Einstein-Yang-Mills from pure Yang-Mills amplitudes

TL;DR

This paper derives new relations that express Einstein-Yang-Mills scattering amplitudes with multiple gravitons and color traces in terms of pure Yang-Mills amplitudes, valid across dimensions and extended to supersymmetric theories.

Contribution

It introduces generalized amplitude relations for Einstein-Yang-Mills theory involving multiple gravitons and traces, extending previous single-graviton results and applicable in any dimension.

Findings

Amplitudes with up to three gravitons and two traces are reducible to pure Yang-Mills amplitudes.

Relations hold for theories extended with dilaton and B-field.

Results are valid in any spacetime dimension and for supersymmetric extensions.

Abstract

We present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations involving up to three gravitons and up to two color traces are reduced to partial amplitudes of pure Yang-Mills theory. In fact, the double-trace identities apply to Einstein-Yang-Mills extended by a dilaton and a B-field. Our results generalize recent work of Stieberger and Taylor for the single graviton case with a single color trace. As the derivation is made in the dimension-agnostic Cachazo-He-Yuan formalism, our results are valid for external bosons in any number of spacetime dimensions. Moreover, they generalize to the superamplitudes in theories with 16 supercharges.