Non-Abelian string junctions as confined monopoles

Abstract

Various dynamical regimes associated with confined monopoles in the Higgs phase of N=2 two-flavor QCD are studied. The microscopic model we deal with has the SU(2)xU(1) gauge group, with a Fayet-Iliopoulos term of the U(1) factor, and large and (nearly) degenerate mass terms of the matter hypermultiplets. We present a complete quasiclassical treatment of the BPS sector of this model, including the full set of the first-order equations, derivations of all relevant zero modes, and derivation of an effective low-energy theory for the corresponding collective coordinates. The macroscopic description is provided by a CP(1) model with or without twisted mass. The confined monopoles -- string junctions of the microscopic theory -- are mapped onto BPS kinks of the CP(1) model. The string junction is 1/4 BPS. Masses and other characteristics of the confined monopoles are matched with those of the CP(1)-model kinks. The matching demonstrates the occurrence of an anomaly in the monopole central charge in 4D Yang-Mills theory. We study what becomes of the confined monopole in the bona fide non-Abelian limit of degenerate mass terms where a global SU(2) symmetry is restored. The solution of the macroscopic model is known e.g. from the mirror description of the CP(1) model. The monopoles, aka CP(1)-model kinks, are stabilized by nonperturbative dynamics of the CP(1) model. We explain an earlier rather puzzling observation of a correspondence between the BPS kink spectrum in the CP(1) model and the Seiberg-Witten solution.