A note on higher-charge configurations for the Faddeev-Hopf model

TL;DR

This paper explores higher-charge solutions in the Faddeev-Hopf model, demonstrating their energy-minimizing properties and employing domain metric adjustments and a reduction technique based on the alpha-Hopf construction.

Contribution

It introduces a method to identify higher-charge solutions satisfying Euler-Lagrange equations using domain metric changes and an alpha-Hopf based reduction technique.

Findings

Higher-charge solutions are found satisfying Euler-Lagrange equations.

Some solutions are proven to be local minima for the reduced energy.

Identification of global minima among these solutions for the original energy.

Abstract

We identify higher-charge configurations that satisfy Euler-Lagrange equations for the (strong coupling limit of) Faddeev-Hopf model, by means of adequate changes of the domain metric and a reduction technique based on $\alpha$-Hopf construction. In the last case it is proved that the solutions are local minima for the reduced energy and we identify among them those who are global minima for the unreduced energy.