Dual superconformal invariance, momentum twistors and Grassmannians

By L. Mason, David Skinner. 2009

341 citations recorded by the source corpus.

Dual superconformal invariance has recently emerged as a hidden symmetry of planar scattering amplitudes in = 4 super Yang-Mills theory. This symmetry can be made manifest by expressing amplitudes in terms of `momentum twistors', as opposed to the usual twistors that make the ordinary superconformal properties manifest. The relation between momentum twistors and on-shell momenta is algebraic, so the translation procedure does not rely on any choice of space-time signature. We show that tree amplitudes and box coefficients are succinctly generated by integration of holomorphic δ-functions in momentum twistors over cycles in a Grassmannian. This is analogous to, although distinct from, recent results obtained by Arkani-Hamed et al. in ordinary twistor space. We also make contact with Hodges' polyhedral representation of NMHV amplitudes in momentum twistor space.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c732ffb9c6bfe26ac10349c0d68ee2c932bd4646

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In Nuclear and High Energy Physics

1. N. Arkani-Hamed
2. S. Caron-Huot
3. J. Trnka
4. F. Cachazo
5. J. Bourjaily
6. L. Mason
7. Tim Adamo
8. C. Cheung

Citations in the corpus

• 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],”
• Scattering amplitudes and Wilson loops in twistor space (2011, methodology): “Useful examples that we will frequently use are δ̄1|4(Z1, Z2, Z3, Z4) = ∫ δ̄2|4(Z1, Z2, Z) ∧ δ̄2|4(Z, Z3, Z4) ∧ D3|4Z [1, 2, 3, 4, 5] = ∫ δ̄2|4(Z1, Z2, Z) ∧ δ̄1|4(Z, Z3, Z4, Z5) ∧ D3|4Z.”
• Local integrals for planar scattering amplitudes (2010, background): “33) This representation in momentum twistor space makes dual superconformal invariance manifest [36, 37].”
• Scattering Amplitudes and the Positive Grassmannian (2012, background): “This should not be too surprising, as the Parke-Taylor amplitude can be thought of as the most concise differential form consistent with super momentum conservation— and we know that any generic set of super-momentum-twistors Z give rise to data (λ̃, η̃) which manifestly conserve super-momentum (Thi”
• Eliminating spurious poles from gauge-theoretic amplitudes (2009, background): “Arkani-Hamed et al. (2009) have recently given the analogue of this formalism for split-signature theory, whilst Mason and Skinner (2009) have also given a parallel derivation.”
• 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).”