Integrability and chemical potential in the (3+1)-dimensional Skyrme model
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.
Keywords
Cite
@article{arxiv.1707.07421,
title = {Integrability and chemical potential in the (3+1)-dimensional Skyrme model},
author = {P. D. Alvarez and F. Canfora and N. Dimakis and A. Paliathanasis},
journal= {arXiv preprint arXiv:1707.07421},
year = {2017}
}
Comments
15 pages; 1 figure; a discussion on the closeness to the topological bound as well as some clarifying comments on the semi-classical quantization have been included. Relevant references have been added. Version accepted for publication on Physics Letters B