Non-Abelian confinement in N=2 supersymmetric QCD: Duality and kinks on confining strings

Recently we observed a crossover transition (in the Fayet-Iliopoulos parameter) from weak to strong coupling in N = 2 supersymmetric QCD with the U(N) gauge group and N-f > N quark flavors. At strong coupling this theory can be described by a dual non-Abelian weakly coupled supersymmetric QCD with the dual gauge group U(N-f - N) and N-f light dyon flavors. Both theories support non-Abelian strings. We continue the study of confinement dynamics in these theories, in particular, metamorphoses of excitation spectra, from a different side. A number of results obtained previously are explained, enhanced and supplemented by analyzing the world-sheet dynamics on the non-Abelian confining strings. The world-sheet theory is the two-dimensional N = (2, 2) supersymmetric weighted CP(N-f - 1) model. We explore the vacuum structure and kinks on the world sheet, corresponding to confined monopoles in the bulk theory. We show that (in the equal quark mass limit) these kinks fall into the fundamental representation of the unbroken global SU(N) x SU(N-f - N) x U(1) group. This result confirms the presence of extra stringy meson states in the adjoint representation of the global group in the bulk theory. The non-Abelian bulk duality is in one-to-one correspondence with a duality taking place in the N (2, 2) supersymmetric weighted CP(N-f - 1) model.