Harmonic Map Analysis of SU(N) Gravitating Skyrmions

TL;DR

This paper develops a harmonic map approach to analyze SU(N) gravitating skyrmions, enabling the derivation of symmetric equations and the numerical construction of solutions for various topological charges, including complex mixtures.

Contribution

It introduces a harmonic map framework for SU(N) Einstein-Skyrme systems, facilitating the study of symmetric equations and numerical solutions for higher N and diverse topological charges.

Findings

Derived SU(N) symmetric equations for gravitating skyrmions.

Numerically constructed SU(3) skyrmions with charges 4, 2, and 0.

Identified configurations with skyrmion-antiskyrmion mixtures.

Abstract

In this paper the SU(N) Einstein-Skyrme system is considered. We express the chiral field (which is not a simple embedding of the SU(2) one) in terms of harmonic maps. In this way, SU(N) spherical symmetric equations can be obtained easily for any $N$ and the gravitating skyrmion solutions of these equations can be studied. In particular, the SU(3) case is considered in detail and three different types of gravitating skyrmions with topological charge 4, 2 and 0, respectively, are constructed numerically. Note that the configurations with topological charge 0 correspond to mixtures of skyrmions and antiskyrmions.