Skyrmions from calorons

TL;DR

This paper derives a gauged Skyrme model from Yang-Mills theory on a specific spacetime, showing that skyrmions can be approximated by calorons and monopoles, and explores their relationships through boundary conditions and limits.

Contribution

It introduces a one-parameter family of gauged Skyrme models derived from Yang-Mills theory, connecting skyrmions, calorons, and monopoles in a unified framework.

Findings

Calorons interpolate between instantons and monopoles in certain limits.

Spherically symmetric solutions exhibit behavior similar to calorons and monopoles.

The model provides insights into the relationships between skyrmions, calorons, and monopoles.

Abstract

We derive a one-parameter family of gauged Skyrme models from Yang-Mills theory on $S^1\times\mathbb{R}^3$, in which skyrmions are well-approximated by calorons and monopoles. In particular we study the spherically symmetric solutions to the model with two distinct classes of boundary conditions, and compare them to calorons and monopoles. Calorons interpolate between instantons and monopoles in certain limits, and we observe similar behaviour in the constructed gauged Skyrme model in the weak and strong coupling limits. This comparison of calorons, monopoles, and skyrmions may be a way to further understand the apparent relationships between skyrmions and monopoles on $\mathbb{R}^3$.