Abelian dominance in low - energy Gluodynamics due to dynamical mass generation ∗

We show that off-diagonal gluons and off-diagonal ghosts acquire their masses dynamically in QCD if the maximal Abelian gauge is adopted. This result strongly supports the Abelian dominance in low-energy region of QCD. The mass generation is shown to occur due to ghost–anti-ghost condensation caused by attractive quartic ghost interactions within the Abelian projected effective gauge theory (derived by one of the authors). In fact, the quartic ghost interaction is indispensable for the renormalizability due to nonlinearity of the maximal Abelian gauge. The ghost–anti-ghost condensation is associated with the spontaneous breaking of global SL(2, R) symmetry recently found by Schaden at least for SU(2) case. Moreover we write down a new extended BRS algebra in the maximal Abelian gauge which should be compared with that of Nakanishi-Ojima for the Lorentz gauge. Finally, we argue that the mass generation may be related to the spontaneous breaking of a supersymmetry OSp(4|2) hidden in the maximal Abelian gauge.