Non-Abelian Strings: From Weak to Strong Coupling and Back via Duality

The crossover transition from weak coupling at large xi to strong coupling at small xi is studied in N = 2 supersymmetric gauge theory with the U(N) gauge group and N-f > N (here xi is the Fayet- Hiopoulos 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) The dual theory has N-f flavors or light dyons, to be compared with N-f quarks in the original U(N) theory Both theories support non-Abelian semilocal strings In each of these two regimes there are two varieties of physical excitations elementary fields and nonperturbative composite states bound by confining 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