A vertex operator algebra construction of the colour-kinematics dual numerator

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 α ′ -weighted commutator induced by the monodromy relations between the colour ordered Yang-Mills amplitudes, which mirrors the α ′ 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.