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

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.Comment: 34 pages, 8 figures. Invited contribution prepared for Review Volume "Etudes on Theoretical Physics" dedicated to 65th anniversary of the Department of Theoretical Physics, Belarus State University, Minsk. Based on a work in collaboration with Jutta Kunz and Burkhard Kleihaus. Any comments and suggestions, especially with respect to references, are welcom