  Debye screening of static chromoelectric fields at high temperature is
investigated at next-to-leading order through one-loop resummed perturbation
theory. At this order the gluon propagator appears to give rise to strong
deviations from a Yukawa form of screening. Generally, an oscillatory behavior
is found which asymptotically becomes repulsive, but in a gauge-dependent
manner. However, these features are strongly sensitive to the existence of
screening of static magnetic fields. It is shown that a small magnetic
screening mass can restore exponential screening with a gauge independent value
of the screening mass, which depends logarithmically on the magnitude of the
magnetic mass. Recent results obtained in temporal axial gauge, which instead
indicate an asymptotic (repulsive) power-law behavior of screening, are also
critically discussed. In order to arrive at a gauge-invariant treatment of
chromoelectric screening, Polyakov loop correlations are considered, both with
and without dynamical gauge symmetry breaking. Again a crucial sensitivity to
the scale of magnetic screening is found. A detailed comparison of the
perturbative results with recent high-precision lattice simulations of the
SU(2) Polyakov loop correlator is made, which are found to agree well with the
perturbative result in the symmetric phase when a magnetic mass $\sim g^2T/4$
is included.
