Abstract
A dual formulation of the S Matrix for \( \mathcal {N} \) = 4 SYM has recently been presented, where all leading singularities of n-particle Nk−2MHV amplitudes are given as an integral over the Grassmannian G(k, n), with cyclic symmetry, parity and superconformal invariance manifest. In this short note we show that the dual superconformal invariance of this object is also manifest. The geometry naturally suggests a partial integration and simple change of variable to an integral over G(k − 2, n). This change of variable precisely corresponds to the mapping between usual momentum variables and the “momentum twistors” introduced by Hodges, and yields an elementary derivation of the momentumtwistor space formula very recently presented by Mason and Skinner, which is manifestly dual superconformal invariant. Thus the G(k, n) Grassmannian formulation allows a direct understanding of all the important symmetries of \( \mathcal {N} \) = 4 SYM scattering amplitudes.
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References
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A Duality For The S Matrix, arXiv:0907.5418 [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].
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].
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [SPIRES].
A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473 [SPIRES].
L. Mason and D. Skinner, Dual Superconformal Invariance, Momentum Twistors and Grassmannians, JHEP 11 (2009) 045 [arXiv:0909.0250] [SPIRES].
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-matrix in Twistor Space, arXiv:0903.2110 [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].
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ArXiv ePrint: 0909.0483
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Arkani-Hamed, N., Cachazo, F. & Cheung, C. The Grassmannian origin of dual superconformal invariance. J. High Energ. Phys. 2010, 36 (2010). https://doi.org/10.1007/JHEP03(2010)036
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DOI: https://doi.org/10.1007/JHEP03(2010)036