Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and ${\mathbb C}P^{N-1}$ Lumps

TL;DR

This paper demonstrates a correspondence between non-Abelian sine-Gordon solitons, ${ m SU}(N)$ Skyrmions, and ${ m extbf{C}P}^{N-1}$ lumps, showing Skyrmions can be stable without the Skyrme term in certain models.

Contribution

The authors construct an effective theory on non-Abelian sine-Gordon solitons and reveal that ${ m extbf{C}P}^{N-1}$ lumps correspond to ${ m SU}(N)$ Skyrmions, illustrating a new physical realization of the rational map Ansatz.

Findings

${ m extbf{C}P}^{N-1}$ lumps represent ${ m SU}(N)$ Skyrmions.

Skyrmions can be stable without the Skyrme term.

Effective theory on solitons is a nonlinear sigma model with target space ${ m extbf{R}} imes { m extbf{C}P}^{N-1}$.

Abstract

Topologically stable non-Abelian sine-Gordon solitons have been found recently in the $U(N)$ chiral Lagrangian and a $U(N)$ gauge theory with two $N$ by $N$ complex scalar fields coupled to each other. We construct the effective theory on a non-Abelian sine-Gordon soliton that is a nonlinear sigma model with the target space ${\mathbb R} \times {\mathbb C}P^{N-1}$. We then show that ${\mathbb C}P^{N-1}$ lumps on it represent $SU(N)$ Skyrmions in the bulk point of view, providing a physical realization of the rational map Ansatz for Skyrmions of the translational (Donaldson) type. We find therefore that Skyrmions can exist stably without the Skyrme term.