Symmetry and Action for Flavor-Kinematics Duality

TL;DR

This paper introduces a novel representation of the nonlinear sigma model that reveals a duality between flavor and kinematics, leading to new insights into amplitude behaviors and duality structures.

Contribution

It presents a new cubic action exhibiting flavor-kinematics duality and derives a novel cubic action for the special Galileon theory from this framework.

Findings

All Feynman diagrams satisfy kinematic Jacobi identities.

Derived a new cubic action for the special Galileon.

Connected soft behavior of amplitudes to Weinberg's soft theorem.

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.