Integrability and chemical potential in the (3+1)-dimensional Skyrme model

TL;DR

This paper analytically constructs Skyrmions and their bound states in (3+1)D using a mapping to the Sine-Gordon model, explores their stability under chemical potential, and introduces topologically protected time-crystals.

Contribution

It provides the first analytic examples of Skyrmions and Skyrmion-anti-Skyrmion bound states in flat (3+1)D space-time and analyzes their stability and time-crystal configurations.

Findings

Analytic bounds on Skyrmion-anti-Skyrmion bound states.

Critical isospin chemical potential for Skyrmion existence.

Construction of topologically protected time-crystals.

Abstract

Using a remarkable mapping from the original (3+1)dimensional Skyrme model to the Sine-Gordon model, we construct the first analytic examples of Skyrmions as well as of Skyrmions--anti-Skyrmions bound states within a finite box in 3+1 dimensional flat space-time. An analytic upper bound on the number of these Skyrmions--anti-Skyrmions bound states is derived. We compute the critical isospin chemical potential beyond which these Skyrmions cease to exist. With these tools, we also construct topologically protected time-crystals: time-periodic configurations whose time-dependence is protected by their non-trivial winding number. These are striking realizations of the ideas of Shapere and Wilczek. The critical isospin chemical potential for these time-crystals is determined.