Non-Abelian Duality and Confinement: from N=2 to N=1 Supersymmetric QCD

Abstract

Recently we discovered and discussed non-Abelian duality in the quark vacua of N=2 super-Yang-Mills theory with the U(N) gauge group and N_f flavors (N_f>N). Both theories from the dual pair support non-Abelian strings which confine monopoles. Now we introduce an N=2-breaking deformation, a mass term \mu{\mathcal A}^2 for the adjoint fields. Starting from a small deformation we eventually make it large which enforces complete decoupling of the adjoint fields. We show that the above non-Abelian duality fully survives in the limit of N=1 SQCD, albeit some technicalities change. For instance, non-Abelian strings which used to be BPS-saturated in the N=2 limit, cease to be saturated in N=1 SQCD. Our duality is a distant relative of Seiberg's duality in N=1 SQCD. Both share some common features but have drastic distinctions. This is due to the fact that Seiberg's duality apply to the monopole rather than quark vacua. More specifically, in our theory we deal with N< N_f<3/2 N massive quark flavors. We consider the vacuum in which N squarks condense. Then we identify a crossover transition from weak to strong coupling. At strong coupling we find a dual theory, U(N_f-N) SQCD, with N_f light dyon flavors. Dyons condense triggering the formation of non-Abelian strings which confine monopoles. Screened quarks and gauge bosons of the original theory decay into confined monopole-antimonopole pairs and form stringy mesons.