Hard Thermal Loops, Quark-Gluon Plasma Response, and T=0 Topology

TL;DR

This paper explores the response of quark-gluon plasma to thermal perturbations, proving the absence of static solitons and constructing explicit solutions within SU(2), while discussing the potential links to topological Chern-Simons theory.

Contribution

It provides new derivations of the non-Abelian Kubo equation, proves the non-existence of static solitons in gauge theories, and constructs explicit SU(2) solutions, linking thermal plasma response to topological field theory.

Findings

Gauge theories do not support static thermal solitons.

Explicit SU(2) solutions demonstrate the theoretical predictions.

Potential connections between thermal loop gauge invariance and topological Chern-Simons theory.

Abstract

I outline various derivations of the non-Abelian Kubo equation, which governs the response of a quark-gluon plasma to hard thermal perturbations. In the static case, it is proven that gauge theories do not support hard thermal solitons. Explicit solutions are constructed within an SU(2) Ansatz and they are shown to support the general result. The time-dependent problem, i.e., non-Abelian plasma waves, has not been completely solved. We express and motivate the hope that the intimate relations linking the gauge-invariance condition for hard thermal loops to the equation of motion for T=0, topological Chern-Simons theory may yield new insight into this field.