## 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.

Original language | English |
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Pages (from-to) | 401-407 |

Number of pages | 7 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 773 |

DOIs | |

State | Published - 2017 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2017 The Author(s)

## ASJC Scopus subject areas

- Nuclear and High Energy Physics