The strong-coupling limit of lattice Landau gauge

We report on our recent study of the gluon and ghost propagators of pure SU(2) minimal lattice Landau gauge in the strong-coupling limit. In this limit, we find evidence of the conformal infrared behaviour of these propagators as predicted by functional continuum methods. However, in the strong-coupling limit this happens for lattice momenta with a^2q^2>1, in units of the lattice spacing a. Deviations from conformal scaling for a^2q^2<1 are well parameterised by a transverse gluon mass. A comparison of various lattice definitions of gauge potentials, all equivalent in the continuum limit, shows that (a) both the critical exponent and coupling can be extracted unambiguously from the high-momentum data in the strong-coupling limit, in good agreement with the continuum predictions; but that on the other hand (b) the massive branch depends on the definition of lattice gluon fields and is thus not unambiguously defined. We demonstrate that this ambiguity is also present in the low-momentum region for commonly used values of the lattice coupling in SU(2).