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Harmony of super form factors

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Abstract

In this paper we continue our systematic study of form factors of half-BPS operators in \( \mathcal{N} = 4 \) super Yang-Mills. In particular, we extend various on-shell techniques known for amplitudes to the case of form factors, including MHV rules, recursion relations, unitarity and dual MHV rules. As an application, we present the solution of the recursion relation for split-helicity form factors. We then consider form factors of the stress-tensor multiplet operator and of its chiral truncation, and write down supersymmetric Ward identities using chiral as well as non-chiral superspace formalisms. This allows us to obtain compact formulae for families of form factors, such as the maximally non-MHV case. Finally we generalise dual MHV rules in dual momentum space to form factors.

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References

  1. A.H. Mueller, On The Asymptotic Behavior Of The Sudakov Form-Factor, Phys. Rev. D 20 (1979) 2037 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  2. J.C. Collins, Algorithm To Compute Corrections To The Sudakov Form-Factor, Phys. Rev. D 22 (1980) 1478 [SPIRES].

    ADS  Google Scholar 

  3. A. Sen, Asymptotic Behavior of the Sudakov Form-Factor in QCD, Phys. Rev. D 24 (1981) 3281 [SPIRES].

    ADS  Google Scholar 

  4. S. Catani and L. Trentadue, Resummation of the QCD Perturbative Series for Hard Processes, Nucl. Phys. B 327 (1989) 323 [SPIRES].

    Article  ADS  Google Scholar 

  5. L. Magnea and G.F. Sterman, Analytic continuation of the Sudakov form-factor in QCD, Phys. Rev. D 42 (1990) 4222 [SPIRES].

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. G.P. Korchemsky and A.V. Radyushkin, Loop Space Formalism And Renormalization Group For The Infrared Asymptotics Of QCD, Phys. Lett. B 171 (1986) 459 [SPIRES].

    Article  ADS  Google Scholar 

  9. G.P. Korchemsky, Asymptotics of the Altarelli-Parisi-Lipatov Evolution Kernels of Parton Distributions, Mod. Phys. Lett. A 4 (1989) 1257 [SPIRES].

    Article  ADS  Google Scholar 

  10. 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 

  11. L.F. Alday, D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, An Operator Product Expansion for Polygonal null Wilson Loops, JHEP 04 (2011) 088 [arXiv:1006.2788] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. N. Beisert et al., Review of AdS/CFT Integrability: An Overview, arXiv:1012.3982 [SPIRES].

  13. L.F. Alday, D. Gaiotto and J. Maldacena, Thermodynamic Bubble Ansatz, JHEP 09 (2011) 032 [arXiv:0911.4708] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  14. L.F. Alday, J. Maldacena, A. Sever and P. Vieira, Y-system for Scattering Amplitudes, J. Phys. A 43 (2010) 485401 [arXiv:1002.2459] [SPIRES].

    MathSciNet  Google Scholar 

  15. 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 

  16. J. Maldacena and A. Zhiboedov, Form factors at strong coupling via a Y-system, JHEP 11 (2010) 104 [arXiv:1009.1139] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. W.L. van Neerven, Infrared Behavior of On-Shell Form-Factors in a N = 4 Supersymmetric Yang-Mills Field Theory, Z. Phys. C 30 (1986) 595 [SPIRES].

    ADS  Google Scholar 

  18. A. Brandhuber, B. Spence, G. Travaglini and G. Yang, Form Factors in N = 4 Super Yang-Mills and Periodic Wilson Loops, JHEP 01 (2011) 134 [arXiv:1011.1899] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. L.V. Bork, D.I. Kazakov and G.S. Vartanov, On form factors in N = 4 SYM, JHEP 02 (2011) 063 [arXiv:1011.2440] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. M.L. Mangano, S.J. Parke and Z. Xu, Duality and Multi-Gluon Scattering, Nucl. Phys. B 298 (1988) 653 [SPIRES].

    Article  ADS  Google Scholar 

  21. F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [SPIRES].

    Article  ADS  Google Scholar 

  22. R. Britto, F. Cachazo and B. Feng, New Recursion Relations for Tree Amplitudes of Gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. R. Britto, F. Cachazo, B. Feng and E. Witten, Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. P. Mansfield, The Lagrangian origin of MHV rules, JHEP 03 (2006) 037 [hep-th/0511264] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press, Cambridge U.K. (1995).

