2009/09/02 by Nima Arkani–Hamed, Nima Arkani-Hamed, Freddy Cachazo +1 · 5 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Geometry #Grassmannian #Gravitational singularity #Homogeneous space #Invariant (physics) #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scattering amplitude #Supersymmetry #Twistor theory #hep-th
paper · pdf · doi:10.1007/jhep03(2010)036
9 pages
arxiv created 2009/09/02 · openalex publication_date 2010/03/01 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.