ADHM skyrmions

TL;DR

This paper introduces an ADHM-based framework for approximating and analyzing skyrmions on  using instanton data, achieving high accuracy and enabling the study of complex nuclear configurations.

Contribution

It develops a novel ADHM-based approximation method for skyrmions, linking instanton data to Skyrme fields and enabling analysis of multi-skyrmion clusters.

Findings

Accurately describes skyrmions with charge   within 2% energy error.

Provides explicit ADHM data for large families of configurations.

Develops factorisation methods for studying skyrmion clusters.

Abstract

We propose, via the Atiyah-Manton approximation, a framework for studying skyrmions on $\mathbb{R}^3$ using ADHM data for Yang-Mills instantons on $\mathbb{R}^4$. We provide a dictionary between important concepts in the Skyrme model and analogous ideas for ADHM data, and describe an efficient process for obtaining approximate Skyrme fields directly from ADHM. We show that the approximation successfully describes all known skyrmions with charge $\mathcal{B} \leq 8$, with energies reproduced within 2% of the true minimisers. We also develop factorisation methods for studying clusters of instantons and skyrmions, generalising early work by Christ-Stanton-Weinberg, and describe some relatively large families of explicit ADHM data. These tools provide a unified framework for describing coalesced highly-symmetric configurations as well as skyrmion clusters, both of which are needed to study nuclear systems in the Skyrme model.