• DOI:10.1103/PhysRevD.70.045004
• Corpus ID: 118956344

Non-Abelian string junctions as confined monopoles

@article{Shifman2004NonAbelianSJ,
  title={Non-Abelian string junctions as confined monopoles},
  author={Mikhail Shifman and Alexei V Yung},
  journal={Physical Review D},
  year={2004},
  volume={70},
  pages={045004}
}

• M. Shifman, A. Yung
• Published 14 March 2004
• Physics
• Physical Review D

Various dynamical regimes associated with confined monopoles in the Higgs phase of $\mathcal{N}=2$ two-flavor QCD are studied. The microscopic model we deal with has the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge group, with a Fayet\char21{}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 ${\mathrm{CP}}^{1}$ model with or without twisted mass. The confined monopoles\char22{}string junctions of the microscopic theory\char22{}are mapped onto BPS kinks of the ${\mathrm{CP}}^{1}$ model. The string junction is $\frac{1}{4}$ BPS. Masses and other characteristics of the confined monopoles are matched with those of the ${\mathrm{CP}}^{1}$-model kinks. The matching demonstrates the occurrence of an anomaly in the monopole central charge in 4D Yang\char21{}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 ${\mathrm{CP}}^{1}$ model. The monopoles, aka ${\mathrm{CP}}^{1}$-model kinks, are stabilized by nonperturbative dynamics of the ${\mathrm{CP}}^{1}$ model. We explain an earlier rather puzzling observation of a correspondence between the BPS kink spectrum in the ${\mathrm{CP}}^{1}$ model and the Seiberg\char21{}Witten solution.