Monte Carlo simulation of non-compact QCD with stochastic gauge fixing

A non-compact lattice model of quantum chromodynamics is studied numerically. Whereas in Wilson's lattice theory the basic variables are the elements of a compact Lie group, the present lattice model resembles the continuum theory in that the basic variables A are elements of the corresponding Lie algebra, a non-compact space. The lattice gauge invariance of Wilson's theory is lost. As in the continuum, the action is a quartic polynomial in A, and a stochastic gauge fixing mechanism - which is covariant in the continuum and avoids Faddeev-Popov ghosts and the Gribov ambiguity - is also transcribed to the lattice. It is shown that the model is self-compactifying, in the sense that the probability distribution is concentrated around a compact region of the hyperplane div A = 0 which is bounded by the Gribov horizon. The model is simulated numerically by a Monte Carlo method based on the random walk process. Measurements of Wilson loops, Polyakov loops and correlations of Polyakov loops are reported and analyzed. No evidence of confinement is found for the values of the parameters studied, even in the strong coupling regime.