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(N-c) 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, D-gl(k(2)) proportional to (k(2))(2kappa-1), kappa approximate to 0.595, and the ghost propagator is infrared singular, D-gh(k(2)) proportional to (k(2))(-kappa-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 alpha(0) = 8.92/N-c for all gauge groups SU(N-c). Above one GeV the running coupling rapidly approaches its perturbative form.