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 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.