Sphaleron solutions of the Skyrme model from Yang-Mills holonomy

TL;DR

This paper presents a method to approximate axially symmetric sphalerons in the Skyrme model using the holonomy of non-BPS Yang-Mills calorons, linking topological properties of calorons to Skyrmion configurations.

Contribution

It introduces a novel approximation technique for Skyrmion-sphaleron solutions based on Yang-Mills caloron holonomy, connecting gauge theory and topological solitons.

Findings

Holonomy of caloron chains approximates Skyrmion chains well.

Approximation accuracy improves when Skyrmion topological charge is twice the caloron Chern-Pontryagin index.

Numerical results support the proposed approximation method.

Abstract

We discuss how an approximation to the axially symmetric sphalerons in the Skyrme model can be constructed from the holonomy of a non-BPS Yang-Mills calorons. These configurations, both in the Skyrme model and in the Euclidean Yang-Mills theory, are characterized by two integers n and m, where n are the winding numbers of the constituents and the second integer m defines type of the solution, it has zero topological charge for even m and for odd values of m the corresponding chain has total topological charge n. It is found numerically that the holonomy of the chains of interpolating calorons--anticalorons provides a reasonably good approximation to the corresponding Skyrmion--antiSkyrmion chains when the topological charge of the Skyrmion constitutents is two times more than the Chern-Pontryagin index of the caloron.