### 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, Section 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

*Nuclear Physics, Section B*,

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

**Abelian Hopfions of the CPn model on R2n+1 and a fractionally powered topological lower bound.** / Radu, Eugen; Tchrakian, D. H.; Yang, Yisong.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 875, no. 2, pp. 388-407. https://doi.org/10.1016/j.nuclphysb.2013.07.006

}

TY - JOUR

T1 - Abelian Hopfions of the CPn model on R2n+1 and a fractionally powered topological lower bound

AU - Radu, Eugen

AU - Tchrakian, D. H.

AU - Yang, Yisong

PY - 2013/10/11

Y1 - 2013/10/11

N2 - Regarding the Skyrme-Faddeev model on R3 as a CP1 sigma model, we propose CPn sigma models on R2n+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 CPn 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 R3, is a fractional power of the topological charge, depending on n. The numerical construction of the simplest ring shaped un-knot Hopfion on R5 is also discussed.

AB - Regarding the Skyrme-Faddeev model on R3 as a CP1 sigma model, we propose CPn sigma models on R2n+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 CPn 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 R3, is a fractional power of the topological charge, depending on n. The numerical construction of the simplest ring shaped un-knot Hopfion on R5 is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=84881541825&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881541825&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2013.07.006

DO - 10.1016/j.nuclphysb.2013.07.006

M3 - Article

VL - 875

SP - 388

EP - 407

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 2

ER -