Abstract
We obtain compact formulae for tree super-amplitudes for 10 and 11-dimensional supergravity and 10-dimensional supersymmetric Yang-Mills and Born-Infeld. These are based on the polarised scattering equations. These incorporate polarization data into a spinor field on the Riemann sphere and arise from a twistorial representation of ambitwistor strings in 10 and 11 dimensions. They naturally extend amplitude formulae to manifest maximal supersymmetry. The framework is the natural generalization of twistorial ambitwistor string formulae found previously in four and six dimensions and is informally motivated from a vertex operator prescription for a family of supersymmetric worldsheet ambitwistor string models.
Highlights
M-theory is approximated by 11d supergravity and is often characterised as the theory that provides the natural geometric backgrounds for supersymmetric membranes
In this paper we propose formulae for the massless tree-level S-matrix of 11d supergravity based on string theories in ambitwistor space, the space of complex null geodesics
Pδab in Thought of as an n ×n matrix with 8 × 8 matrix entries, it is possible to introduce a reduced quasideterminants that are equivalent to the CHY reduced determinants and Pfaffians, we plan to follow up with some of these details in due course [21]
Summary
M-theory is approximated by 11d supergravity and is often characterised as the theory that provides the natural geometric backgrounds for supersymmetric membranes. We give the basic structure of ambitwistor string vertex operators in these coordinates and show how they lead to polarized scattering equations in 10 and 11 dimensions. It is a key fact that for each solution to the scattering equations ki · P (σi) = 0, with momenta and polarization data in general position, there exists a unique λaα satisfying (2.8) and (2.11), [21].
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