Hard Thermal Loops, Static Response and the Composite Effective Action

TL;DR

This paper analyzes the static properties of non-Abelian gauge theories at high temperature, proving the absence of certain solitons and instantons, and deriving key equations from the composite effective action that describe screening effects.

Contribution

It demonstrates that static non-Abelian Kubo equations lack finite energy solutions and derives these equations from the composite effective action, linking gauge invariance to thermal loop dynamics.

Findings

No finite energy solutions for static non-Abelian Kubo equations

Absence of static instantons in gauge theories

Reproduction of electric field screening with a gauge invariant Debye mass

Abstract

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. 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 sqrt((N+N_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.