Elusiveness of infrared critical exponents in Landau gauge Yang-Mills theories

We solve a truncated system of coupled Dyson-Schwinger equations for the gluon and ghost propagators in SU(Nc) Yang-Mills theories in Faddeev-Popov quantization on a four-torus. This compact space-time manifold provides an efficient mean to solve the gluon and ghost Dyson-Schwinger equations without any angular approximations. We verify that analytically two powerlike solutions in the very far infrared seem possible. However, only one of these solutions can be matched to a numerical solution for nonvanishing momenta. For a bare ghost-gluon vertex this implies that the gluon propagator is only weakly infrared vanishing, Dgl(k²)∝(k²)^2κ-1, κ≈0.595, and the ghost propagator is infrared singular, Dgh(k²)∝(k²)^-κ-1. For nonvanishing momenta our solutions are in agreement with the results of recent SU(2) Monte Carlo lattice calculations. The running coupling possesses an infrared fixed point. We obtain α(0)=8.92/Nc for all gauge groups SU(Nc). Above one GeV the running coupling rapidly approaches its perturbative form.