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

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 ${\alpha }^{\prime }$-weighted commutator induced by the monodromy relations between the colour ordered Yang-Mills amplitudes, which mirrors the ${\alpha }^{\prime }$ 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.

25 pages. v2: minor corrections version to be published