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

Abstract

We revisited the formalism of 110 polarized scattering equation by Geyer and Mason from the perspective of spinor frame approach and spinor moving frame formulation of the 110 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 110 ambitwistor superstring, including S0(16), and the description of ambitwistor superstring as a dynamical system in an 110 superspace enlarged by bosonic directions parametrized by 517 tensorial central charge coordinates Z mu nu and Z mu nu rho sigma 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 super amplitude, 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 110 systems. The useful formulation of 100 ambitwistor superstring considers it as a dynamical system in superspace enlarged with 126 tensorial central charge coordinates Z(mu nu rho sigma kappa).