Proposal of a novel type of vacuum condensates and quark confinement

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1. We have succeeded to construct a composite operator of mass dimension two from the gluon and ghost field, which is both BRST and anti-BRST invariant. We have proposed a vacuum condensation of mass dimension two. The existence of such a vacuum condensate of mass dimension two implies that off-diagonal gluons acquire their mass. This has yielded for the first time a theoretical explanation for the infrared Abelian dominance which is expected to hold from the viewpoint of dual superconductor picture of QCD vacuum enabling us to explain quark confinement. In fact, the existence of such a vacuum condensate was supported from a physical interpretation, operator product expansion in the gluon and ghost proopagators, the ultra-violet asymptotic solution of the coupled Schwinger-Dyson equation for the gluon and ghost propagators, and numerical simulations on a lattice.2. To extract degrees of freedom for magnetic monopoles explicitly in Yang-Mills theory, we have given a new viewpoint for the non-linear change of variables for the Yang-Mills field called the Cho-Faddeev-Niemi decomposition. This enables one to define the magnetic monopole in the gauge-invariant way. We have shown how to construct a gauge-invariant mass term for gluons.We have pointed out that the Nielsen-Olesen instability for the Savvidy vacuum is cured by a certain type of color magnetic condensation originating from magnetic monopole configurations which provide the mass for off-diagonal gluons in Yang-Mills theory. In fact, such a novel type of magnetic condensation is shown to occur by calculating the effective potential in one-loop level for the SU(2) Yang-Mills theory.3. Moreover, we have suggested that the gauge-invariant vacuum condensation of mass dimension two leads to the Faddeev model with knot soliton solution, which could be a low-energy effective theory of Yang--Mills theory.