Static knot energy, Hopf charge, and universal growth law

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We present a family of static knotted soliton energy functionals governing the configuration maps from the Euclidean space R4 n - 1 into the unit sphere S2 n so that the knot charges are naturally represented by the Hopf invariants in the homotopy group π4 n - 1 (S2 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 EN of knotted solitons of the Hopf charge N satisfies the universal fractional-exponent growth law EN ∼ | 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 languageEnglish (US)
Pages (from-to)455-463
Number of pages9
JournalNuclear Physics B
Issue number3
StatePublished - Jul 24 2006


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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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