  We propose a generalized Skyrme-Faddeev type theory with an additional scalar
field. In a special case of model parameters one has a theory which admits
exact knot solutions given by a class of exact toroidal solitons from
Aratyn-Ferreira-Zimerman (AFZ) integrable CP1 model. In a general case the
theory admits an exact knot solution for a unit Hopf charge. For higher Hopf
charges we perform numeric analysis of the solutions and obtain estimates for
the knot energies using energy minimization procedure based on ansatz with AFZ
field configurations and with rational functions. We show that AFZ
configurations provide a better approximate solutions. The corresponding knot
energies are in a good agreement with a standard law for the low energy bound,
E_H\simeq Q_H^{3/4}.

High Energy Physics - Theory