Z-SYMMETRY AND POLYAKOV LOOPS IN HOT ABELIAN GAUGE-THEORIES

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