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Perturbation theory for non-Abelian gauge theories at finite temperature isplagued by infrared divergences caused by magnetic soft modes $\sim g^2T$,which correspond to the fields of a 3d Yang-Mills theory. We revisit a gaugeinvariant resummation scheme to solve this problem by self-consistent massgeneration using an auxiliary scalar field, improving over previous attempts intwo respects. First, we generalise earlier SU(2) treatments to SU(N). Second,we obtain a gauge independent two-loop gap equation, correcting an error in theliterature. The resulting two-loop approximation to the magnetic massrepresents a $\sim 15%$ correction to the leading one-loop value, indicating areasonable convergence of the resummation.

Resummation scheme for 3d Yang-Mills and the two-loop magnetic mass for hot gauge theories