JNR Skyrmions

TL;DR

This paper introduces a new formula for constructing Skyrme fields in three-dimensional space, providing good approximations to Skyrmions with energies close to numerical solutions, inspired by the JNR ansatz for Yang-Mills instantons.

Contribution

It presents an analogous formula to the JNR ansatz for Skyrme fields, enabling the generation of approximate Skyrmions from simple geometric data.

Findings

Generated Skyrme fields closely approximate known Skyrmions

Energies of constructed Skyrmions are within a few percent of numerical solutions

The method offers a simple way to produce Skyrmion configurations

Abstract

The JNR ansatz provides a simple formula to obtain families of charge N self-dual SU(2) Yang-Mills instantons in four-dimensional Euclidean space, from the free data of N+1 distinct points with associated positive weights. Here an analogous formula is presented for Skyrme fields in three-dimensional Euclidean space. These families of Skyrme fields include good approximations to a range of Skyrmions, with energies that are typically within a few percent of the numerically computed solutions.