Flavour-kinematics duality for Goldstone modes

TL;DR

This paper explores a flavour-kinematics duality among scalar effective field theories with Goldstone modes, revealing a unified structure that connects their symmetries, amplitudes, and potential gravity analogs.

Contribution

It establishes a novel off-shell mapping and on-shell amplitude factorization linking non-linear sigma models, multi-DBI, and Galileon theories via flavour-kinematics duality.

Findings

Identification of off-shell mappings between theories

Factorization of amplitudes into flavour and kinematic numerators

Implications for gravity interactions through scalar exchanges

Abstract

Three scalar effective field theories have special properties in terms of non-linear symmetries, soft limits and on-shell constructability that arise from their Goldstone nature: the non-linear $\sigma$-model, multi-DBI theory and the special Galileon. We discuss how these theories are related via flavour-kinematics duality, analogous to the colour-kinematics duality between gravity and gauge theories. At the off-shell level, we identify a specific mapping between the three theories that is crucially dependent on their non-linear symmetries. Similarly, we demonstrate how the on-shell amplitudes factorise into BCJ numerators describing flavour and a scalar version of kinematics, naturally leading to the inclusion of graviton exchange in the $SO(M,N)$ non-linear $\sigma$-model. Finally, we map those numerators onto each other, and comment on a similar relation to tensor kinematics. Our results highlight a common structure that underlies the physics of different Goldstone modes.