  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. We show that, in the
parity invariant case, where the tree-level Coulomb potential is logarithmic,
there is a Berezinskii-Kosterlitz-Thouless transition at a critical temperature
($T_c=e^2/8\pi+{\cal O}(e^4/m)$, when the ratio of the electromagnetic coupling
and the temperature to the electron mass is small). Above $T_c$ the electric
charge is not confined and the system is in a Debye plasma phase, whereas below
$T_c$ 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.

High Energy Physics - Theory;Condensed Matter;High Energy Physics - Lattice;High Energy Physics - Phenomenology