$\mathbb{C}\mathrm{P}^2$ Skyrmion with Fermion Backreaction

TL;DR

This paper studies how localized fermions influence the shape of a $ ext{CP}^2$ Skyrmion, revealing that fermion backreaction causes the Skyrmion to deform and become more concentrated, which could impact the understanding of soliton-fermion interactions.

Contribution

It provides the first detailed analysis of fermion backreaction on a $ ext{CP}^2$ Skyrmion, showing deformation effects neglected in previous fixed-background models.

Findings

Skyrmion profile deforms due to fermion backreaction

Deformation results in increased concentration of the Skyrmion

Backreaction may mimic the effects of a potential term

Abstract

When fermions interact with a topological soliton, they localize on the soliton. In studies of such systems, solitons are often treated as fixed background fields, and the backreaction due to the fermion localization is usually neglected for simplicity. In this work, we investigate the backreaction of localized fermions on a $\mathbb{C}\mathrm{P}^2$ Skyrmion. We find that the Skyrmion profile deforms in response, becoming more concentrated around the localized fermions. We also discuss the possibility that this backreaction may play a role analogous to that of the potential term.