Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory

TL;DR

This paper explores the low-energy behavior of SU(2) Yang-Mills theory, revealing spin-charge separation, conformal covariance, and connections to nonlinear sigma models and gravity-like structures, with implications for stable solitons and symmetry breaking.

Contribution

It introduces a novel low-energy reformulation of SU(2) Yang-Mills theory featuring spin-charge separation and a covariant form resembling gravity, highlighting new parameters and soliton solutions.

Findings

Spin and charge separation in low-energy SU(2) Yang-Mills theory.

Reformulation of the Lagrangian into a covariant form with Einstein-Hilbert structure.

Presence of stable knotted solitons and a new dimensionful parameter.

Abstract

In the low energy domain of four-dimensional SU(2) Yang-Mills theory the spin and the charge of the gauge field can become separated from each other. The ensuing field variables describe the interacting dynamics between a version of the O(3) nonlinear $\sigma$-model and a nonlinear Grassmannian $\sigma$-model, both of which may support closed knotted strings as stable solitons. Lorentz transformations act projectively in the O(3) model which breaks global internal rotation symmetry and removes massless Goldstone bosons from the particle spectrum. The entire Yang-Mills Lagrangian can be recast into a generally covariant form with a conformally flat metric tensor. The result contains the Einstein-Hilbert Lagrangian together with a nonvanishing cosmological constant, and insinuates the presence of a novel dimensionfull parameter in the Yang-Mills theory.