Skyrme Crystal from a Twisted Instanton on a Four-Torus

TL;DR

This paper presents a novel method to approximate the minimal energy Skyrme crystal using the holonomy of a twisted Yang-Mills instanton on a four-torus, achieving near-optimal energy levels.

Contribution

It introduces a new approach linking twisted instantons to Skyrme crystals, providing an analytical fit to numerical data for better approximation.

Findings

Skyrme crystal energy within 2% of known solutions

Uses twisted instanton holonomy to generate Skyrme fields

Provides an analytical fit to numerical instanton data

Abstract

We describe how an approximation to the minimal energy Skyrme crystal can be obtained from the holonomy of a Yang-Mills instanton. The appropriate instanton is twisted on a four-torus and has instanton number equal to one half. It generates a Skyrme field with the correct topological and symmetry properties of the crystal. An explicit solution for the instanton is not known, but an analytical fit to numerical data is available and using this we obtain a Skyrme crystal whose energy is only 2 percent above that of the (numerically) known solution.