×

Spinor helicity and dual conformal symmetry in ten dimensions. (English) Zbl 1298.81163

Summary: 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.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
83E15 Kaluza-Klein and other higher-dimensional theories
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Z. Xu, D.H. Zhang and L. Chang, Helicity amplitudes for multiple bremsstrahlung in massless nonabelian gauge theories, Nucl. Phys.B 291 (1987) 392. · doi:10.1016/0550-3213(87)90479-2
[2] 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].
[3] 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]. · doi:10.1016/0550-3213(85)90285-8
[4] P. De Causmaecker, R. Gastmans, W. Troost and T.T. Wu, Helicity amplitudes for massless QED, Phys. Lett.B 105 (1981) 215.
[5] 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].
[6] S.J. Parke and T.R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett.56 (1986) 2459 [SPIRES]. · doi:10.1103/PhysRevLett.56.2459
[7] F.A. Berends and W.T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys.B 306 (1988) 759 [SPIRES]. · doi:10.1016/0550-3213(88)90442-7
[8] F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP09 (2004) 006 [hep-th/0403047] [SPIRES]. · doi:10.1088/1126-6708/2004/09/006
[9] 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]. · Zbl 1207.81088 · doi:10.1016/j.nuclphysb.2005.02.030
[10] 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]. · doi:10.1103/PhysRevLett.94.181602
[11] C. Cheung and D. O’Connell, Amplitudes and spinor-helicity in six dimensions, JHEP07 (2009) 075 [arXiv:0902.0981] [SPIRES]. · doi:10.1088/1126-6708/2009/07/075
[12] R. Boels, Covariant representation theory of the Poincaré algebra and some of its extensions, JHEP01 (2010) 010 [arXiv:0908.0738] [SPIRES]. · Zbl 1269.81172 · doi:10.1007/JHEP01(2010)010
[13] T. Dennen, Y.-t. Huang and W. Siegel, Supertwistor space for 6D maximal super Yang-Mills, JHEP04 (2010) 127 [arXiv:0910.2688] [SPIRES]. · Zbl 1272.81114 · doi:10.1007/JHEP04(2010)127
[14] 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].
[15] A. Brandhuber, D. Korres, D. Koschade and G. Travaglini, One-loop amplitudes in six-dimensional (1, 1) theories from generalised unitarity, JHEP02 (2011) 077 [arXiv:1010.1515] [SPIRES]. · Zbl 1294.81091 · doi:10.1007/JHEP02(2011)077
[16] J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP01 (2007) 064 [hep-th/0607160] [SPIRES]. · doi:10.1088/1126-6708/2007/01/064
[17] 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].
[18] L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP06 (2007) 064 [arXiv:0705.0303] [SPIRES]. · doi:10.1088/1126-6708/2007/06/064
[19] 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].
[20] 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]. · Zbl 1219.81227
[21] 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]. · Zbl 1273.81201 · doi:10.1016/j.nuclphysb.2007.11.002
[22] 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]. · Zbl 1219.81191 · doi:10.1016/j.nuclphysb.2007.11.007
[23] 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]. · Zbl 1203.81175 · doi:10.1016/j.nuclphysb.2009.10.013
[24] 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]. · Zbl 1203.81112 · doi:10.1016/j.nuclphysb.2009.11.022
[25] N. Berkovits and J. Maldacena, Fermionic T-duality, dual superconformal symmetry and the amplitude/Wilson loop connection, JHEP09 (2008) 062 [arXiv:0807.3196] [SPIRES]. · Zbl 1245.81267 · doi:10.1088/1126-6708/2008/09/062
[26] N. Beisert, R. Ricci, A.A. Tseytlin and M. Wolf, Dual superconformal symmetry from AdS5 × S5superstring integrability, Phys. Rev.D 78 (2008) 126004 [arXiv:0807.3228] [SPIRES].
[27] J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory, JHEP05 (2009) 046 [arXiv:0902.2987] [SPIRES]. · doi:10.1088/1126-6708/2009/05/046
[28] 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].
[29] N. Arkani-Hamed, F. Cachazo and C. Cheung, The grassmannian origin of dual superconformal invariance, JHEP03 (2010) 036 [arXiv:0909.0483] [SPIRES]. · Zbl 1271.81099 · doi:10.1007/JHEP03(2010)036
[30] L.F. Alday, J.M. Henn, J. Plefka and T. Schuster, Scattering into the fifth dimension of N = 4 super Yang-Mills, JHEP01 (2010) 077 [arXiv:0908.0684] [SPIRES]. · Zbl 1269.81079 · doi:10.1007/JHEP01(2010)077
[31] S. Weinberg, The quantum theory of fields. Vol. 1: foundations, Cambridge University Press, Cambridge U.K. (1995), p. 609.
[32] N. Arkani-Hamed and J. Kaplan, On tree amplitudes in gauge theory and gravity, JHEP04 (2008) 076 [arXiv:0801.2385] [SPIRES]. · Zbl 1246.81103 · doi:10.1088/1126-6708/2008/04/076
[33] N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP09 (2010) 016 [arXiv:0808.1446] [SPIRES]. · Zbl 1291.81356 · doi:10.1007/JHEP09(2010)016
[34] L.J. Mason and D. Skinner, The Complete Planar S-matrix of N = 4 SYM as a Wilson Loop in Twistor Space, JHEP12 (2010) 018 [arXiv:1009.2225] [SPIRES]. · Zbl 1294.81122 · doi:10.1007/JHEP12(2010)018
[35] M. Bullimore, L. Mason and D. Skinner, MHV diagrams in momentum twistor space, arXiv:1009.1854 [SPIRES]. · Zbl 1294.81094
[36] S. Caron-Huot, Notes on the scattering amplitude/Wilson loop duality, JHEP07 (2011) 058 [arXiv:1010.1167] [SPIRES]. · Zbl 1298.81357 · doi:10.1007/JHEP07(2011)058
[37] A. Brandhuber, B. Spence, G. Travaglini and G. Yang, A note on dual MHV diagrams in N = 4 SYM, JHEP12 (2010) 087 [arXiv:1010.1498] [SPIRES]. · Zbl 1294.81092 · doi:10.1007/JHEP12(2010)087
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.