Magnetic Hopfions in the Faddeev-Skyrme-Maxwell model

TL;DR

This paper introduces new magnetic Hopfion solutions in the Faddeev-Skyrme-Maxwell model, revealing how magnetic coupling influences soliton structures and flux configurations based on boundary conditions and gauge strength.

Contribution

It presents novel magnetic Hopfion solutions and analyzes how magnetic coupling affects their transmutation and flux structure in the Faddeev-Skyrme-Maxwell model.

Findings

Magnetic fluxes are governed by preimages of specific points in the field.

Coupling allows soliton transmutations depending on boundary conditions.

Flux structures depend on gauge coupling strength.

Abstract

We construct new solutions of the Faddeev-Skyrme-Maxwell model, which represent Hopf solitons coupled to magnetic fluxes. It turns out that coupling to the magnetic field allows for transmutations of the solitons, however, the results depend both on the type of the vacuum boundary condition and on the strength of the gauge coupling. It is shown that the structure of the magnetic fluxes of a gauged Hopfion is governed by the preimages of the points $\phi_3=\pm 1$.