    Book  Google Scholar 

  26. R. Britto, B. Feng, R. Roiban, M. Spradlin and A. Volovich, All split helicity tree-level gluon amplitudes, Phys. Rev. D 71 (2005) 105017 [hep-th/0503198] [SPIRES].

    ADS  Google Scholar 

  27. A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav. 1 (1984) 469 [SPIRES].

    Article  ADS  Google Scholar 

  28. A. Galperin, E. Ivanov, V. Ogievetsky and E. Sokatchev, Harmonic Superspace, Cambridge University Press, Cambridge U.K. (2001)

    Book  MATH  Google Scholar 

  29. B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: Part I, arXiv:1103.3714 [SPIRES].

  30. B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: Part II, arXiv:1103.4353 [SPIRES].

  31. V.P. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett. B 214 (1988) 215 [SPIRES].

    Article  ADS  Google Scholar 

  32. 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 

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

    MathSciNet  ADS  Google Scholar 

  34. A. Brandhuber, P. Heslop and G. Travaglini, MHV Amplitudes in N = 4 Super Yang-Mills and W ilson Loops, Nucl. Phys. B 794 (2008) 231 [arXiv:0707.1153] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  35. A. Brandhuber, B. Spence and G. Travaglini, Tree-Level Formalism, arXiv:1103.3477 [SPIRES].

  36. 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 

  37. E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. 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 

  39. 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 

  40. 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 

  41. H. Elvang, D.Z. Freedman and M. Kiermaier, SUSY Ward identities, Superamplitudes and Counterterms, arXiv:1012.3401 [SPIRES].

  42. K.A. Intriligator, Bonus symmetries of N = 4 super-Yang-Mills correlation functions via AdS duality, Nucl. Phys. B 551 (1999) 575 [hep-th/9811047] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. B. Eden, P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Extremal correlators in four-dimensional SCFT, Phys. Lett. B 472 (2000) 323 [hep-th/9910150] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  44. B. Eden, C. Schubert and E. Sokatchev, Three-loop four-point correlator in N = 4 SYM, Phys. Lett. B 482 (2000) 309 [hep-th/0003096] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. L.J. Dixon, E.W.N. Glover and V.V. Khoze, MHV rules for Higgs plus multi-gluon amplitudes, JHEP 12 (2004) 015 [hep-th/0411092] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. Y.-t. Huang, Non-Chiral S-matrix of N = 4 Super Yang-Mills, arXiv:1104.2021 [SPIRES].

  47. 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 

  48. 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 

  49. Z. Bern, L.J. Dixon and D.A. Kosower, Two-Loop g → gg Splitting Amplitudes in QCD, JHEP 08 (2004) 012 [hep-ph/0404293] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  50. R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  51. H. Elvang, D.Z. Freedman and M. Kiermaier, Proof of the MHV vertex expansion for all tree amplitudes in N = 4 SYM theory, JHEP 06 (2009) 068 [arXiv:0811.3624] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  52. A. Brandhuber, P. Heslop and G. Travaglini, A note on dual superconformal symmetry of the N = 4 super Yang-Mills S-matrix, Phys. Rev. D 78 (2008) 125005 [arXiv:0807.4097] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  53. N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  54. L.J. Mason and D. Skinner, The Complete Planar S-matrix of N = 4 SYM as a Wilson Loop in Twistor Space, JHEP 12 (2010) 018 [arXiv:1009.2225] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  55. M. Bullimore, L.J. Mason and D. Skinner, MHV Diagrams in Momentum Twistor Space, JHEP 12 (2010) 032 [arXiv:1009.1854] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  56. A. Brandhuber, B. Spence, G. Travaglini and G. Yang, A Note on Dual MHV Diagrams in N = 4 SYM, JHEP 12 (2010) 087 [arXiv:1010.1498] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  57. 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 

  58. A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473 [SPIRES].

  59. 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 

  60. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom

    A. Brandhuber, Ö. Gürdoğan, R. Mooney, G. Travaglini & G. Yang

  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, U.S.A.

    A. Brandhuber & G. Travaglini

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  1. A. Brandhuber
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  2. Ö. Gürdoğan
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  3. R. Mooney
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  4. G. Travaglini
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  5. G. Yang
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Correspondence to G. Yang.

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ArXiv ePrint: 1107.5067

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Brandhuber, A., Gürdoğan, Ö., Mooney, R. et al. Harmony of super form factors. J. High Energ. Phys. 2011, 46 (2011). https://doi.org/10.1007/JHEP10(2011)046

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