Infinite symmetries in the Skyrme model

TL;DR

This paper reveals that the Skyrme model contains an integrable submodel with infinite local conserved currents, specifically including topological charge ±1 Skyrmions, opening new avenues for exact solution methods.

Contribution

It identifies a novel integrable submodel within the Skyrme theory characterized by infinite conserved currents, based on a specific SU(2) decomposition.

Findings

Skyrme theory has an integrable submodel with infinite conserved currents.

Topological charge ±1 Skyrmions belong to this integrable sector.

Potential for developing exact solution methods in Skyrme theory.

Abstract

We show that the Skyrme theory possesses a submodel with an infinite number of local conserved currents. The constraints leading to the submodel explore a decomposition of SU(2) with a complex field parametrizing the symmetric space SU(2)/U(1) and a real field in the direction of U(1). We demonstrate that the Skyrmions of topological charges $\pm 1$ belong to such integrable sector of the theory. Our results open ways to the development of exact methods, compensating for the non-existence of a BPS type sector in the Skyrme theory.