Quark confinement from colour confinement

Abstract

We relate quark confinement, as measured by the Polyakov-loop order parameter, to colour confinement, as described by the Kugo–Ojima/Gribov–Zwanziger scenario. We identify a simple criterion for quark confinement based on the IR behaviour of ghost and gluon propagators, and compute the order-parameter potential from the knowledge of Landau-gauge correlation functions with the aid of the functional RG. Our approach predicts the deconfinement transition in quenched QCD to be of first order for SU(3) and second order for SU(2) – in agreement with general expectations. As an estimate for the critical temperature, we obtain Tc≃284 MeV for SU(3).