Collective coordinates of the Skyrme model coupled with fermions

TL;DR

This paper explores the mathematical structure of the Skyrme model coupled with fermions, constructing a fiber bundle over its moduli space and analyzing the effects of fermion interactions on its geometric properties.

Contribution

It introduces a fiber bundle framework for the Skyrme model with fermions and examines how fermion interactions influence the moduli space geometry.

Findings

Fermion interactions turn the moduli space into a real vector bundle.

The bundle admits a natural SO(2n+1) connection.

Potential for non-trivial holonomy in the extended model.

Abstract

The problem of construction of fiber bundle over the moduli space of the Skyrme model is considered. We analyse an extension of the original Skyrme model which includes the minimal interaction with fermions. An analogy with modili space of the fermion-monopole system is used to construct a fiber bundle structure over the skyrmion moduli space. The possibility of the non-trivial holonomy appearance is considered. It is shown that the effect of the fermion interaction turns the $n$-skyrmion moduli space into a real vector bundle with natural $SO(2n+1)$ connection.