The polarized scattering equations for 6d superamplitudes

TL;DR

The paper develops polarized scattering equations in six dimensions, encoding spinor polarization data to produce new tree-level superamplitudes for 6d theories with maximal supersymmetry. Grounded in a chiral ambitwistor-string picture, the approach yields a consistent measure and a set of integrands (including $\det'H$, $\det'A$, and Pfaffians) that extend 4d twistorial results and survive dimensional reduction to massive 4d Coulomb-branch amplitudes. Supersymmetry is incorporated via a representation that produces a compact exponential factor $e^{F}$, ensuring invariance and enabling a unified treatment of SYM, supergravity, D5, and M5 sectors. Reduction to 4d reproduces known massive refinements and clarifies the role of polarization data in amplitudes, while the framework avoids the even/odd $n$ caveats of prior 6d constructions. The work opens avenues for worldsheet realizations of new theories and broader application of polarized scattering equations beyond the present set.

Abstract

We introduce a spinorial version of the scattering equations, the \emph{polarized scattering equations}, that incorporates spinor polarization data. They lead to new formulae for tree-level scattering amplitudes in six dimensions that directly extend to maximal supersymmetry. They give a quite distinct framework from that of Cachazo et al.; in particular, the formulae do not change character from even to odd numbers of particles. We find new ingredients for integrands for maximally supersymmetric Yang-Mills, gravity, M5 and D5 branes. We explain how the polarized scattering equations and supersymmetry representations arise from an ambitwistor-string with target given by a super-twistor description of the geometry of super-ambitwistor space for six dimensions. On reduction to four dimensions the polarized scattering equations give rise to massive analogues of the 4d refined scattering equations for amplitudes on the Coulomb branch. At zero mass this framework naturally generalizes the twistorial version of the ambitwistor string in four dimensions.