On tree amplitudes of supersymmetric Einstein-Yang-Mills theory

TL;DR

This work constructs a compact, four-dimensional, single-trace tree-level S-matrix for supersymmetric Einstein–Yang–Mills theory by a CHY-like integral formula with spinor-helicity momenta. The amplitude is written as an integral over punctured sphere moduli, with parity-conjugate reduced determinants $\det'\Phi$ and $\det'\tilde{\Phi}$, a generalized Parke–Taylor factor $\mathrm{PT}$, and a supersymmetric exponential encoding, yielding a formula that is manifestly SUSY and parity-invariant and reduces to RSVW/CS in pure YM/gravity sectors. The authors demonstrate correct three-point amplitudes and show the expected factorization behavior via degeneration of the Riemann sphere into two components, capturing both gluon and graviton exchange channels, and they connect the construction to potential ambi-twistor string origins. This framework provides a compact, field-theoretic realization of sEYM amplitudes and suggests pathways to multitrace generalizations and a twistor-string interpretation.

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.