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

TL;DR

This paper refines the polarized scattering equations for 11D supergravity superamplitudes using spinor and superstring formalisms, revealing new gauge symmetries and fermionic equations, and compares with the 10D case.

Contribution

It provides a rigorous derivation of polarized scattering equations in 11D supergravity from ambitwistor superstring formalism, including gauge fixing and fermionic superpartner equations.

Findings

Derived the supertwistor form of the polarized scattering equation.

Identified hidden gauge symmetries including SO(16).

Discovered a fermionic differential equation for superamplitudes.

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 $Z^{\mu\nu\rho\sigma\kappa}$.