Local and renormalizable action from the gribov horizon

We derive a local, renormalizable action for non-abelian gauge theories, which expresses the restriction of the domain of the functional integral to the interior of the Gribov horizon, and show that the divergences may be absorbed by field and coupling constant renormalization. The condition that the euclidean functional integral extends up to the boundary of the classical configuration space provides an absolute normalization of the gauge field and eliminates the perturbative coupling constant g2 in favor of a dimensionful parameter γ. In D = 4 dimensions, with dimensional regularization, the coupling constant g2(ϵ) is found, in zeroth order, to vanish with ϵ = 4 − D, in accordance with asymptotic freedom. In consequence of the restriction of the classical configuration space, the poles of the gluon propagator are shifted, in zeroth order, to an unphysical location at p2 = ±iγ12, but the glueball channel contains a physical cut with positive spectral function.