SU(N) Skyrmions from Instantons

TL;DR

This paper extends the Atiyah-Manton scheme to construct explicit approximations of static spherically symmetric SU(N) skyrmions with various baryon numbers using instantons and harmonic maps into complex projective spaces.

Contribution

It generalizes the Atiyah-Manton approach to SU(N) skyrmions and provides explicit constructions using harmonic maps, expanding the understanding of skyrmion solutions.

Findings

Explicit approximations for SU(N) skyrmions with various baryon numbers.

Method to derive skyrmions from instantons via harmonic maps.

Extension of the Atiyah-Manton scheme to higher SU(N) groups.

Abstract

Atiyah and Manton have outlined a scheme to obtain approximations to the SU(2) skyrmions from instantons in $\R^4$. In this paper we apply this scheme to construct, in an explicit form, approximations to static spherically symmetric SU(N) skyrmions with various baryon numbers. In particular we show how to obtain the skyrmions from instantons using harmonic maps into complex projective spaces.