Monopole Loops Research Articles

Behaviour of gluons at high temperature: K. Kajantie, Department of Theoretical Physics, University of Helsinki, Siltavuorenpenger 20 C, SF-00170 Helsinki 17, Finland and J. Kapusta, CERN-Geneva, Switzerland and School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455

We introduce the dual Ginzburg-Landau (DGL) theory as a low energy effective theory of QCD. We study color confinement and dynamical chiral symmetry breaking of nonperturbative QCD by using the DGL theory, where color monopole and its condensation play an essential role on the nonperturbative dynamics in the infrared region. As a result of the dual Meissner effect, the linear static quark potential, which characterizes the quark confinement, is obtained in the long distance. We investigate then the dynamical chiral symmetry breaking by using the Schwinger-Dyson equation, where the gluon propagator includes the nonperturbative effect related to monopole condensation. We find a large enhancement of the chiral-symmetry breaking when the dual Meissner effect takes place. We study the recovery of the chiral symmetry and the deconfinement at finite temperature in the DGL theory. We discuss then the essential assumption of the DGL theory, which is the abelian dominance for the infrared physics, in the maximal abelian (MA) gauge in lattice QCD. The lattice QCD simulation demonstrates that the non-abelian gluons have a finite mass of order of 1 GeV in the MA gauge. We introduce further the instanton configuration as the source of the color monopole. In the MA gauge, a monopole circles around an instanton and with the increase of the instanton density, the monopole loop connects many instantons and a complicated monopole loop covers the whole 4 dimensional space. This study indicates that instantons may be playing an essential role even for color confinement.

Condensed Monopoles and Abelian Confinement

We show that contribution of monopole loops to the functional integral in four-dimensional lattice (quantum electrodynamics) can be mapped on to scalar quantum electro-dynamics. The phase transition where the monopole loops become very long then corresponds to the onset of the Higgs-Kibble mechanism and confinement due to the dual Meissner effect.