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 Nf=N flavors of fundamental matter (quarks). The Fayet-Iliopoulos term ξ triggers the squark condensation and leads to the formation of non-Abelian strings. There are two adjustable parameters in this model: ξ and the quark mass difference Δm. We obtain the phase diagram on the (ξ,Δm) plane. At large ξ and small Δm 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 ξ the theory exhibits a crossover to the Abelian (Seiberg-Witten) regime. Instead of N2 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 ZN 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=∞.