Symmetry and Action for Flavor-Kinematics Duality

TL;DR

The paper proposes a cubic-action formulation of the nonlinear sigma model that makes flavor–kinematics duality a symmetry, with kinematic Jacobi identities arising from current conservation under combined internal-spacetime symmetries. This structure renders the color-kinematics-like relations manifest and enables a straightforward double copy to a cubic action for the special Galileon, clarifying the link between NLSM amplitudes and higher-derivative scalar theories. The authors demonstrate explicit amplitudes, derive a kinematic algebra, and connect the framework to infrared behavior via Weinberg soft theorems, including extensions to reproduce soft theorems in an augmented theory up to ten points. The approach provides a unifying perspective on amplitude relations in scalar theories, highlights the role of a kinematic algebra, and offers a clean route to the double-copy construction for Galileon-type theories.

Abstract

We propose a new representation of the nonlinear sigma model that exhibits a manifest duality between flavor and kinematics. The fields couple exclusively through cubic Feynman vertices which also serve as the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities. Substituting flavor for kinematics, we derive a new cubic action for the special Galileon theory. In this picture, the vanishing soft behavior of amplitudes is a byproduct of the Weinberg soft theorem.