Sphaleron solutions of the Skyrme model from Yang–Mills holonomy

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 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 constituents is two times more than the Chern–Pontryagin index of the caloron.