Symmetric Instantons and Skyrme Fields

TL;DR

This paper constructs a symmetric charge seven instanton and derives a Skyrme field that models a complex Skyrmion scattering process, advancing understanding of topological solitons.

Contribution

It explicitly constructs a symmetric instanton and links it to a Skyrme field modeling Skyrmion interactions, including a scattering process.

Findings

Existence of a charge seven icosahedrally symmetric instanton

Skyrme field approximating minimal energy charge seven Skyrmion

Modeling of Skyrmion scattering process with symmetry

Abstract

By explicit construction of the ADHM data, we prove the existence of a charge seven instanton with icosahedral symmetry. By computing the holonomy of this instanton we obtain a Skyrme field which approximates the minimal energy charge seven Skyrmion. We also present a one parameter family of tetrahedrally symmetric instantons whose holonomy gives a family of Skyrme fields which models a Skyrmion scattering process, where seven well-separated Skyrmions collide to form the icosahedrally symmetric Skyrmion.