A confinement-deconfinement phase transition in hot 2+1 dimensional QED

We show that, at finite temperature, parity-invariant electrodynamics with massive electrons in 2+1 dimensions can exist in both confined and deconfined phases. We argue that an order parameter for the confinement-deconfinement phase transition is the Polyakov loop operator whose average measures the free energy of a test charge that is not an integer multiple of the electron charge. The effective field theory for the Poluyakov loop operator is a 2-dimensional Euclidean scalar field theory with global discrete symmetry Z, the additive group of the integers. We argue that the realization of this symmetry governs confinement and that the confinement-deconfinement phase transition is of Berezinskii-Kosterlitz-Thouless type. We compute the effective action to one-loop order and show that when the electron mass m is much grater than the temperature T and dimensional coupling e^2, the effective field theory is the Sine-Gordon model. In this limit, we estimate the critical temperature, T_critic=e^2/8 pi (1+e^2/12 pi m+...).