Hard thermal loops, static response, and the composite effective action

First, we investigate the static non-Abelian Kubo equation. We prove that it does not possess finite energy solutions; thereby we establish that gauge theories do not support hard thermal solitons. This general result is verified by a numerical solution of the equations. A similar argument shows that ‘‘static’’ instantons are absent. In addition, we note that the static equations reproduce the expected screening of the non-Abelian electric field by a gauge-invariant Debye mass m=gT √(N+${\mathit{N}}_{\mathit{F}}$/2)/3 . Second, we derive the non-Abelian Kubo equation from the composite effective action. This is achieved by showing that the requirement of stationarity of the composite effective action is equivalent, within a kinematical approximation scheme, to the condition of gauge invariance for the generating functional of hard thermal loops.