Fractional Skyrmion molecules in a $\mathbb{C}P^{N-1}$ model

TL;DR

This paper investigates fractional Skyrmions in a $ ext{CP}^2$ baby Skyrme model with an extended potential, revealing stable and metastable molecular solutions with discrete symmetries through numerical analysis.

Contribution

It introduces a generalized potential in the $ ext{CP}^2$ model and demonstrates the existence of various stable and metastable fractional Skyrmion molecules with symmetry properties.

Findings

Stable, metastable, and unstable Skyrmion solutions identified.

Solutions exhibit discrete symmetries linked to field congruencies.

Numerical methods used to analyze complex molecular configurations.

Abstract

We study fractional Skyrmions in a $\mathbb{C}P^2$ baby Skyrme model with a generalization of the easy-plane potential. By numerical methods, we find stable, metastable, and unstable solutions taking the shapes of molecules. Various solutions possess discrete symmetries, and the origin of those symmetries are traced back to congruencies of the fields in homogeneous coordinates on $\mathbb{C}P^2$.