Non-Abelian duality and confinement in N=2 supersymmetric QCD

In N = 2 supersymmetric QCD with the U(N) gauge group and N-f > N we study the crossover transition from the weak coupling regime at large xi to strong coupling at small xi, where xi is the Fayet-Iliopoulos parameter. We find that at strong coupling a dual non-Abelian weakly coupled N 2 theory exists, which describes low-energy physics at small xi. The dual gauge group is U(N-f - N), and the dual theory has N-f flavors of light dyons, to be compared with N-f quarks in the originalU(N) theory. Both, the original and dual theories are Higgsed and share the same global symmetry SU(N) X SU(N-f - N) X U(1), albeit the physical meaning of the SU(N) and SU(N-f - N) factors is different in the large- and small-xi regimes. Both regimes support non-Abelian semilocal strings. In each of these two regimes particles that are in the adjoint representations with respect to one of the factor groups exist in two varieties: elementary fields and composite states bound by strings. These varieties interchange upon transition from one regime to the other. We conjecture that the composite stringy states can be related to Seiberg's M fields. The bulk duality that we observed translates into a two-dimensional duality on the world sheet of the non-Abelian strings. At large xi the internal dynamics of the semilocal non-Abelian strings is described by the sigma model of N orientational and (N-f - N) size moduli, while at small xi the roles of orientational and size moduli interchange. The Bogomol'nyi-Prasad-Sommerfield spectra of two dual sigma models (describing confined monopoles/dyons of the bulk theory) coincide. It would be interesting to trace parallels between the non-Abelian duality we found and string theory constructions.