Infrared divergences in three-dimensional gauge theories

The loop expansion in massless three-dimensional gauge theories develops infrared divergences starting at the two-loop level. However, we show that the divergences in QCD3 which arise through the three-loop level (g6) can be removed by using a residual gauge freedom in covariant gauges. Divergences in gauge-invariant amplitudes arise at g8 order, as shown explicitly for the Wilson loop. Massless scalar QED develops a gauge-invariant singularity at order g4, which can be canceled by changing the perturbative vacuum.