Toroidal solitons in 3+1 dimensional integrable theories

Details Toroidal solitons in 3+1 dimensional integrable theories Toroidal solitons in 3+1 dimensional integrable theories

1999-02-20

arxiv.org/abs/hep-th/9902141v1

Phys.Lett. B456 (1999) 162-170

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 14 pgs

Scientific paper

10.1016/S0370-2693(99)00499-2

We analyze the integrability properties of models defined on the symmetric space SU(2)/U(1) in 3+1 dimensions, using a recently proposed approach for integrable theories in any dimension. We point out the key ingredients for a theory to possess an infinite number of local conservation laws, and discuss classes of models with such property. We propose a 3+1-dimensional, relativistic invariant field theory possessing a toroidal soliton solution carrying a unit of topological charge given by the Hopf map. Construction of the action is guided by the requirement that the energy of static configuration should be scale invariant. The solution is constructed exactly. The model possesses an infinite number of local conserved currents. The method is also applied to the Skyrme-Faddeev model, and integrable submodels are proposed.

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