Non-Abelian String Junctions as Confined Monopoles

TL;DR

This paper investigates confined monopoles in N=2 two-flavor QCD, mapping string junctions to CP(1) model kinks, and demonstrates their properties and stability through a detailed microscopic and macroscopic analysis.

Contribution

It provides a complete quasiclassical treatment of BPS monopoles, including zero modes and effective theories, and links microscopic monopole solutions to CP(1) model kinks, revealing an anomaly in the monopole central charge.

Findings

Confined monopoles are mapped onto BPS kinks of the CP(1) model.

Masses and characteristics of monopoles match those of CP(1) model kinks.

The study demonstrates an anomaly in the monopole central charge in 4D Yang-Mills theory.

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.