A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator

TL;DR

This paper presents a novel vertex operator approach to construct kinematic numerators in Yang-Mills amplitudes, revealing a deep algebraic structure related to string theory and diffeomorphisms.

Contribution

It introduces a vertex operator expression for kinematic numerators using the momentum kernel formalism, connecting string theory monodromy relations with the colour-kinematics duality.

Findings

Derives a vertex operator expression for kinematic numerators.

Shows the algebra contains the Lie algebra of diffeomorphisms.

Links string theory monodromy relations to colour-kinematics duality.

Abstract

We derive a vertex operator based expression for the kinematic numerators of Yang-Mills amplitudes by applying the momentum kernel formalism to open string amplitudes. The expression involves an $\alpha'$-weighted commutator induced by the monodromy relations between the colour ordered Yang-Mills amplitudes, which mirrors the $\alpha'$ deformed colour structure observed in open string and semi-abelian $Z$-theory. The kinematic algebra given by this construction contains the Lie algebra of diffeomorphism as an obvious sub-algebra.