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 using the gauge-connection formalism in relation to the SU($N_c$) 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 the 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 the 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 of the QCD action. Finally, we generalize the framework of the abelian projection, {\it i.e.} the extraction of the abelian gauge manifold from QCD, by introducing the `gluonic Higgs field' ${\vec{\varphi }}_D[A_{\mu }(x)]$ defined from the $\mathrm{SU}(N_c)$ covariant derivative ${\hat{D}}_{\mu }$. By way of ${\vec{\varphi }}_D[A_{\mu }(x)]$, the maximally abelian projection can be performed in the gauge-covariant manner without the notion of gauge fixing in principle.

46 pages (3 text-files, 10 figures, uses elsart.cls, elsart.sty, elsart12.sty)

References in corpus (7)

• Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in the Maximally Abelian Gauge in Lattice QCD
• Abelian Magnetic Monopole Dominance in Quark Confinement
• Semi-analytical Proof of Abelian Dominance on Confinement in the Maximally Abelian Gauge
• Flux-Tube Ring and Glueball Properties in the Dual Ginzburg-Landau Theory
• Instantons and Monopoles in the Nonperturbative QCD
• Quark Confinement Physics from Quantum Chromodynamics
• Monopole Clustering and Color Confinement in the Multi-Instanton System

Cited by in corpus (14)

• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• Anatomy of the lattice magnetic monopoles
• Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function
• Lattice construction of Cho-Faddeev-Niemi decomposition and gauge invariant monopole
• Gluon Propagators in Maximally Abelian Gauge in SU(3) Lattice QCD
• Confinement and Chiral Symmetry Breaking via Domain-Like Structures in the QCD Vacuum
• Maximal Abelian gauge and a generalized BRST transformation
• Strong randomness of off-diagonal gluon phases and off-diagonal gluon mass in the maximally abelian gauge in QCD
• Clear correlation between monopoles and the chiral condensate in SU(3) QCD
• Local correlation among the chiral condensate, monopoles, and color magnetic fields in Abelian projected QCD
• Analytical relation between quark confinement and chiral symmetry breaking in odd-number lattice QCD
• Gluonic-Excitation Energies and Abelian Dominance in SU(3) QCD
• Abelianization of QCD in the Maximally Abelian Gauge and the Nambu-'t Hooft Picture for Color Confinement
• Color-magnetic correlations in SU(2) and SU(3) lattice QCD