Exact vortex solutions in an extended Skyrme-Faddeev model

TL;DR

This paper presents the first exact analytical vortex solutions in an extended Skyrme-Faddeev model, which may shed light on the low energy behavior of SU(2) Yang-Mills theory.

Contribution

It constructs the first exact vortex solutions in a 3+1 dimensional extension of the Skyrme-Faddeev model, revealing special scale-invariant sectors with conserved charges.

Findings

Exact vortex solutions are scale invariant and satisfy Bogomolny equations.

Solutions have energies proportional to topological charge.

Vortices can support light-speed waves with additional Noether charge.

Abstract

We construct exact vortex solutions in 3+1 dimensions to a theory which is an extension, due to Gies, of the Skyrme-Faddeev model, and that is believed to describe some aspects of the low energy limit of the pure SU(2) Yang-Mills theory. Despite the efforts in the last decades those are the first exact analytical solutions to be constructed for such type of theory. The exact vortices appear in a very particular sector of the theory characterized by special values of the coupling constants, and by a constraint that leads to an infinite number of conserved charges. The theory is scale invariant in that sector, and the solutions satisfy Bogomolny type equations. The energy of the static vortex is proportional to its topological charge, and waves can travel with the speed of light along them, adding to the energy a term proportional to a U(1) Noether charge they create. We believe such vortices may play a role in the strong coupling regime of the pure SU(2) Yang-Mills theory.