Dirac-Yang monopoles and their regular counterparts

TL;DR

This paper explores the hierarchy of Dirac-Yang monopoles across all dimensions, introduces their regular counterparts, and discusses their topological significance and potential applications.

Contribution

It defines the hierarchy of Dirac-Yang monopoles and presents two classes of their regular counterparts in all dimensions, expanding understanding of monopole solutions.

Findings

Hierarchy of Dirac-Yang monopoles established

Two classes of regular monopole counterparts identified

Topological context for monopole study provided

Abstract

The Dirac-Yang monopoles are singular Yang--Mills field configurations in all Euclidean dimensions. The regular counterpart of the Dirac monopole in D=3 is the t Hooft-Polyakov monopole, the former being simply a gauge transform of the asymptotic fields of the latter. Here, regular counterparts of Dirac-Yang monopoles in all dimensions, are described. In the first part of this talk the hierarchy of Dirac--Yang (DY) monopoles will be defined, in the second part the motivation to study these in a topoical context will be briefly presented, and in the last part, two classes of regular counterparts to the DY hierarchy will be presented.