Recursion and worldsheet formulae for 6d superamplitudes

Abstract

Recently two of the authors presented a spinorial extension of the scattering equations, the `polarized scattering equations' that incorporates spinor polarization data. These led to new worldsheet amplitude formulae for a variety of gauge, gravity and brane theories in six dimensions that naturally incorporate fermions and directly extend to maximal supersymmetry. This paper provides a number of improvements to the original formulae, together with extended details of the construction, examples and full proofs of some of the formulae by BCFW recursion and factorization. We show how our formulae reduce to corresponding formulae for maximally supersymmetric gauge, gravity and brane theories in five and four dimensions. In four dimensions our framework naturally gives the twistorial version of the 4d ambitwistor string, giving new insights into the nature of the refined and polarized scattering equations they give rise to, and on the relations between its measure and the CHY measure. Our formulae exhibit a natural double-copy structure being built from `half-integrands'. We give further discussion of the matrix of theories and formulae to which our half-integrands give rise, including controversial formulae for amplitudes involving Gerbes.

arXiv comment82 pages, 69 pages of article + appendices & refs. Final version for publication

References in corpus (51)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Perturbative Gauge Theory As A String Theory In Twistor Space
• New Recursion Relations for Tree Amplitudes of Gluons
• Scattering of Massless Particles in Arbitrary Dimension
• The Amplituhedron
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Scattering Equations and KLT Orthogonality
• Ambitwistor strings and the scattering equations
• On Tree Amplitudes in Gauge Theory and Gravity
• On the Tree-Level S-Matrix of Yang-Mills Theory
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• On-Shell Recursion Relations for Effective Field Theories
• Amplitudes and Spinor-Helicity in Six Dimensions
• Ambitwistor strings in 4-dimensions
• One-loop amplitudes on the Riemann sphere
• Strongly Coupled Gravity and Duality
• Infinite Tension Limit of the Pure Spinor Superstring
• Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension
• Parity Invariance For Strings In Twistor Space
• Gravity from Rational Curves
• Supertwistor space for 6D maximal super Yang-Mills
• Perturbative gravity at null infinity
• Heterotic and bosonic string amplitudes via field theory
• The Momentum Amplituhedron
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• Twistor-Strings, Grassmannians and Leading Singularities
• Simple superamplitudes in higher dimensions
• Local Spacetime Physics from the Grassmannian
• All Googly Amplitudes from the B-model in Twistor Space
• Amplitudes of 3D and 6D Maximal Superconformal Theories in Supertwistor Space
• OSp supergroup manifolds, superparticles and supertwistors
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Evaluation of the CHY Gauge Amplitude
• Ambitwistor formulations of $R^2$ gravity and $(DF{)}^2$ gauge theories
• 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
• Twistor/ambitwistor strings and null-superstrings in spacetime of D=4,10 and 11 dimensions
• Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity
• Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian
• A Link Representation for Gravity Amplitudes
• Supersymmetric S-matrices from the worldsheet in 10 and 11d
• An analytic superfield formalism for tree superamplitudes in D=10 and D=11
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• On 10D SYM superamplitudes

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• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Spinor-helicity formalism for massive and massless amplitudes in five dimensions
• Ambitwistor Strings in Six and Five Dimensions
• From Twistor-Particle Models to Massive Amplitudes