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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)×U(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.

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The key quantity of the heavy quark theory is the quark mass m Q . Since quarks are unobservable one can suggest different definitions of m Q . One of the most popular choices is the pole quark mass routinely used in perturbative calculations and in some analyses based on heavy quark expansions. We show that no precise definition of the pole mass can be given in the full theory once non-perturbative effects are included. Any definition of this quantity suffers from an intrinsic uncertainty of order Λ QCD /m Q . This fact is succinctly described by the existence of an infrared renormalon generating a factorial divergence in the high-order coefficients of the α s series; the corresponding singularity in the Borel plane is situated at 2π/b. A peculiar feature is that this renormalon is not associated with the matrix element of a local operator. The difference Λ ≡ M H Q − m pole Q can still be defined in Heavy Quark Effective Theory, but only at the price of introducing an explicit dependence on a normalization point µ: Λ(µ). Fortunately the pole mass m Q (0) per se does not appear in calculable observable quantities.

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