Strongly coupled Skyrme-Faddeev-Niemi hopfions

TL;DR

This paper investigates exact Hopf solitons in a strongly coupled Skyrme-Faddeev-Niemi model on S^3 x R, revealing different types of solutions with unique energy-charge relations depending on the potential and Hopf index.

Contribution

It provides explicit solutions for Hopf solitons in the strongly coupled limit, including compact and non-compact types, and analyzes their energy bounds and topological properties.

Findings

Compact hopfions saturate a Bogomolny bound with E ~ |Q|^{1/2}

Non-compact hopfions do not saturate the bound and have E ~ |Q|

Potentials with two vacua produce shell-like hopfions.

Abstract

The strongly coupled limit of the Skyrme-Faddeev-Niemi model (i.e., without quadratic kinetic term) with a potential is considered on the spacetime S^3 x R. For one-vacuum potentials two types of exact Hopf solitons are obtained. Depending on the value of the Hopf index, we find compact or non-compact hopfions. The compact hopfions saturate a Bogomolny bound and lead to a fractional energy-charge formula E \sim |Q|^{1/2}, whereas the non-compact solitons do not saturate the bound and give E \sim |Q|. In the case of potentials with two vacua compact shell-like hopfions are derived. Some remarks on the influence of the potential on topological solutions in the full Skyrme-Faddeev-Niemi model or in (3+1) Minkowski space are also made.