Instanton vibrations of the 3-Skyrmion

TL;DR

This paper calculates the Atiyah-Drinfeld-Hitchin-Manin matrix for a tetrahedrally symmetric 3-instanton and analyzes its vibrations, comparing them to known 3-Skyrmion vibration spectra.

Contribution

It provides a detailed calculation of the ADHM matrix for a symmetric 3-instanton and links its vibrations to the 3-Skyrmion spectrum, offering new insights into their symmetry properties.

Findings

Decomposition of vibrations under tetrahedral symmetry

Comparison with existing 3-Skyrmion vibration spectrum

Identification of specific vibrational modes

Abstract

The Atiyah-Drinfeld-Hitchin-Manin matrix corresponding to a tetrahedrally symmetric 3-instanton is calculated. Some small variations of the matrix correspond to vibrations of the instanton-generated 3-Skyrmion. These vibrations are decomposed under tetrahedral symmetry and this decomposition is compared to previous knowledge of the 3-Skyrmion vibration spectrum.