Colour-kinematics duality, double copy, and homotopy algebras

TL;DR

This paper explores the extension of colour-kinematics duality from tree-level to loop-level in gauge theories, proposing a reformulation using homotopy algebra structures to better understand gravity-gauge theory relations.

Contribution

It introduces a new off-shell reformulation of colour-kinematics duality at loop level using homotopy algebras, advancing the theoretical understanding of gauge-gravity relations.

Findings

Loop integrands can exhibit a generalized colour-kinematics duality.

Homotopy algebra structures naturally describe off-shell reformulations.

The approach bridges tree-level duality with loop-level conjectures.

Abstract

Colour-kinematics duality is a remarkable property of Yang-Mills theory. Its validity implies a relation between gauge theory and gravity scattering amplitudes, known as double copy. Albeit fully established at the tree level, its extension to the loop level is conjectural. Lifting the on-shell, scattering amplitudes-based description to the level of action functionals, we argue that a theory that exhibits tree-level colour-kinematics duality can be reformulated in a way such that its loop integrands manifest a generalised form of colour-kinematics duality. Moreover, we show how the structures of higher homotopy theory naturally describe this off-shell reformulation of colour-kinematics duality.