Monopoles and gluon fields in QCD in the maximally abelian gauge

Abstract

We study monopoles and gluon fields in QCD in the maximally abelian (MA) gauge in the context of the dual superconductor picture for confinement. In the abelian gauge, unit charge magnetic monopoles appear, but multi-charge monopoles do not in general cases. The appearance of the monopole is studied in relation to the SU(Nc) singular gauge transformation. The relevant role of off-diagonal gluons is found for the appearance of monopoles in the abelian gauge in QCD. We study the gluon-field properties around the monopole in the MA gauge in terms of the action density using lattice QCD. The monopole provides infinitely large field fluctuations in the abelian sector. In the MA gauge, off-diagonal gluons are strongly suppressed but largely remain around the monopole, which indicates the effective size and the structure of monopoles. We find large cancellation between the abelian part and the off-diagonal part of the action density around the monopole in the MA gauge. Owing to this cancellation, the monopole can appear in QCD without large cost to the QCD action. Finally, we generalize the framework of the abelian projection, i.e. the extraction of the abelian gauge manifold from QCD, by introducing the `gluonic Higgs field' φD[Aμ(x)] defined from the SU(Nc) covariant derivative D̂μ. By way of φD[Aμ(x)], the maximally abelian projection can be performed in a gauge-covariant manner without the notion of gauge fixing in principle.