Kaluza-Klein from Colour-Kinematics Duality for Massive Fields

TL;DR

This paper demonstrates that imposing colour-kinematics duality on a broad class of massive four-dimensional theories uniquely determines them to be the Kaluza-Klein reduction of five-dimensional Yang-Mills theory, including its higher derivative operators.

Contribution

It shows that requiring colour-kinematics duality in massive theories constrains the Lagrangian to the known Kaluza-Klein form of 5d Yang-Mills, revealing a deep connection between duality and higher-dimensional origins.

Findings

The 4d effective theory matches the Kaluza-Klein reduction of 5d Yang-Mills.

Colour-kinematics duality fixes the form of the Lagrangian uniquely.

Higher derivative operators are consistent with the double copy structure.

Abstract

We consider a broad class of massive four dimensional effective theories describing an infinite tower of charged massive spin 1 states, interacting with massless spin 1 and spin 0. The spectrum is chosen to be the same as that appears in the Kaluza-Klein theory reduction of 5d Yang-Mills to ensure the absence of any spurious poles in a possible double copy formulation. The effective theories are characterized by multiple different couplings between different fields which are unconstrained by symmetries and low energy criteria. Remarkably, by demanding that the scattering amplitudes preserve colour-kinematics duality for different scattering processes, required for the existence of a massive double copy, we find that our 4d Lagrangian is fixed uniquely to the Kaluza-Klein compactification of 5d Yang-Mills theory together with its known double copy consistent higher derivative operators.