Color-kinematics duality from an algebra of superforms

TL;DR

This paper introduces a new algebraic framework based on superforms and BV-like structures to derive color-kinematics duality in Yang-Mills theory, aiming for a first-principles proof.

Contribution

It proposes a novel approach using superforms and a generalized BV algebra to derive the color-kinematics duality from field theory principles.

Findings

Establishes a connection between superforms and the homotopy algebra of Yang-Mills theory.

Shows that the algebra of color-stripped Yang-Mills can be obtained as a quotient of a superform-based algebra.

Lays groundwork for deriving the duality from first principles via BV$_{ olinebreak}$_{ ext{infinity}}^{ olinebreak}$$^{ olinebreak}$ algebra structures.

Abstract

Color-kinematics duality states that the kinematic numerators of the cubic tree-level Yang-Mills scattering amplitudes obey the same symmetry properties that the color factors obey due to the Jacobi identity. We present a novel strategy for deriving this duality, based on the differential forms on a superspace. This space of superforms carries a generalization of a Batalin-Vilkovisky (BV) algebra (BV$^{\square}$ algebra). We show that the homotopy algebra of color-stripped Yang-Mills theory is obtained as a quotient of this space in which a subspace, which is an ideal `up to homotopy', is modded out. This algebra is a subsector of a BV$_{\infty}^{\square}$ algebra. Deriving the latter would provide a first-principle proof of color-kinematics duality from field theory.