The Kinematic Algebra From the Self-Dual Sector

TL;DR

This paper uncovers a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory that governs the kinematic numerators of tree-level MHV amplitudes, revealing a duality with the colour algebra and implications for perturbative gravity.

Contribution

It identifies a new diffeomorphism algebra in the self-dual sector and demonstrates its role as the kinematic dual to the colour algebra in Yang-Mills theory.

Findings

Diffeomorphism algebra determines MHV amplitude numerators.

Kinematic numerators are BCJ squares of Yang-Mills numerators.

Gravity numerators are squares of Yang-Mills numerators.

Abstract

We identify a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory, and show that it determines the kinematic numerators of tree-level MHV amplitudes in the full theory. These amplitudes can be computed off-shell from Feynman diagrams with only cubic vertices, which are dressed with the structure constants of both the Yang-Mills colour algebra and the diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We further study perturbative gravity, both in the self-dual and in the MHV sectors, finding that the kinematic numerators of the theory are the BCJ squares of the Yang-Mills numerators.