## Abstract

We present a family of static knotted soliton energy functionals governing the configuration maps from the Euclidean space R^{4 n - 1} into the unit sphere S^{2 n} so that the knot charges are naturally represented by the Hopf invariants in the homotopy group π_{4 n - 1} (S^{2 n}) and the special case n = 1 recovers the classical Faddeev knot energy. We establish the general result that the minimum energy or the knot mass E_{N} of knotted solitons of the Hopf charge N satisfies the universal fractional-exponent growth law E_{N} ∼ | N |^{(4 n - 1) / 4 n}, in which the fractional exponent depends only on the dimensions of the domain and range spaces of the configuration maps but does not depend on the detailed structure of the knot energy.

Original language | English (US) |
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Pages (from-to) | 455-463 |

Number of pages | 9 |

Journal | Nuclear Physics B |

Volume | 747 |

Issue number | 3 |

DOIs | |

State | Published - Jul 24 2006 |

## Keywords

- Faddeev knots
- Hopf fibration
- Knot energy
- Skyrme energy
- Sobolev inequalities
- Sublinear growth
- Universality

## ASJC Scopus subject areas

- Nuclear and High Energy Physics