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A surprise in the amplitude/Wilson loop duality

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Abstract

One of the many remarkable features of MHV scattering amplitudes is their conjectured equality to lightlike polygon Wilson loops, which apparently holds at all orders in perturbation theory as well as non-perturbatively. This duality is usually expressed in terms of purely four-dimensional quantities obtained by appropriate subtraction of the IR and UV divergences from amplitudes and Wilson loops respectively. In this paper we demonstrate, by explicit calculation, the completely unanticipated fact that the equality continues to hold at two loops through \( \mathcal{O}\left( \epsilon \right) \) in dimensional regularization for both the four-particle amplitude and the (parity-even part of the) five-particle amplitude.

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References

  1. L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  2. J.M. Drummond, G.P. Korchemsky and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [arXiv:0707.0243] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. A. Brandhuber, P. Heslop and G. Travaglini, MHV Amplitudes in N = 4 super Yang-Mills and Wilson loops, Nucl. Phys. B 794 (2008) 231 [arXiv:0707.1153] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  4. J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, On planar gluon amplitudes/Wilson loops duality, Nucl. Phys. B 795 (2008) 52 [arXiv:0709.2368] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  5. 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, Nucl. Phys. B 826 (2010) 337 [arXiv:0712.1223] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. C. Anastasiou, Z. Bern, L.J. Dixon and D.A. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett. 91 (2003) 251602 [hep-th/0309040] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. F. Cachazo, M. Spradlin and A. Volovich, Iterative structure within the five-particle two-loop amplitude, Phys. Rev. D 74 (2006) 045020 [hep-th/0602228] [SPIRES].

    ADS  Google Scholar 

  8. Z. Bern, M. Czakon, D.A. Kosower, R. Roiban and V.A. Smirnov, Two-loop iteration of five-point N = 4 super-Yang-Mills amplitudes, Phys. Rev. Lett. 97 (2006) 181601 [hep-th/0604074] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. Z. Bern, L.J. Dixon and V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D 72 (2005) 085001 [hep-th/0505205] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  10. M. Spradlin, A. Volovich and C. Wen, Three-loop leading singularities and BDS Ansatz for five particles, Phys. Rev. D 78 (2008) 085025 [arXiv:0808.1054] [SPIRES].

    ADS  Google Scholar 

  11. L.F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT , JHEP 11 (2007) 068 [arXiv:0710.1060] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. 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] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  13. V. Del Duca, C. Duhr and V.A. Smirnov, An analytic result for the two-loop hexagon Wilson loop in N = 4 SYM, JHEP 03 (2010) 099 [arXiv:0911.5332] [SPIRES].

    Article  Google Scholar 

  14. V. Del Duca, C. Duhr and V.A. Smirnov, The two-loop hexagon Wilson loop in N = 4 SYM, JHEP 05 (2010) 084 [arXiv:1003.1702] [SPIRES].

    Article  Google Scholar 

  15. J.-H. Zhang, On the two-loop hexagon Wilson loop remainder function in N = 4 SYM, arXiv:1004.1606 [SPIRES].

  16. J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys. B 828 (2010) 317 [arXiv:0807.1095] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys. B 815 (2009) 142 [arXiv:0803.1466] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S Matrix, Phys. Rev. D 15 (1977) 996 [SPIRES].

    ADS  Google Scholar 

  20. M.T. Grisaru and H.N. Pendleton, Some properties of scattering amplitudes in supersymmetric theories, Nucl. Phys. B 124 (1977) 81 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  21. M.L. Mangano and S.J. Parke, Multi-parton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [SPIRES].

    Article  ADS  Google Scholar 

  22. L.J. Dixon, Calculating scattering amplitudes efficiently, hep-ph/9601359 [SPIRES].

  23. S. Catani, The singular behaviour of QCD amplitudes at two-loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [SPIRES].

    ADS  Google Scholar 

  24. G.F. Sterman and M.E. Tejeda-Yeomans, Multi-loop amplitudes and resummation, Phys. Lett. B 552 (2003) 48 [hep-ph/0210130] [SPIRES].

    ADS  Google Scholar 

  25. D.A. Kosower and P. Uwer, One-loop splitting amplitudes in gauge theory, Nucl. Phys. B 563 (1999) 477 [hep-ph/9903515] [SPIRES].

    Article  ADS  Google Scholar 

  26. Z. Bern, V. Del Duca, W.B. Kilgore and C.R. Schmidt, The infrared behavior of one-loop QCD amplitudes at next-to-next-to-leading order, Phys. Rev. D 60 (1999) 116001 [hep-ph/9903516] [SPIRES].

    ADS  Google Scholar 

  27. F. Cachazo, M. Spradlin and A. Volovich, Leading singularities of the two-loop six-particle MHV amplitude, Phys. Rev. D 78 (2008) 105022 [arXiv:0805.4832] [SPIRES].

