Colour-kinematics duality, double copy, and homotopy algebras

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.

6 pages, proceedings of ICHEP 2022

References in corpus (4)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Kinematic Lie Algebras From Twistor Spaces

Cited by in corpus (5)

• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Generalised wavefunction coefficients and acyclonesto-cosmohedra
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Ambitwistor Yang-Mills Theory Revisited