Skip to main content
SpringerLink
Log in

Simple superamplitudes in higher dimensions

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We provide simple superspaces based on a formulation of spinor helicity in general even dimensions. As a distinguishing feature these spaces admit a fermionic super-momentum conserving delta function solution to the on-shell supersymmetry Ward identities. Using these solutions, we present beautifully simple formulae for the complete three, four and five point superamplitudes in maximal super Yang-Mills theory in eight dimensions, and for the three and four point superamplitudes in ten dimensional type IIB super-gravity. In addition, we discuss the exceptional kinematics of the three point amplitude, and the supersymmetric spinorial BCFW recursion, in general dimensions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L.J. Dixon, Scattering amplitudes: the most perfect microscopic structures in the universe, J. Phys. A 44 (2011) 454001 [arXiv:1105.0771] [INSPIRE].

    ADS  Google Scholar 

  2. S.J. Parke and T. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  5. C. Cheung and D. O’Connell, Amplitudes and spinor-helicity in six dimensions, JHEP 07 (2009) 075 [arXiv:0902.0981] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  6. R. Boels, Covariant representation theory of the Poincaré algebra and some of its extensions, JHEP 01 (2010) 010 [arXiv:0908.0738] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  7. S. Caron-Huot and D. O’Connell, Spinor helicity and dual conformal symmetry in ten dimensions, JHEP 08 (2011) 014 [arXiv:1010.5487] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  8. T. Dennen, Y.-t. Huang and W. Siegel, Supertwistor space for 6D maximal super Yang-Mills, JHEP 04 (2010) 127 [arXiv:0910.2688] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  9. Z. Bern, J.J. Carrasco, T. Dennen, Y.-t. Huang and H. Ita, Generalized unitarity and six-dimensional helicity, Phys. Rev. D 83 (2011) 085022 [arXiv:1010.0494] [INSPIRE].

    ADS  Google Scholar 

  10. A. Brandhuber, D. Korres, D. Koschade and G. Travaglini, One-loop amplitudes in six-dimensional (1,1) theories from generalised unitarity, JHEP 02 (2011) 077 [arXiv:1010.1515] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. T. Dennen and Y.-t. Huang, Dual conformal properties of six-dimensional maximal super Yang-Mills amplitudes, JHEP 01 (2011) 140 [arXiv:1010.5874] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  12. R.H. Boels, Three particle superstring amplitudes with massive legs, JHEP 06 (2012) 026 [arXiv:1201.2655] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  13. A. Van Proeyen, Tools for supersymmetry, hep-th/9910030 [INSPIRE].

  14. M.A.A. van Leeuwen, A.M. Cohen and B. Lisser, LiE, A Package for Lie Group Computations (1992), http://young.sp2mi.univ-poitiers.fr/~marc/LiE/.

  15. H. Kawai, D. Lewellen and S. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  16. R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  17. 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].

    Article  ADS  MathSciNet  Google Scholar 

  18. 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].

    ADS  MathSciNet  Google Scholar 

  19. N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  20. G. Policastro and D. Tsimpis, R 4 , purified, Class. Quant. Grav. 23 (2006) 4753 [hep-th/0603165] [INSPIRE].

    Article  ADS  MATH  MathSciNet  Google Scholar 

  21. R. Metsaev, Eleven dimensional supergravity in light cone gauge, Phys. Rev. D 71 (2005) 085017 [hep-th/0410239] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  22. Y.-t. Huang and A.E. Lipstein, Dual superconformal symmetry of N = 6 Chern-Simons theory, JHEP 11 (2010) 076 [arXiv:1008.0041] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  23. B. Czech, Y.-t. Huang and M. Rozali, Amplitudes for multiple M5 branes, arXiv:1110.2791 [INSPIRE].

  24. Z. Bern, L.J. Dixon, D. Dunbar, M. Perelstein and J. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B 530 (1998)401 [hep-th/9802162] [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. II. Institut für Theoretische Physik Universität Hamburg, Luruper Chaussee 149, D-22761, Hamburg, Germany

    Rutger H. Boels

  2. Niels Bohr International Academy and DISCOVERY center, Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen, Denmark

    Donal O’Connell

Authors
  1. Rutger H. Boels
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Donal O’Connell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rutger H. Boels.

Additional information

ArXiv ePrint: 1201.2653

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boels, R.H., O’Connell, D. Simple superamplitudes in higher dimensions. J. High Energ. Phys. 2012, 163 (2012). https://doi.org/10.1007/JHEP06(2012)163

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2012)163

Keywords

Search

Navigation