Multimonopoles and closed vortices in SU(2) Yang-Mills-Higgs theory

TL;DR

This paper reviews classical monopole solutions in SU(2) Yang-Mills-Higgs theory, introduces new axially symmetric solutions, and classifies configurations including monopole chains, vortices, and monopole-vortex bound states.

Contribution

It presents new classes of static axially symmetric monopole solutions and proposes a classification scheme based on the 2D Poincare index.

Findings

Constructed monopole-antimonopole chains in equilibrium

Described closed vortex solutions around the symmetry axis

Classified monopole-vortex configurations using topological indices

Abstract

We review classical monopole solutions of the SU(2) Yang-Mills-Higgs theory. The first part is a pedagogical introduction into to the basic features of the celebrated 't Hooft - Polyakov monopole. In the second part we describe new classes of static axially symmetric solutions which generalise 't Hooft - Polyakov monopole. These configurations are either deformations of the topologically trivial sector or the sectors with different topological charges. In both situations we construct the solutions representing the chains of monopoles and antimonopoles in static equilibrium. The solutions of another type are closed vortices which are centred around the symmetry axis and form different bound systems. Configurations of the third type are monopoles bounded with vortices. We suggest classification of these solutions which is related with 2d Poincare index.