Hopf solitons and Hopf Q-balls on S3
Departamento de Fisica de Particulas, Universidad de Santiago and Instituto Galego de Fisica de Altas Enerxias (IGFAE), 15782, Santiago de Compostela, Spain
2 Institute of Physics, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland
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Revised: 8 April 2006
Published online: 7 June 2006
Field theories with a S2-valued unit vector field living on S3×ℝ space-time are investigated. The corresponding eikonal equation, which is known to provide an integrable sector for various sigma models in different spaces, is solved giving static as well as time-dependent multiply knotted configurations on S3 with arbitrary values of the Hopf index. Using these results, we then find a set of hopfions with topological charge QH=m2, m∈Z, in the integrable subsector of the pure CP1 model. In addition, we show that the CP1 model with a potential term provides time-dependent solitons. In the case of the so-called “new baby Skyrme” potential we find, e.g., exact stationary hopfions, i.e., topological Q-balls. Our results further enable us to construct exact static and stationary Hopf solitons in the Faddeev–Niemi model with or without the new baby Skyrme potential. Generalizations for a large class of models are also discussed.
© Springer-Verlag, 2006