (2002), http://www.livingreviews.org/lrr-2002-5.
  12. N. E. J. Bjerrum-Bohr, P. H. Damgaard, T. Sondergaard, and P. Vanhove, J. High Energy Phys. 06 (2010) 003; C. R. Mafra, 11 (2010) 096.
  13. S. H. Henry Tye and Y. Zhang, J. High Energy Phys. 06 (2010) 071.
  14. M. Kiermaier, Amplitudes 2010, Queen Mary, University of London, http://www.strings.ph.qmul.ac.uk/~theory/Amplitudes2010/Talks/MK2010.pdf.
  15. N. E. J. Bjerrum-Bohr, P. H. Damgaard, T. Sondergaard, and P. Vanhove, J. High Energy Phys. 01 (2011) 001.
  16. B. Feng, R. Huang, and Y. Jia, Phys. Lett. B 695, 350 (2011).
  17. R. Monteiro and D. O’Connell, J. High Energy Phys. 07 (2011) 007.
  18. C. R. Mafra, O. Schlotterer, and S. Stieberger, J. High Energy Phys. 07 (2011) 092.
  19. T. Sondergaard, Nucl. Phys. B821, 417 (2009); C. R. Mafra, J. High Energy Phys. 01 (2010) 007; P. Vanhove, arXiv:1004.1392; Y. Jia, R. Huang, and C. Y. Liu, Phys. Rev. D 82, 065001 (2010); N. E. J. Bjerrum-Bohr, P. H. Damgaard, B. Feng, and T. Sondergaard, 82, 107702 (2010); Phys. Lett. B 691, 268 (2010); B. Feng and S. He, J. High Energy Phys. 09 (2010) 043; N. E. J. Bjerrum-Bohr, P. H. Damgaard, B. Feng, and T. Sondergaard, 09 (2010) 067; D. Vaman and Y. P. Yao, 11 (2010) 028; C. R. Mafra, arXiv:1007.4999; B. Feng, S. He, R. Huang, and Y. Jia, J. High Energy Phys. 10 (2010) 109; Y. Abe, Nucl. Phys. B842, 475 (2011); J. Bjornsson, J. High Energy Phys. 01 (2011) 002; J. H. Huang, R. Huang, and Y. Jia, J. Phys. A 44, 425401 (2011); C. R. Mafra, O. Schlotterer, S. Stieberger, and D. Tsimpis, Nucl. Phys. B846, 359 (2011); H. Nastase and H. J. Schnitzer, J. High Energy Phys. 01 (2011) 048; J. Broedel and R. Kallosh, 06 (2011) 024; N. E. J. Bjerrum-Bohr, P. H. Damgaard, H. Johansson, and T. Sondergaard, 05 (2011) 039; Y. J. Du, B. Feng, and C. H. Fu, 08 (2011) 129; C. R. Mafra, O. Schlotterer, and S. Stieberger, arXiv:1106.2645.
  20. Z. Bern and T. Dennen, Phys. Rev. Lett. 107, 081601 (2011).
  21. J. J. M. Carrasco and H. Johansson (unpublished).
  22. Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, Nucl. Phys. B425, 217 (1994).
  23. J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, arXiv:0808.0491.
  24. Z. Bern, M. Czakon, D. A. Kosower, R. Roiban, and V. A. Smirnov, Phys. Rev. Lett. 97, 181601 (2006).
  25. F. Cachazo, arXiv:0803.1988.
  26. M. Spradlin, A. Volovich, and C. Wen, Phys. Rev. D 78, 085025 (2008).
  27. Z. Bern, J. S. Rozowsky, and B. Yan, Phys. Lett. B 401, 273 (1997).
  28. Z. Bern, J. J. M. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, Phys. Rev. D 78, 105019 (2008).
  29. Z. Bern, J. J. M. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, Phys. Rev. D 82, 125040 (2010).
  30. Z. Bern, L. J. Dixon, M. Perelstein, and J. S. Rozowsky, Nucl. Phys. B546, 423 (1999).
  31. Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, Fortschr. Phys. 59, 561 (2011); L. J. Dixon, arXiv:1005.2703; Z. Bern, J. J. M. Carrasco, and H. Johansson, arXiv:0902.3765.
