Static knot energy, Hopf charge, and universal growth law

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Abstract

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

Original languageEnglish (US)
Pages (from-to)455-463
Number of pages9
JournalNuclear Physics B
Volume747
Issue number3
DOIs
StatePublished - Jul 24 2006

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Keywords

  • 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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