Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian

Abstract

Recently, twistor-like formulations of tree amplitudes involving $n$ massless particles have been proposed for various 6D supersymmetric theories. The formulas are based on two different forms of the scattering equations: one based on rational maps and the other based on polarized scattering equations. We show that both formulations can be interpreted in terms of a symplectic (or complex Lagrangian) Grassmannian, $\mathbb{LG}(n,2n)$, and that they correspond to different ways of fixing the $\mathrm{GL}(n,\mathbb{C})$ symmetry of $\mathbb{LG}(n,2n)$. This provides an understanding of the equivalence of these different-looking formulas, and it leads to new twistor-like formulas for 6D superamplitudes.

32 pages

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Cited by in corpus (11)

• On the Double Copy for Spinning Matter
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• The orthogonal momentum amplituhedron and ABJM amplitudes
• The momentum amplituhedron of SYM and ABJM from twistor-string maps
• Spinor-helicity formalism for massive and massless amplitudes in five dimensions
• Notes on gravity multiplet correlators in $Ad{S}_3\times S^3$
• Recursion and worldsheet formulae for 6d superamplitudes
• On the geometry of the orthogonal momentum amplituhedron
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D