  32. M. B. Green, J. G. Russo, and P. Vanhove, J. High Energy Phys. 06 (2010) 075.
  33. H. Elvang, D. Z. Freedman, and M. Kiermaier, J. Phys. A 44, 454009 (2011); N. Beisert, H. Elvang, D. Z. Freedman, M. Kiermaier, A. Morales, and S. Stieberger, Phys. Lett. B 694, 265 (2010); H. Elvang, D. Z. Freedman, and M. Kiermaier, J. High Energy Phys. 11 (2010) 016.
  34. G. Bossard, C. Hillmann, and H. Nicolai, J. High Energy Phys. 12 (2010) 052; R. Kallosh, arXiv:1103.4115; G. Bossard and H. Nicolai, J. High Energy Phys. 08 (2011) 074.
  35. P. S. Howe and K. S. Stelle, Phys. Lett. B 554, 190 (2003).
  36. Z. Bern, L. J. Dixon, and R. Roiban, Phys. Lett. B 644, 265 (2007).
  37. Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson, D. A. Kosower, and R. Roiban, Phys. Rev. Lett. 98, 161303 (2007).
  38. Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, Phys. Rev. Lett. 103, 081301 (2009).
  39. J. Bjornsson and M. B. Green, J. High Energy Phys. 08 (2010) 132.
  40. G. Bossard, P. S. Howe, K. S. Stelle, and P. Vanhove, Classical Quantum Gravity 28, 215005 (2011); G. Bossard, P. S. Howe, and K. S. Stelle, J. High Energy Phys. 01 (2011) 020.
  41. R. Kallosh and P. Ramond, arXiv:1006.4684; R. Kallosh, Phys. Rev. D 80, 105022 (2009).
  42. M. B. Green, J. H. Schwarz, and L. Brink, Nucl. Phys. B198, 474 (1982).
  43. N. Marcus and A. Sagnotti, Nucl. Phys. B256, 77 (1985).
  44. Z. Bern, L. J. Dixon, D. C. Dunbar, M. Perelstein, and J. S. Rozowsky, Nucl. Phys. B530, 401 (1998).
  45. Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, Nucl. Phys. B425, 217 (1994); B435, 59 (1995).
  46. Z. Bern, L. J. Dixon, and D. A. Kosower, Nucl. Phys. B513, 3 (1998).
  47. Z. Bern, V. Del Duca, L. J. Dixon and D. A. Kosower, Phys. Rev. D 71, 045006 (2005).
  48. R. Britto, F. Cachazo, and B. Feng, Nucl. Phys. B725, 275 (2005).
  49. Z. Bern and Y. t. Huang, J. Phys. A 44, 454003 (2011).
  50. L. J. Dixon, J. Phys. A 44, 454001 (2011).
  51. J. J. M. Carrasco and H. Johansson, J. Phys. A 44, 454004 (2011).
  52. R. Britto, J. Phys. A 44, 454006 (2011).
  53. Z. Bern, J. J. M. Carrasco, and H. Johansson, Nucl. Phys. B, Proc. Suppl. 205-206, 54 (2010).
  54. Z. Bern, J. J. M. Carrasco, H. Ita, H. Johansson, and R. Roiban, Phys. Rev. D 80, 065029 (2009).
  55. J. Brödel and J. J. M. Carrasco, Phys. Rev. D 84, 085009 (2011).
  56. Z. Bern, J. J. M. Carrasco, H. Johansson, and D. A. Kosower, Phys. Rev. D 76, 125020 (2007).
  57. Z. Bern and A. G. Morgan, Nucl. Phys. B467, 479 (1996).
  58. Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, Phys. Lett. B 394, 105 (1997).
  59. D. Binosi and L. Theussl, Comput. Phys. Commun. 161, 76 (2004); D. Binosi, J. Collins, C. Kaufhold, and L. Theussl, 180, 1709 (2009).
  60. J. A. M. Vermaseren, Comput. Phys. Commun. 83, 45 (1994).

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Phys. Rev. D 85, 025006– Published 13 January, 2012
  • Received 4 July 2011
Article part of CHORUS

© 2012 American Physical Society

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