Quantum Nonabelian Monopoles

There are several reasons to be interested in quantum, nonabelian monopoles. First, if confinement of QCD is a sort of dual superconductor, it is likely to be one of nonabelian variety. Then the effective degrees of freedom involve nonabelian, and not, better understood abelian monopoles. Second, the phenomenon of confinement has to do with fully quantum mechanical, and not semi-classical, behavior of the monopoles. Thirdly, the very concept of nonabelian monopoles is, as we shall see, intrinsically quantum mechanical, in contrast to that of the ’t Hooft-Polyakov monopole carrying an abelian charge only. A semi-classical consideration only might easily lead us astray. Finally, some recent developments on nonabelian BPS vortices provide further hints on the subtle nature of nonabelian monopoles and related dual gauge transformations. These considerations are sufficient motivations to give a renewed look on the topological as well as dynamical aspects of these soliton states, in particular in relation to N = 2 gauge theories.