Pions as Gluons in Higher Dimensions

TL;DR

The paper develops a dimensionally reduced framework in which pions arise as higher-dimensional gluons, yielding a purely cubic NLSM with color-kinematics duality whose kinematic algebra originates from the higher-dimensional Poincaré group. Applying the same reduction to gravity produces a quartic BI action and, after a second reduction, a cubic SG action, with the double copy structure emerging naturally from the cubic sectors. Weight counting and transverse constraints justify truncations, making the actions substantially simpler for perturbative computations while preserving the correct tree-level amplitudes. This work clarifies the origin of the kinematic algebra and establishes an action-level realization of the transmutations that relate YM, NLSM, BI, and SG, with potential implications for loop order and Goldstone-boson connections.

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.