We discuss the Z symmetry of finite temperature QED, which is related to the confinement properties of the theory. We show the correlators of Polyakov loop operators with incommensurate charges can be used as order parameters for this symmetry. The screening or confining properties of lower dimensional abelian gauge theories are analyzed. In the Schwinger model, the Z-symmetry is broken and the system is in a screening phase; with a non-vanishing fermion mass the symmetry is recovered and the system confines. In parity invariant 2+1-dimensional QED, there is a phase transition between phases with unbroken and broken realizations of this symmetry. This confinement–deconfinement transition is of the Berezinskii–Kosterlitz–Thouless (BKT) type. When there is a topological mass the model exhibits a screening phase. However, if the topological mass is much smaller than the other dimensional parameters there is a vestige of the BKT transition separating regions with screening and confining behavior.
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