The origin of the KLT relations and nonlinear relations for Yang-Mills amplitudes

TL;DR

This paper explains the origin of KLT relations for graviton amplitudes through gauge invariance and unitarity, revealing nonlinear relations among Yang-Mills amplitudes valid in any dimension.

Contribution

It provides a kinematic analysis that derives KLT relations and uncovers nonlinear relations for Yang-Mills amplitudes, extending understanding beyond four dimensions.

Findings

KLT relations stem from gauge invariance and unitarity.

Nonlinear relations among Yang-Mills amplitudes are identified.

Results hold for arbitrary spacetime dimensions.

Abstract

By means of a kinematic analysis of tree level graviton amplitudes we find, at least through six points, that the reason of their decompositon as a sum over products of Yang-Mills amplitudes is on-shell gauge invariance and unitarity. As a by-product of our analysis we find nonlinear relations obeyed by Yang-Mills amplitudes. All our results are valid for arbitrary spacetime dimensions.