Unusual identities for QCD at tree-level

TL;DR

The paper introduces helicity-dependent quadratic relations among color-ordered Yang–Mills amplitudes, linking pairs of amplitudes from different helicity sectors via a momentum-kernel $S$. These identities are dual to gravity relations like KLT and reduce to known BCJ structures under certain limits, while not requiring gravitons themselves. The authors sketch an inductive BCFW-based proof and demonstrate concrete 5- and 6-point examples, illustrating nontrivial cancellations and cross-helicity connections. The results reveal a deeper, gravity-informed structure in perturbative gauge theory with potential practical impact on simplifying high-multiplicity amplitude computations and suggest avenues for extension to loop level.

Abstract

We discuss a set of recently discovered quadratic relations between gauge theory amplitudes. Such relations give additional structural simplifications for amplitudes in QCD. Remarkably, their origin lie in an analogous set of relations that involve also gravitons. When certain gluon helicities are flipped we obtain relations that do not involve gravitons, but which refer only to QCD.