Soliton stability in some knot soliton models

Details Soliton stability in some knot soliton models Soliton stability in some knot soliton models

2006-07-26

arxiv.org/abs/hep-th/0607216v1

J.Math.Phys.48:022305,2007

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, LaTex file

Scientific paper

10.1063/1.2435986

We study the issue of stability of static soliton-like solutions in some non-linear field theories which allow for knotted field configurations. Concretely, we investigate the AFZ model, based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charge (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not even critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model, which is based on a sigma-model type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier.

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