Instantons and the Buckyball

TL;DR

This paper proves the existence of a highly symmetric SU(2) Yang-Mills instanton with a buckyball structure, constructed explicitly via ADHM data, confirming predictions from Skyrmion theory.

Contribution

It provides the first explicit construction and verification of a charge seventeen instanton with buckyball symmetry, linking Skyrmion predictions to concrete instanton solutions.

Findings

Explicit ADHM data for the instanton is constructed.

The topological charge density exhibits a buckyball structure.

The existence of the symmetric instanton is rigorously proved.

Abstract

The study of Skyrmions predicts that there is an icosahedrally symmetric charge seventeen SU(2) Yang-Mills instanton in which the topological charge density, for fixed Euclidean time, is localized on the edges of the truncated icosahedron of the buckyball. In this paper the existence of such an instanton is proved by explicit construction of the associated ADHM data. A topological charge density isosurface is displayed which verifies the buckyball structure of the instanton.