Monopole Condensation in Gauge Theory Vacuum

We study the relation between the abelian monopole condensation and the deconfinement phase transition of the finite-temperature pure QCD. The expectation value of the monopole contribution to the Polyakov loop becomes zero when a long monopole loop is distributed uniformly in the configuration of the confinement phase. On the other hand, it becomes non-zero when the long monopole loop disappears in the deconfinement phase. We also discuss the relation between the monopole be...

We discuss phenomenology of the vacuum condensate <(A_\mu)^2> in pure gauge theories, where A_\mu is the gauge potential. Both Abelian and non-Abelian cases are considered. In case of the compact U(1) the non-perturbative part of the condensate <(A_\mu)^2> is saturated by monopoles. In the non-Abelian case, a two-component picture for the condensate is presented according to which finite values of order \Lambda_{QCD}^2 are associated both with large and short distances. We ob...

Aspects of the monopole condensation picture of confinement are discussed. First, the nature of the monopole singularities in the abelian projection approach is analysed. Their apparent gauge dependence is shown to have a natural interpretation in terms of 't~Hooft-Polyakov-like monopoles in euclidean SU(2) gauge theory. Next, the results and predictions of a realization of confinement through condensation of such monopoles are summarized and compared with numerical data.

The evidence for dual superconductivity as a mechanism for color confinement is reviewed. New developments are presented for full QCD, i.e. in the presence of dynamical quarks.

We study whether broken dual gauge symmetry, as detected by a monopole order parameter introduced by the Pisa group, is necessarily associated with the confinement phase of a lattice gauge theory. We find a number of examples, including SU(2) gauge-Higgs theory, mixed fundamental-adjoint SU(2) gauge theory, and pure SU(5) gauge theory, which appear to indicate a dual gauge symmetry transition in the absence of a transition to or from a confined phase. While these results are ...

We discuss the effect of the choice of an Abelian projection on the dual superconductor mechanism of confinement in SU(2) gluodynamics. Using qualitative arguments we show that the dual superconductor Lagrangian corresponding to the Abelian Polyakov gauge has a different structure compared to the dual Lagrangian in the Maximal Abelian gauge. A difference between these Lagrangians reflects the fact that in continuum limit the monopoles should be static in the Abelian Polyakov ...

We study the properties of the QCD vacuum in the dual Ginzburg-Landau theory, where QCD-monopole condensation leads to the linear confinement potential. Using the effective potential, we find monopole dominance for chiral-symmetry breaking. The effective mass of off-diagonal (charged) gluons is estimated as $M_{ch} \simeq 1.31$ GeV. The gluon condensate is calculated as $<\frac{\alpha_{s}}{\pi}G^2 > = (344 MeV)^4$.

Central role played by certain non-Abelian monopoles (of Goddard-Nuyts-Olive-Weinberg type) in the infrared dynamics in many confining vacua of softly broken ${\cal N}=2$ supersymmetric gauge theories, has recently been clarified. We discuss here the main lessons to be learned from these studies for the confinement nechanism in QCD.

The status of our understanding of confinement is reviewed. The evidence from lattice is that monopole condensation, or dual superconductivity, is at work. Confinement is an order-disorder transition. Different monopole species look equivalent, indicating that the symmetry of the disordered phase is more interesting that we understand.

An effective monopole action is derived from vacuum configurations after abelian projection in the maximally abelian gauge in $SU(2)$ QCD. Entropy dominance over energy of monopole loops is seen on the renormalized lattice with the spacing $b>b_c\simeq 5.2\times10^{-3} \Lambda_L^{-1}$ when the physical volume of the system is large enough. QCD confinement may be interpreted as the (dual) Meissner effect due to the monopole condensation.