CHARGE SCREENING AND CONFINEMENT IN HOT 3-D QED

We examine the possibility of a confinement-deconfinement phase transi tion at finite temperature in both parity-invariant and topologically massive three-dimensional quantum electrodynamics. We review an argume nt showing that the abelian version of the Polyakov loop operator is a n order parameter for confinement, even in the presence of dynamical e lectrons. In the parity-invariant case, where the tree-level Coulomb p otential is logarithmic, we show that there is a confinement-deconfine ment transition of the Berezinskii-Kosterlitz-Thouless (BKT) type, The critical temperature is T-c = e(2)/8 pi + O(e(4)/m), when the ratios of the electromagnetic coupling and the temperature to the electron ma ss are small. Above T-c the electric charge is not confined and the sy stem is in a Debye plasma phase, whereas below T-c the electric charge s are confined by a logarithmic Coulomb potential, qualitatively descr ibed 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 th at 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 vestig e of the BKT transition of the parity-invariant system, separating reg ions with screening and deconfining behavior.