Pions as Gluons in Higher Dimensions

TL;DR

This paper presents a novel higher-dimensional framework where pions are modeled as gluons, leading to new cubic actions for nonlinear sigma, Born-Infeld, and Galileon theories, revealing deep connections via color-kinematics duality.

Contribution

It introduces a higher-dimensional reformulation of pions as gluons, deriving cubic actions for multiple theories and elucidating their double copy relationships through a unified algebraic structure.

Findings

Derived a cubic action for the nonlinear sigma model.

Constructed a new quartic action for Born-Infeld theory.

Established a cubic action for the special Galileon.

Abstract

We derive the nonlinear sigma model as a peculiar dimensional reduction of Yang-Mills theory. In this framework, pions are reformulated as higher-dimensional gluons arranged in a kinematic configuration that only probes cubic interactions. This procedure yields a purely cubic action for the nonlinear sigma model which exhibits a symmetry enforcing color-kinematics duality. Remarkably, the associated kinematic algebra originates directly from the Poincare algebra in higher dimensions. Applying the same construction to gravity yields a new quartic action for Born-Infeld theory and, applied once more, a cubic action for the special Galileon theory. Since the nonlinear sigma model and special Galileon are subtly encoded in the cubic sectors of Yang-Mills theory and gravity, respectively, their double copy relationship is automatic.