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.

arXiv comment32 pages

References in corpus (25)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Relations for Gauge-Theory Amplitudes
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Scattering of Massless Particles in Arbitrary Dimension
• The Amplituhedron
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• A Duality For The S Matrix
• On the Tree-Level S-Matrix of Yang-Mills Theory
• Mellin amplitudes for $Ad{S}_5\times S^5$
• Amplitudes and Spinor-Helicity in Six Dimensions
• Ambitwistor strings in 4-dimensions
• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• Scattering in Three Dimensions from Rational Maps
• Gravity from Rational Curves
• Supertwistor space for 6D maximal super Yang-Mills
• Yangian Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• ABJM amplitudes and the positive orthogonal grassmannian
• Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• The polarized scattering equations for 6d superamplitudes
• M5-Brane and D-Brane Scattering Amplitudes
• All Tree Amplitudes of 6D $(2,0)$ Supergravity: Interacting Tensor Multiplets and the $K3$ Moduli Space
• Secants of Lagrangian Grassmannians
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d

Cited by in corpus (12)

• On the Double Copy for Spinning Matter
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• The momentum amplituhedron of SYM and ABJM from twistor-string maps
• The orthogonal momentum amplituhedron and ABJM amplitudes
• 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
• 6D dual superconformal algebra