Abstract
The spinor helicity formalism in four dimensions has become a very useful tool both for understanding the structure of amplitudes and also for practical numerical computation of amplitudes. Recently, there has been some discussion of an extension of this formalism to higher dimensions. We describe a particular implementation of the spinor-helicity method in ten dimensions. Using this tool, we study the tree-level S-matrix of ten dimensional super Yang-Mills theory, and prove that the theory enjoys a dual conformal symmetry. Implications for four-dimensional computations are discussed.
Similar content being viewed by others
References
Z. Xu, D.H. Zhang and L. Chang, Helicity amplitudes for multiple bremsstrahlung in massless nonabelian gauge theories, Nucl. Phys. B 291 (1987) 392.
J.F. Gunion and Z. Kunszt, Improved analytic techniques for tree graph calculations and the \( Ggq\bar{q} \) lepton anti-lepton subprocess, Phys. Lett. B 161 (1985) 333 [SPIRES].
R. Kleiss and W.J. Stirling, Spinor techniques for calculating \( p\bar{p} \to {{{{W^\pm }}} \left/ {{{Z_0}}} \right.} \) + jets, Nucl. Phys. B 262 (1985) 235 [SPIRES].
P. De Causmaecker, R. Gastmans, W. Troost and T.T. Wu, Helicity amplitudes for massless QED, Phys. Lett. B 105 (1981) 215.
F.A. Berends, R. Kleiss, P. De Causmaecker, R. Gastmans and T.T. Wu, Single bremsstrahlung processes in gauge theories, Phys. Lett. B 103 (1981) 124 [SPIRES].
S.J. Parke and T.R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56 (1986) 2459 [SPIRES].
F.A. Berends and W.T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys. B 306 (1988) 759 [SPIRES].
F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [SPIRES].
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].
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].
C. Cheung and D. O’Connell, Amplitudes and spinor-helicity in six dimensions, JHEP 07 (2009) 075 [arXiv:0902.0981] [SPIRES].
R. Boels, Covariant representation theory of the Poincaré algebra and some of its extensions, JHEP 01 (2010) 010 [arXiv:0908.0738] [SPIRES].
T. Dennen, Y.-t. Huang and W. Siegel, Supertwistor space for 6D maximal super Yang-Mills, JHEP 04 (2010) 127 [arXiv:0910.2688] [SPIRES].
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] [SPIRES].
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] [SPIRES].
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].
Z. Bern, M. Czakon, L.J. Dixon, D.A. Kosower and V.A. Smirnov, The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 75 (2007) 085010 [hep-th/0610248] [SPIRES].
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [SPIRES].
Z. Bern, J.J.M. Carrasco, H. Johansson and D.A. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops, Phys. Rev. D 76 (2007) 125020 [arXiv:0705.1864] [SPIRES].
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].
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].
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].
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].
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].
N. Berkovits and J. Maldacena, Fermionic T-duality, dual superconformal symmetry and the amplitude/Wilson loop connection, JHEP 09 (2008) 062 [arXiv:0807.3196] [SPIRES].
N. Beisert, R. Ricci, A.A. Tseytlin and M. Wolf, Dual superconformal symmetry from AdS 5 × S 5 superstring integrability, Phys. Rev. D 78 (2008) 126004 [arXiv:0807.3228] [SPIRES].
J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory, JHEP 05 (2009) 046 [arXiv:0902.2987] [SPIRES].
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].
N. Arkani-Hamed, F. Cachazo and C. Cheung, The grassmannian origin of dual superconformal invariance, JHEP 03 (2010) 036 [arXiv:0909.0483] [SPIRES].
L.F. Alday, J.M. Henn, J. Plefka and T. Schuster, Scattering into the fifth dimension of N = 4 super Yang-Mills, JHEP 01 (2010) 077 [arXiv:0908.0684] [SPIRES].
S. Weinberg, The quantum theory of fields. Vol. 1: foundations, Cambridge University Press, Cambridge U.K. (1995), p. 609.
N. Arkani-Hamed and J. Kaplan, On tree amplitudes in gauge theory and gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [SPIRES].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [SPIRES].
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].
M. Bullimore, L. Mason and D. Skinner, MHV diagrams in momentum twistor space, arXiv:1009.1854 [SPIRES].
S. Caron-Huot, Notes on the scattering amplitude/Wilson loop duality, JHEP 07 (2011) 058 [arXiv:1010.1167] [SPIRES].
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].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Caron-Huot, S., O’Connell, D. Spinor helicity and dual conformal symmetry in ten dimensions. J. High Energ. Phys. 2011, 14 (2011). https://doi.org/10.1007/JHEP08(2011)014
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2011)014