Goldstone bosons and fermions in QCD

We consider the version of QCD in Euclidean Landau gauge in which the restriction to the Gribov region is implemented by a local, renormalizable action. This action depends on the Gribov parameter γ, with dimensions of (mass)4, whose value is fixed in terms of ΛQCD, by the gap equation, known as the horizon condition, δΓδγ=0, where Γ is the quantum effective action. The restriction to the Gribov region suppresses gluons in the infrared, which nicely explains why gluons are not in the physical spectrum, but this only makes more mysterious the origin of the long-range force between quarks. In the present article we exhibit the symmetries of Γ, and show that the solution to the gap equation, which defines the classical vacuum, spontaneously breaks some of the symmetries of Γ. This implies the existence of massless Goldstone bosons and fermions that do not appear in the physical spectrum. Some of the Goldstone bosons may be exchanged between quarks, and are candidates for a long-range confining force. As an exact result we also find that in the infrared limit the gluon propagator vanishes like k2.