A model for gauged skyrmions with low binding energies

TL;DR

This paper develops a gauged Skyrme model derived from Yang-Mills theory, approximates charge 1 skyrmions using calorons, and explores their magnetic properties to suggest a more realistic Skyrme-Maxwell theory with low binding energies.

Contribution

It introduces a new approach to model gauged skyrmions with boundary conditions breaking SU(2) to U(1), using calorons for energy minimization and magnetic moment calculations.

Findings

Calorons with non-trivial holonomy provide effective skyrmion approximations.

Calculated magnetic dipole moments match experimental proton and neutron values.

Proposes a Skyrme-Maxwell model capable of low binding energies.

Abstract

We consider gauged skyrmions with boundary conditions which break the gauge from $\mathrm{SU}(2)$ to $\mathrm{U}(1)$ in models derived from Yang-Mills theory. After deriving general topological energy bounds, we approximate charge $1$ energy minimisers using KvBLL calorons with non-trivial asymptotic holonomy, use them to calibrate the model to optimise the ratio of energy to lower bound, and compare them with solutions to full numerical simulation. Skyrmions from calorons with non-trivial asymptotic holonomy exhibit a non-zero magnetic dipole moment, which we calculate explicitly, and compare with experimental values for the proton and the neutron. We thus propose a way to develop a physically realistic Skyrme-Maxwell theory, with the potential for exhibiting low binding energies.