Vortices in the extended Skyrme-Faddeev model

We construct analytical and numerical vortex solutions for an extended Skyrme-Faddeev model in a $(3+1)$ dimensional Minkowski space-time. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the kinetic term, and a potential which breaks the $SO(3)$ symmetry down to $SO(2)$. The construction makes use of an ansatz, invariant under the joint action of the internal $SO(2)$ and three commuting $U(1)$ subgroups of the Poincar\'e group, and which reduces the equations of motion to an ordinary differential equation for a profile function depending on the distance to the ${x}^{3}$ axis. The vortices have finite energy per unit length, and have waves propagating along them with the speed of light. The analytical vortices are obtained for a special choice of potentials, and the numerical ones are constructed using the successive over relaxation method for more general potentials. The spectrum of solutions is analyzed in detail, especially its dependence upon special combinations of coupling constants.

Перевод пока недоступен