The Grassmannian origin of dual superconformal invariance

By N. Arkani-Hamed, F. Cachazo, C. Cheung. 2009

209 citations recorded by the source corpus.

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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/86150144234accfcf1d5f74c697563a3d1e88262

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In Nuclear and High Energy Physics

1. N. Arkani-Hamed
2. S. Caron-Huot
3. L. Dixon
4. F. Cachazo
5. J. Trnka
6. J. Drummond
7. L. Mason
8. M. Spradlin

Citations in the corpus

• Scattering Amplitudes and the Positive Grassmannian (2012, methodology): “In this subsection, we will review the arguments presented in [16] in order to discover that on-shell forms are quite surprisingly also invariant under an additional super-conformal symmetry.”
• Symmetries of Tree-level Scattering Amplitudes in N = 6 Superconformal Chern{Simons Theory (2010, background): “These contributions have been shown to be (cyclic by construction) Yangian invariants [38].”
• Heptagons from the Steinmann cluster bootstrap (2016, background): “From this representation it is also possible to prove their invariance under ordinary superconformal transformations [84, 85], or in other words their Yangian invariance [86].”
• Unification of residues and Grassmannian dualities (2009, background): “The resulting form, in terms of a (k − 2) × n matrix D is given by [3, 4],”
• Motivic amplitudes and cluster coordinates (2013, background): “This Grassmannian, describing the external kinematic data of an amplitude, may look unrelated to those which star in [27–32] and involve also ‘internal’ data related to loop integration variables.”
• Local integrals for planar scattering amplitudes (2010, background): “33) This representation in momentum twistor space makes dual superconformal invariance manifest [36, 37].”
• The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, background): “This was quickly realized [35] to be completely equivalent to a second form in momentum twistor space [36], with Ln,k+2(λ, λ̃, η̃) = M tree MHV × Yn,k(Z).”
• Scattering amplitudes and Wilson loops in twistor space (2011, background): “The first papers to show that all leading singularities live in the Grassmannian were [48, 56], while the Yangian invariance of the formula was investigated in [57, 60].”