Eliminating spurious poles from gauge-theoretic amplitudes

  • Andrew HodgesEmail author


This note addresses the problem of spurious poles in gauge-theoretic scattering amplitudes. New twistor coordinates for the momenta are introduced, based on the concept of dual conformal invariance. The cancellation of spurious poles for a class of NMHV amplitudes is greatly simplified in these coordinates. The poles are eliminated altogether by defining a new type of twistor integral, dual to twistor diagrams as previously studied, and considerably simpler. The geometric features indicate a supersymmetric extension of the formalism at least to all NMHV amplitudes, allowing the dihedral symmetry of the super-amplitude to be made manifest. More generally, the definition of ‘momentum-twistor’ coordinates suggests a powerful new approach to the study of scattering amplitudes.


Supersymmetric gauge theory Scattering Amplitudes 


  1. [1]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    A.P. Hodges, Twistor diagrams for all tree amplitudes in gauge theory: a Helicity-independent formalism, hep-th/0512336 [INSPIRE].
  4. [4]
    N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-matrix in twistor space, JHEP 03 (2010) 110 [arXiv:0903.2110] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    A.P. Hodges, Twistor diagram recursion for all gauge-theoretic tree amplitudes, hep-th/0503060 [INSPIRE].
  6. [6]
    L. Mason and D. Skinner, Scattering amplitudes and BCFW recursion in twistor space, JHEP 01 (2010) 064 [arXiv:0903.2083] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    A.P. Hodges, Scattering amplitudes for eight gauge fields, hep-th/0603101 [INSPIRE].
  8. [8]
    N. Arkani-Hamed et al., Scattering amplitudes and the positive Grassmannian, arXiv:1212.5605 [INSPIRE].
  9. [9]
    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] [INSPIRE].MathSciNetADSGoogle Scholar
  10. [10]
    J. Drummond, J. Henn, V. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    J. Drummond, J. Henn, G. 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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    A.P. Hodges, A twistor approach to the regularization of divergences, Proc. Roy. Soc. Lond. A 397 (1985) 341 [INSPIRE].MathSciNetADSGoogle Scholar
  13. [13]
    L. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and Grassmannians, JHEP 11 (2009) 045 [arXiv:0909.0250] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    N. Arkani-Hamed, F. Cachazo and C. Cheung, The Grassmannian origin of dual superconformal invariance, JHEP 03 (2010) 036 [arXiv:0909.0483] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    J. Drummond and L. Ferro, Yangians, Grassmannians and T-duality, JHEP 07 (2010) 027 [arXiv:1001.3348] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    J.L. Bourjaily, Efficient tree-amplitudes in N = 4: automatic BCFW recursion in Mathematica, arXiv:1011.2447 [INSPIRE].
  17. [17]
    N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A. Hodges and J. Trnka, A note on polytopes for scattering amplitudes, JHEP 04 (2012) 081 [arXiv:1012.6030] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    A. Hodges, The box integrals in momentum-twistor geometry, arXiv:1004.3323 [INSPIRE].
  19. [19]
    L. Mason and D. Skinner, Amplitudes at weak coupling as polytopes in AdS5, J. Phys. A 44 (2011) 135401 [arXiv:1004.3498] [INSPIRE].MathSciNetADSGoogle Scholar
  20. [20]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Local integrals for planar scattering amplitudes, JHEP 06 (2012) 125 [arXiv:1012.6032] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    A. Hodges, New expressions for gravitational scattering amplitudes, arXiv:1108.2227 [INSPIRE].
  23. [23]
    A. Hodges, A simple formula for gravitational MHV amplitudes, arXiv:1204.1930 [INSPIRE].

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Mathematical InstituteOxfordU.K.

Personalised recommendations