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 and show that the expression used by Geyer and Mason to motivate their ansatz for the solution of polarized scattering equation, can be obtained 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 µν and Z µνρσκ . 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 µνρσκ .

Recursion and worldsheet formulae for 6d superamplitudes

“…Indeed closely related models were proposed over the years by Bandos and coworkers [30,[62][63][64][65][66]. Bandos takes the attitude that the additional constraints should not be imposed, and instead that it should be possible to find genuine M-theory physics in these extra degrees of freedom [62,67,68].…”

Spinor Moving Frame, Polarized Scattering Equation for 11D Supergravity, and Ambitwistor Superstring

“…In this contribution, following [42], we have revisited the formalism of the 11D polarized scattering equations in [21] with the use of the spinor frame approach (or the Lorentz harmonic approach), some different applications of which to the description of 11D and 10D amplitudes were searched for in [18][19][20]. In particular, we have addressed the problem of rigorous derivation of the equations for the spinorial meromorphic function ( ) and its fermionic superpartner ( ) from the spinor moving frame formulation of an 11D ambitwistor superstring [35].…”

“…It was proposed in [21], where its relation to a modified version of the 11D ambitwistor superstring action of [35] was claimed. Below, we show, following [42], that the appropriate model is actually described by the original action of [35] and obtain the form of a meromorphic spinor function ( ) and the polirized counterpart of the scattering equation in the form of Eq. (25) on this basis.…”

“…In this contribution based on [42], we revisit the 11D polarized scattering equation formalism of [21] and its ambitwistor superstring origin by using the spinor frame approach. We show that the correct basis to derive the polarized scattering equation is provided by the 11D ambitwistor superstring of [35], rather than its modification suggested in [21].…”

Cubic interactions for arbitrary spin $$ \mathcal{N} $$ -extended massless supermultiplets in 4d flat space

“…7. Twistor methods addressed, e.g., in Refs [69,70],. could also be helpful for studying interactions of massless supermultiplets in higher dimensions.…”