Crossover between Abelian and non-Abelian confinement in N=2 supersymmetric QCD

In this paper we investigate the nature of the transition from Abelian to non-Abelian confinement (i.e. crossover vs phase transition). To this end we consider the basic N=2 model where non-Abelian flux tubes (strings) were first found: supersymmetric QCD with the U(N) gauge group and N-f=N flavors of fundamental matter (quarks). The Fayet-Iliopoulos term xi triggers the squark condensation and leads to the formation of non-Abelian strings. There are two adjustable parameters in this model: xi and the quark mass difference Delta m. We obtain the phase diagram on the (xi,Delta m) plane. At large xi and small Delta m the world-sheet dynamics of the string orientational moduli is described by the N=2 two-dimensional CP(N-1) model. We show that as we reduce xi the theory exhibits a crossover to the Abelian (Seiberg-Witten) regime. Instead of N-2 degrees of freedom of non-Abelian theory, now only N degrees of freedom survive in the low-energy spectrum. Dyons with certain quantum numbers condense, leading to the formation of the Abelian Z(N) strings whose fluxes are fixed inside the Cartan subalgebra of the gauge group. As we increase N this crossover grows exceedingly sharper, becoming a genuine phase transition at N=infinity.