Gauged multisoliton baby Skyrme model

Abstract

We present a study of U (1) gauged modification of the 2+1 dimensional planar Skyrme model with a particular choice of the symmetry breaking potential term which combines a short-range repulsion and a long-range attraction. In the absence of the gauge interaction the multi-solitons of the model are aloof, they consist of the individual constituents which are well separated. Peculiar feature of the model is that there are usually several different stable static multi-soliton solutions of rather similar energy in a topological sector of given degree. We investigated the pattern of the solutions and find new previously unknown local minima. It is shown that coupling of the aloof planar multi-Skyrmions to the magnetic field strongly affects the pattern of interaction between the constituents. We analyse the dependency of the structure of the solutions, their energies and magnetic fluxes on the strength of the gauge coupling. It is found that, generically, in the strong coupling limit the coupling to the gauge field results in effective recovering of the rotational invariance of the configuration.

Magnetic Hopfions in the Faddeev-Skyrme-Maxwell model

“…[28,38]. The fields are discretized on the grid with 100 3 or 150 3 points with grid spacing Δx ¼ 0.1.…”

“…Unlike the gauged planar baby-Skyrme model [27][28][29], in the three-dimensional Faddeev-Skyrme-Maxwell model (1), the Uð1Þ gauging prescription (3) is not necessarily correlated with the vacuum boundary condition imposed on the scalar field. The topological restriction on the scalar field is that on the spatial boundary ⃗ ϕ must approach the same vacuum value regardless of direction, and then R 3 ↦ S 3 .…”

“…Note that under a spatial rescaling x → λx, this term in the action scales as λ −1 ; i.e., it has the same scaling properties as the quartic in the derivative Skyrme term. The flat metric is g μν ¼ diagð1; −1; −1; −1Þ, and the coupling of the scalar triplet to the gauge field is given by the covariant derivative [27,28,33,34] …”

“…Hence, the Hopfions are invariant with respect to the global SOð2Þ symmetry of the vacuum. This allows us to construct the Uð1Þ gauged Faddeev-Skyrme-Maxwell theory by analogy with the extension of the gauged planar baby-Skyrme model [27][28][29]. Clearly, electromagnetic interaction will strongly affect the usual pattern of interaction in the system of Hopfions.…”

Fractional Hopfions in the Faddeev-Skyrme model with a symmetry breaking potential

“…To find the stationary points of the energy functional (2.4) with the potential (2.6) we make use of the numerical minimization technique described in [45,46]. The fields are discretized on the grid with 150 3 , or 200 3 point with spatial grid spacings ∆x = 0.1, 0.06 or ∆x = 0.05.…”