Simplex-like Structures of Maximally Supersymmetric Scattering Amplitudes

Abstract

We elaborate the two-fold simplex-like structures of tree amplitudes in planar maximally supersymmetric Yang-Mills (N=4 SYM), through its connection to a mathematical structure known as the positive Grassmannian. Exploiting the reduced Grassmannian geometry and the matrix form of on-shell recursion relation in terms of super momentum twistors, we manifest that tree amplitudes can be remarkably refined via the essential building blocks named as fully-spanning cells. For a fixed number of negative helicities, an amplitude can be entirely captured by finite, compact information of the relevant fully-spanning cells up to an arbitrarily large number of external particles.

5 pages, 2 figures. Introductory overview of 1609.08627. Figures improved for v3

References in corpus (8)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• All tree-level amplitudes in N=4 SYM
• The Amplituhedron from Momentum Twistor Diagrams
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• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
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Cited by in corpus (1)

• Cyclicity of All Anti-NMHV and N${}^2$MHV Tree Amplitudes in N=4 SYM