Charge screening and confinement in the hot 3-D QED

We examine the possibility of a confinement-deconfinement phase transition at finite temperature in both parity-invariant and topologically massive three-dimensional quantum electrodynamics. We review an argument showing that the abelian version of the Polyakov loop operator is an order parameter for confinement, even in the presence of dynamical electrons. In the parity-invariant case, where the tree-level Coulomb potential is logarithmic, we show that there is a confinement-deconfinement transition of the Berezinskii-Kosterlitz-Thouless (BKT) type. The critical temperature is Tc = e2/8π + O(e4/m), when the ratios of the electromagnetic coupling and the temperature to the electron mass are small. Above Tc the electric charge is not confined and the system is in a Debye plasma phase, whereas below Tc the electric charges are confined by a logarithmic Coulomb potential, qualitatively described by the tree-level interaction. When there is a topological mass, no matter how small, in a strict sense the theory is not confining at any temperature. The model exhibits a screening phase, analogous to that found in the Schwinger model and two-dimensional QCD with massless adjoint matter. However, if the topological mass is much smaller than the other dimensional parameters, there is a temperature for which the range of the Coulomb interaction changes from the inverse topological mass to the inverse electron mass. We speculate that this is a vestige of the BKT transition of the parity-invariant system, separating regions with screening and deconfining behavior.