Open AccessSpinning Hopf solitons onS3× Bbb R
Author(s) -
A.C.R. do Bonfim,
L. A. Ferreira
Publication year - 2006
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2006/03/097
Subject(s) - ansatz , diffeomorphism , mathematical physics , mathematics , group (periodic table) , conformal map , conformal symmetry , bounded function , invariant (physics) , soliton , space (punctuation) , hopf fibration , symmetry group , physics , conformal group , discrete group , conformal field theory , pure mathematics , mathematical analysis , quantum mechanics , geometry , linguistics , philosophy , nonlinear system
We consider a field theory with target space being the two dimensional sphereS^2 and defined on the space-time S^3 x R. The Lagrangean is the square of thepull-back of the area form on S^2. It is invariant under the conformal groupSO(4,2) and the infinite dimensional group of area preserving diffeomorphismsof S^2. We construct an infinite number of exact soliton solutions withnon-trivial Hopf topological charges. The solutions spin with a frequency whichis bounded above by a quantity proportional to the inverse of the radius ofS^3. The construction of the solutions is made possible by an ansatz whichexplores the conformal symmetry and a U(1) subgroup of the area preservingdiffeomorphism group.Comment: 12 pages, 1 eps figure, plain late
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