On tree amplitudes of supersymmetric Einstein-Yang-Mills theory

TL;DR

This paper introduces a new formula for tree-level scattering amplitudes in four-dimensional supersymmetric Einstein-Yang-Mills theory, unifying gravity and gauge interactions with manifest supersymmetry and parity.

Contribution

It provides a novel, unified formula for all single trace tree amplitudes in supersymmetric Einstein-Yang-Mills theory using scattering equations and spinor helicity variables.

Findings

Formula reduces to known twistor-string results in special sectors

Supports on solutions of scattering equations with spinor helicity variables

Behaves correctly under factorization, consistent with physical expectations

Abstract

We present a new formula for all single trace tree amplitudes in four dimensional super Yang-Mills coupled to Einstein supergravity. Like the Cachazo-He-Yuan formula, our expression is supported on solutions of the scattering equations, but with momenta written in terms of spinor helicity variables. Supersymmetry and parity are both manifest. In the pure gravity and pure Yang-Mills sectors, it reduces to the known twistor-string formulae. We show that the formula behaves correctly under factorization and sketch how these amplitudes may be obtained from a four-dimensional (ambi)twistor string.