Static Monopoles and Their Anti-Configurations

TL;DR

This paper explores new exact solutions of monopole and antimonopole configurations with various symmetries, classifying them into different types, and introduces their anti-configurations with reversed magnetic charges, expanding understanding of BPS solutions.

Contribution

It presents a classification of new monopole, multimonopole, and antimonopole solutions with different symmetries and constructs their anti-configurations, highlighting solutions with infinite energy and half-integer charges.

Findings

Classified monopole solutions by symmetry and configuration type.

Constructed anti-configurations with reversed magnetic charges.

Identified solutions with half-integer topological charges.

Abstract

Recently, we have reported on the existence of some monopoles, multimonopole, and antimonopoles configurations. In this paper we would like to present more monopoles, multimonopole, and antimonopoles configurations of the magnetic ansatz of Ref.\cite{kn:9} when the parameters $p$ and $b$ of the solutions takes different serial values. These exact solutions are a different kind of BPS solution. They satisfy the first order Bogomol'nyi equation but possess infinite energy. They can have radial, axial, or rotational symmetry about the z-axis. We classified these serial solutions as (i) the multimonopole at the origin; (ii) the finitely separated 1-monopoles; (iii) the screening solutions of multimonopole and (iv) the axially symmetric monopole solutions. We also give a construction of their anti-configurations with all the magnetic charges of poles in the configurations reversed. Half-integer topological magnetic charge multimonopole also exist in some of these series of solutions.