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 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 ∆m. We obtain the phase diagram on the (ξ, ∆m) plane. At large ξ and small ∆m the worldsheet dynamics of the string orientational moduli is described by 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 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 becomes exceedingly sharper becoming a genuine phase transition at N = ∞.