Physics of non-Abelian confinement and the dual gauge symmetry: Many faces of flavor symmetry

We review the physics of confinement based on non-Abelian dual superconductor picture, relying on exact solutions in N = 2 supersymmetric QCD and based on the recent developments in our understanding of non-Abelian vortices and monopoles. The non-Abelian monopoles, though they are basically just the 't Hooft-Polyakov SU(2) monopoles embedded in various corners of the larger gauge group, require flavor symmetry in an essential way for their very existence. The phenomenon of flavor-color-flavor separation characterizes the multiple roles flavor symmetry plays in producing quantum-mechanical non-Abelian monopoles.