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

Abstract

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 ξtriggers the squark condensation and leads to the formation of non-Abelian strings. There are two adjustable parameters in this model: ξand the quark mass difference Δm. We obtain the phase diagram on the (ξ, Δm) plane. At large ξand small Δm the world-sheet dynamics of the string orientational moduli is described by N=2 two-dimensional CP(N-1) model. We show that as we reduce ξthe 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 =\infty.

40 pages, 4 figures

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• Non-Abelian Duality and Confinement: from N=2 to N=1 Supersymmetric QCD
• r Duality and "Instead-of-Confinement" Mechanism in N=1 Supersymmetric QCD
• Large-N Solution of the Heterotic CP(N-1) Model with Twisted Masses
• Moduli Space Potentials for Heterotic non-Abelian Flux Tubes: Weak Deformation
• Strong versus Weak Coupling Confinement in N=2 Supersymmetric QCD
• Higher Winding Strings and Confined Monopoles in N=2 SQCD
• Non-Abelian Strings: From Weak to Strong Coupling and Back via Duality
• Softly broken $\mathcal{N}=2$ SQCD: mass spectra in vacua with unbroken $Z_{2N_c-N_F}$ symmetry