On the effects of the Chern-Simons term in an Abelian gauged Skyrme model in $d=4+1$ dimensions

TL;DR

This paper investigates how the Chern-Simons term affects the properties of an Abelian gauged Skyrme model in 4+1 dimensions, revealing unusual relations between energy, charge, and angular momentum through numerical analysis.

Contribution

It demonstrates the impact of the Chern-Simons term on the mass-energy, electric charge, and baryon number relations in a 4+1 dimensional gauged Skyrme model, extending previous 2+1 dimensional findings.

Findings

Unusual E-Qe-J relations due to Chern-Simons dynamics.

Solutions with varying magnetic field asymptotics.

Numerical analysis on an effective radial symmetry subsystem.

Abstract

We study an Abelian gauged $O(5)$ Skyrme model in $4+1$ dimensions, featuring the $F^4$ Maxwell and the Chern-Simons terms. Our aim is to expose the mechanism, discovered in the analogous Abelian gauged $O(3)$ Skyrme model in $2+1$ dimensions, which leads to the unusual relation of the mass-energy $E$ to the electric charge $Q_e$ and angular momentum $J$, and, to the change in the value of the "baryon number" $q$ due to the influence of the Abelian field on the Skyrmion. Chern-Simons dynamics together with the dynamics of the gauged Skyrme scalar, allows for solutions with varying asymptotic values of the magnetic field, resulting in these unusual properties listed. Numerical work is carried out on an effective one dimensional subsystem resulting from imposition of an enhaced radial symmetry on ${\mathbb R}^4$.