Amplitude relations in heterotic string theory and Einstein-Yang-Mills

TL;DR

This paper demonstrates that heterotic string theory's tree-level amplitudes involving gluons and gravitons can be expressed in terms of gauge multiplet amplitudes, providing new relations valid at all orders in string tension and connecting to Einstein-Yang-Mills theory.

Contribution

It derives explicit amplitude relations for heterotic string theory with multiple gravitons and gluons, generalizing to superamplitudes and offering an alternative proof of Einstein-Yang-Mills relations.

Findings

Amplitude relations valid to all orders in α'

Explicit formulas for up to three gravitons and two traces

Connection between heterotic string amplitudes and Einstein-Yang-Mills

Abstract

We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension $\alpha'$ and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.