    ADS  Google Scholar 

  28. C. Anastasiou et al., Two-loop polygon wilson loops in N = 4 SYM, JHEP 05 (2009) 115 [arXiv:0902.2245] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. J.G.M. Gatheral, Exponentiation of Eikonal cross-sections in nonabelian gauge theories, Phys. Lett. B 133 (1983) 90 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  30. J. Frenkel and J.C. Taylor, Nonabelian Eikonal exponentiation, Nucl. Phys. B 246 (1984) 231 [SPIRES].

    Article  ADS  Google Scholar 

  31. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. 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] [SPIRES].

    Article  ADS  Google Scholar 

  33. I.A. Korchemskaya and G.P. Korchemsky, On lightlike Wilson loops, Phys. Lett. B 287 (1992) 169 [SPIRES].

    ADS  Google Scholar 

  34. P. Heslop and V.V. Khoze, Regular Wilson loops and MHV amplitudes at weak and strong coupling, JHEP 06 (2010) 037 [arXiv:1003.4405] [SPIRES].

    Article  Google Scholar 

  35. M.B. Green, J.H. Schwarz and L. Brink, N = 4 Yang-Mills and N = 8 supergravity as limits of string theories, Nucl. Phys. B 198 (1982) 474 [SPIRES].

    Article  ADS  Google Scholar 

  36. Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated pentagon integrals, Nucl. Phys. B 412 (1994) 751 [hep-ph/9306240] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  37. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One-loop self-dual and N = 4 super Yang-Mills, Phys. Lett. B 394 (1997) 105 [hep-th/9611127] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  38. Z. Bern, J.S. Rozowsky and B. Yan, Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills, Phys. Lett. B 401 (1997) 273 [hep-ph/9702424] [SPIRES].

    ADS  Google Scholar 

  39. Z. Bern, J. Rozowsky and B. Yan, Two-loop N = 4 supersymmetric amplitudes and QCD, hep-ph/9706392 [SPIRES].

  40. M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Commun. 175 (2006) 559 [hep-ph/0511200] [SPIRES].

    Article  ADS  Google Scholar 

  41. A.V. Smirnov and V.A. Smirnov, On the resolution of singularities of multiple Mellin-Barnes integrals, Eur. Phys. J. C 62 (2009) 445 [arXiv:0901.0386] [SPIRES].

    Article  ADS  Google Scholar 

  42. T. Hahn, CUBA: A library for multidimensional numerical integration, Comput. Phys. Commun. 168 (2005) 78 [hep-ph/0404043] [SPIRES].

    Article  ADS  Google Scholar 

  43. D. Maître, HPL, a Mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun. 174 (2006) 222 [hep-ph/0507152] [SPIRES].

    Article  ADS  Google Scholar 

  44. T. Huber and D. Maître, HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters, Comput. Phys. Commun. 175 (2006) 122 [hep-ph/0507094] [SPIRES].

    Article  ADS  Google Scholar 

  45. G. Georgiou, NullWilson loops withaself-crossingandtheWilson loop/amplitude conjecture, JHEP 09 (2009) 021 [arXiv:0904.4675] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. G. Duplancic and B. Nizic, Dimensionally regulated one-loop box scalar integrals with massless internal lines, Eur. Phys. J. C 20 (2001) 357 [hep-ph/0006249] [SPIRES].

    Article  ADS  Google Scholar 

  47. A. Brandhuber, B.J. Spence and G. Travaglini, One-loop gauge theory amplitudes in N = 4 super Yang-Mills from MHV vertices, Nucl. Phys. B 706 (2005) 150 [hep-th/0407214] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  48. A. Brandhuber, B. Spence and G. Travaglini, From trees to loops and back, JHEP 01 (2006) 142 [hep-th/0510253] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Centre for Research in String Theory, Department of Physics, Queen Mary University of London, London, E1 4NS, U.K.

    Andreas Brandhuber, Panagiotis Katsaroumpas, Bill Spence & Gabriele Travaglini

  2. Institute for Particle Physics Phenomenology, Department of Mathematical Sciences and Department of Physics, Durham University, Durham, DH1 3LE, U.K.

    Paul Heslop

  3. Department of Physics, Brown University, Providence, Rhode Island, 02912, U.S.A.

    Dung Nguyen & Marcus Spradlin

Authors
  1. Andreas Brandhuber
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  2. Paul Heslop
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  3. Panagiotis Katsaroumpas
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  4. Dung Nguyen
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  5. Bill Spence
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  6. Marcus Spradlin
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  7. Gabriele Travaglini
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Correspondence to Gabriele Travaglini.

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ArXiv ePrint: 1004.2855

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Brandhuber, A., Heslop, P., Katsaroumpas, P. et al. A surprise in the amplitude/Wilson loop duality. J. High Energ. Phys. 2010, 80 (2010). https://doi.org/10.1007/JHEP07(2010)080

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