Heavy quark potential and the phase transitions in the continuum theory at finite temperature

Abstract

Heavy quark potential in the continuum theory at finite temperature is calculated in different phases by using the Polyakov loop as the order parameter. We find the linearly rising potential in the confinement phase, the Debye screened potential in the deconfinement phase and the perturbative $r^{-2}$ dependence at very high temperatures. Within the approximation used in this paper we report an evidence of the first order phase transition accompanied by the $SU(2)$ symmetry restoration at very high temperatures in the static three dimensional theory.