# Infrared divergences in three-dimensional gauge theories Academic Article

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• 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 QC${\mathrm{D}}_{3}$ which arise through the three-loop level (${g}^{6}$) can be removed by using a residual gauge freedom in covariant $\ensuremath{\alpha}$ gauges. Divergences in gauge-invariant amplitudes arise at ${g}^{8}$ order, as shown explicitly for the Wilson loop. Massless scalar QED develops a gauge-invariant singularity at order ${g}^{4}$, which can be canceled by changing the perturbative vacuum.