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

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.

Highlights

One of the most beautiful examples of the interplay between topology and field theory is provided by the Skyrme theory [1]
Applications of Skyrme model are encountered in gravitational physics, for instance in cosmology [18, 19] or black holes physics where it has been found that the “no hair” conjecture can be violated [20, 21, 22, 23, 24, 25]
We have derived an analytic upper bound for the number of Skyrmion–anti-Skyrmion bound states in terms of the parameters of the model

Summary

Introduction

One of the most beautiful examples of the interplay between topology and field theory is provided by the Skyrme theory [1]. By using the original spherical hedgehog ansatz of Skyrme, Klebanov proposed a phenomenological approach to the analysis of Skyrmions at finite density a long time ago [27] By following his point of view and using the technique of [28] [29], a non-vanishing isospin chemical potential was introduced in [30] [31]. A generalized hedgehog ansatz was proposed, which provides with a strategy to construct a non-spherical hedgehog-like ansatz with the right properties (see [32, 33, 34, 35], [36], [37], [38], [39], [40], [41] and references therein) both in the Skyrme and in the Yang-Mills-Higgs cases By using this technique, we construct analytic and topologically non-trivial solutions of the Skyrme model without spherical symmetry living within a finite box in flat space-times.

The Skyrme Model

Sine-Gordon and Skyrmions

Inclusion of chemical potential

Time crystals

The chemical potential

Conclusions