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

P. D. Alvarez; F. Canfora; N. Dimakis; A. Paliathanasis

doi:10.1016/j.physletb.2017.08.073

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arXiv · 1707.07421

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

P. D. Alvarez·F. Canfora·N. Dimakis·A. Paliathanasis

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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.

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P. D. Alvarez, F. Canfora, N. Dimakis, A. Paliathanasis. 2017-07-24. Integrability and chemical potential in the (3+1)-dimensional Skyrme model. https://doi.org/10.1016/j.physletb.2017.08.073

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