Magnetic ZN symmetry in 2+1 dimensions

This review describes the role of magnetic symmetry in (2 + 1)-dimensional gauge theories. In confining theories without matter fields in fundamental representation the magnetic symmetry is spontaneously broken. Under some mild assumptions, the low-energy dynamics is determined universally by this spontaneous breaking phenomenon. The degrees of freedom in the effective theory are magnetic vortices. Their role in confining dynamics is similar to that played by pions and a in the chiral symmetry breaking dynamics. I give an explicit derivation of the effective theory in (2 + 1)-dimensional weakly coupled confining models and argue that it remains qualitatively the same in strongly coupled (2 + 1)-dimensional gluodynamics. Confinement in this effective theory is a very simple classical statement about the long range interaction between topological solitons, which follows (as a result of a simple direct classical calculation) from the structure of the effective Lagrangian. I show that if fundamentally charged dynamical fields are present the magnetic symmetry becomes local rather than global. The modifications to the effective low energy description in the case of heavy dynamical fundamental matter are discussed. This effective Lagrangian naturally yields a bag like description of baryonic excitations. I also discuss the fate of the magnetic symmetry in gauge theories with the Chern-Simons term.