### Abstract

Regarding the Skyrme-Faddeev model on R^{3} as a CP^{1} sigma model, we propose CP^{n} sigma models on R^{2n+1} as generalisations which may support finite energy Hopfion solutions in these dimensions. The topological charge stabilising these field configurations is the Chern-Simons charge, namely the volume integral of the Chern-Simons density which has a local expression in terms of the composite connection and curvature of the CP^{n} field. It turns out that subject to the sigma model constraint, this density is a total divergence. We prove the existence of a topological lower bound on the energy, which, as in the Vakulenko-Kapitansky case in R^{3}, is a fractional power of the topological charge, depending on n. The numerical construction of the simplest ring shaped un-knot Hopfion on R^{5} is also discussed.

Original language | English (US) |
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Pages (from-to) | 388-407 |

Number of pages | 20 |

Journal | Nuclear Physics B |

Volume | 875 |

Issue number | 2 |

DOIs | |

State | Published - Oct 11 2013 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

^{n}model on R

^{2n+1}and a fractionally powered topological lower bound.

*Nuclear Physics B*,

*875*(2), 388-407. https://doi.org/10.1016/j.nuclphysb.2013.07.006