Harmony of super form factors

  • A. Brandhuber
  • Ö. Gürdoğan
  • R. Mooney
  • G. Travaglini
  • G. Yang
Article

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.

Keywords

Supersymmetric gauge theory Extended Supersymmetry Duality in Gauge Field Theories Gauge Symmetry 

References

  1. [1]
    A.H. Mueller, On The Asymptotic Behavior Of The Sudakov Form-Factor, Phys. Rev. D 20 (1979) 2037 [SPIRES].MathSciNetADSGoogle Scholar
  2. [2]
    J.C. Collins, Algorithm To Compute Corrections To The Sudakov Form-Factor, Phys. Rev. D 22 (1980) 1478 [SPIRES].ADSGoogle Scholar
  3. [3]
    A. Sen, Asymptotic Behavior of the Sudakov Form-Factor in QCD, Phys. Rev. D 24 (1981) 3281 [SPIRES].ADSGoogle Scholar
  4. [4]
    S. Catani and L. Trentadue, Resummation of the QCD Perturbative Series for Hard Processes, Nucl. Phys. B 327 (1989) 323 [SPIRES].ADSCrossRefGoogle Scholar
  5. [5]
    L. Magnea and G.F. Sterman, Analytic continuation of the Sudakov form-factor in QCD, Phys. Rev. D 42 (1990) 4222 [SPIRES].ADSGoogle Scholar
  6. [6]
    S. Catani, The singular behaviour of QCD amplitudes at two-loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [SPIRES].ADSCrossRefGoogle Scholar
  7. [7]
    G.F. Sterman and M.E. Tejeda-Yeomans, Multi-loop amplitudes and resummation, Phys. Lett. B 552 (2003) 48 [hep-ph/0210130] [SPIRES].ADSCrossRefGoogle Scholar
  8. [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].ADSCrossRefGoogle Scholar
  9. [9]
    G.P. Korchemsky, Asymptotics of the Altarelli-Parisi-Lipatov Evolution Kernels of Parton Distributions, Mod. Phys. Lett. A 4 (1989) 1257 [SPIRES].ADSCrossRefGoogle Scholar
  10. [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].MathSciNetADSGoogle Scholar
  11. [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].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    N. Beisert et al., Review of AdS/CFT Integrability: An Overview, arXiv:1012.3982 [SPIRES].
  13. [13]
    L.F. Alday, D. Gaiotto and J. Maldacena, Thermodynamic Bubble Ansatz, JHEP 09 (2011) 032 [arXiv:0911.4708] [SPIRES].ADSMathSciNetCrossRefGoogle Scholar
  14. [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].MathSciNetGoogle Scholar
  15. [15]
    L.F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [arXiv:0710.1060] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    J. Maldacena and A. Zhiboedov, Form factors at strong coupling via a Y-system, JHEP 11 (2010) 104 [arXiv:1009.1139] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  17. [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].ADSGoogle Scholar
  18. [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].MathSciNetADSCrossRefGoogle Scholar
  19. [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].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    M.L. Mangano, S.J. Parke and Z. Xu, Duality and Multi-Gluon Scattering, Nucl. Phys. B 298 (1988) 653 [SPIRES].ADSCrossRefGoogle Scholar
  21. [21]
    F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [SPIRES].ADSCrossRefGoogle Scholar
  22. [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].MathSciNetADSCrossRefGoogle Scholar
  23. [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].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    P. Mansfield, The Lagrangian origin of MHV rules, JHEP 03 (2006) 037 [hep-th/0511264] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press, Cambridge U.K. (1995).CrossRefGoogle Scholar
  26. [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].ADSGoogle Scholar
  27. [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].ADSCrossRefGoogle Scholar
  28. [28]
    A. Galperin, E. Ivanov, V. Ogievetsky and E. Sokatchev, Harmonic Superspace, Cambridge University Press, Cambridge U.K. (2001)MATHCrossRefGoogle Scholar
  29. [29]
    B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: Part I, arXiv:1103.3714 [SPIRES].
  30. [30]
    B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: Part II, arXiv:1103.4353 [SPIRES].
  31. [31]
    V.P. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett. B 214 (1988) 215 [SPIRES].ADSCrossRefGoogle Scholar
  32. [32]
    L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  33. [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].MathSciNetADSGoogle Scholar
  34. [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].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    A. Brandhuber, B. Spence and G. Travaglini, Tree-Level Formalism, arXiv:1103.3477 [SPIRES].
  36. [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].MathSciNetADSCrossRefGoogle Scholar
  37. [37]
    E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  38. [38]
    M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S Matrix, Phys. Rev. D 15 (1977) 996 [SPIRES].ADSGoogle Scholar
  39. [39]
    M.T. Grisaru and H.N. Pendleton, Some Properties of Scattering Amplitudes in Supersymmetric Theories, Nucl. Phys. B 124 (1977) 81 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  40. [40]
    M.L. Mangano and S.J. Parke, Multi-Parton Amplitudes in Gauge Theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [SPIRES].ADSCrossRefGoogle Scholar
  41. [41]
    H. Elvang, D.Z. Freedman and M. Kiermaier, SUSY Ward identities, Superamplitudes and Counterterms, arXiv:1012.3401 [SPIRES].
  42. [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].MathSciNetADSCrossRefGoogle Scholar
  43. [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].MathSciNetADSCrossRefGoogle Scholar
  44. [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].MathSciNetADSCrossRefGoogle Scholar
  45. [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].MathSciNetADSCrossRefGoogle Scholar
  46. [46]
    Y.-t. Huang, Non-Chiral S-matrix of N = 4 Super Yang-Mills, arXiv:1104.2021 [SPIRES].
  47. [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].MathSciNetADSCrossRefGoogle Scholar
  48. [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].ADSCrossRefGoogle Scholar
  49. [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].MathSciNetADSCrossRefGoogle Scholar
  50. [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].MathSciNetADSCrossRefGoogle Scholar
  51. [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].MathSciNetADSCrossRefGoogle Scholar
  52. [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].MathSciNetADSGoogle Scholar
  53. [53]
    N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  54. [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].MathSciNetADSCrossRefGoogle Scholar
  55. [55]
    M. Bullimore, L.J. Mason and D. Skinner, MHV Diagrams in Momentum Twistor Space, JHEP 12 (2010) 032 [arXiv:1009.1854] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  56. [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].MathSciNetADSCrossRefGoogle Scholar
  57. [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].MathSciNetADSCrossRefGoogle Scholar
  58. [58]
    A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473 [SPIRES].
  59. [59]
    A. Brandhuber, B. Spence and G. Travaglini, From trees to loops and back, JHEP 01 (2006) 142 [hep-th/0510253] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  60. [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].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • A. Brandhuber
    • 1
    • 2
  • Ö. Gürdoğan
    • 1
  • R. Mooney
    • 1
  • G. Travaglini
    • 1
    • 2
  • G. Yang
    • 1
  1. 1.Centre for Research in String Theory, School of Physics and AstronomyQueen Mary University of LondonLondonUnited Kingdom
  2. 2.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.

Personalised recommendations