Strongly coupled Skyrme-Faddeev-Niemi hopfions

Understand

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|.