Z(N) topology and color confinement in non-Abelian gauge theories

The problems of monopole condensation and color confinement in the Yang-Mills theory are discussed. External 'quarks' were introduced into the Yang-Mills theory. Quarks are confined by electric vortices. The essential part of the vortices may be discussed in terms of the Abelian components. On the other hand, the gauge invariance of the system would be recovered by taking into account non-Abelian quantum fluctuation. The condensation of magnetic root monopoles was analyzed. The Yang-Mills vacuum may be considered to be a condensed phase of magnetic root monopoles. By assuming that the Abelian components dominate the long distance behavior of the Yang-Mills theory, it can be shown that electric weight charges are confined by electric Z(N) vortices. The partition function of a statistical system composed of magnetic monopoles interacting according to the Lagrangian was evaluated. (Kato, T.)