Some exact infrared properties of gluon and ghost propagators and long-range force in QCD

We derive some exact relations in Landau gauge that follow from a cut-off at the Gribov horizon which is then implemented by a local, renormalizable action involving auxiliary bose and fermi ghosts. The fermi ghost propagator is more singular than $1\mathrm{/}{k}^2$ at $k=0$, and the relation $\alpha_D + 2 \alpha_G = (D

• 4)/2$ holds between the infrared critical exponents of the gluon and ghost propagators $D(k)$ and $G(k)$ in $D$ Euclidean dimensions. Finally, in $D$ Euclidean dimensions, there is a long-range force, transmitted by the propagator of the auxiliary bose ghost that corresponds to a linearly rising potential with tensor coupling to colored quarks that is proportional to the renormalization-group invariant $g^{2}D(k)G^2(k)$. A comparison with numerical results is discussed.