Fractional Skyrmions and their molecules

Abstract

We study a Skyrme-type model with a quadratic potential for a field with ${S}^{2}$ vacua. We consider two flavors of the model, the first is the Skyrme model and the second has a sixth-order derivative term instead of the Skyrme term; both with the added quadratic potential. The model contains molecules of half Skyrmions, each of them is a global (anti)monopole with baryon number $1/2$. We numerically construct solutions with baryon numbers one through six, and find stable solutions which look like beads on rings. We also construct a molecule with fractional Skyrmions having the baryon numbers $1/3+2/3$, by adding a linear potential term.