On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring

Abstract

We revisited the formalism of 11D polarized scattering equation by Geyer and Mason from the perspective of spinor frame approach and spinor moving frame formulation of the 11D ambitwistor superstring action. In particular, we rigorously obtain the equation for the spinor function on Riemann sphere from the supertwistor form of the ambitwistor superstring action, write its general solution and use it to derive the polarized scattering equation. We show that the expression used by Geyer and Mason to motivate their ansatz for the solution of polarized scattering equation can be obtained from our solution after a suitable gauge fixing. To this end we use the hidden gauge symmetries of the 11D ambitwistor superstring, including $SO(16)$, and the description of ambitwistor superstring as a dynamical system in an 11D superspace enlarged by bosonic directions parametrized by 517 tensorial central charge coordinates $Z^{\underline{\mu }\underline{\nu }}$ and $Z^{\underline{\mu }\underline{\nu }\underline{\rho }\underline{\sigma }\underline{\kappa }}$. We have also found the fermionic superpartner of the polarized scattering equation. This happens to be a differential equation in fermionic variables imposed on the superamplitude, rather then just a condition on the scattering data as the bosonic polarized scattering equation is. D=10 case is also discussed stressing the similarities and differences with 11D systems. The useful formulation of 10D ambitwistor superstring considers it as a dynamical system in superspace enlarged with 126 tensorial central charge coordinates $Z^{\mu \nu \rho \sigma \kappa }$.

1+41 pages, no figures. V2: Misprints corrected. Minor changes

References in corpus (20)

• Holography from Conformal Field Theory
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Amplitudes and Spinor-Helicity in Six Dimensions
• Ambitwistor strings in 4-dimensions
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• A Worldsheet Theory for Supergravity
• New relation for AdS amplitudes
• Scattering Equations: From Projective Spaces to Tropical Grassmannians
• The polarized scattering equations for 6d superamplitudes
• Twistor methods for AdS${}_5$
• M5-Brane and D-Brane Scattering Amplitudes
• All Tree Amplitudes of 6D $(2,0)$ Supergravity: Interacting Tensor Multiplets and the $K3$ Moduli Space
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• The complex null string, Galilean conformal algebra and scattering equations
• Twistor/ambitwistor strings and null-superstrings in spacetime of D=4,10 and 11 dimensions
• Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian
• Twistor string as tensionless superstring

Cited by in corpus (3)

• Recursion and worldsheet formulae for 6d superamplitudes
• Ambitwistor Strings in Six and Five Dimensions
• M5-Brane Amplitudes