Magnetic screening in the hot gluon system

TL;DR

This paper analyzes the gluon transverse self-energy in high-temperature pure Yang-Mills theory, revealing that most contributions vanish except those related to Euclidean 3D Yang-Mills self-energy, connecting perturbative and non-perturbative results.

Contribution

It provides a detailed gauge-invariant analysis of the gluon self-energy at high temperature, linking perturbative calculations with non-perturbative insights from 3D Yang-Mills theory.

Findings

Most contributions to the self-energy vanish at fourth order.

Remaining contributions are related to Euclidean 3D Yang-Mills theory.

The analysis confirms gauge-fixing independence of the results.

Abstract

The gluon transverse self-energy of the pure Yang-Mills system at high-temperature is analysed in the static limit and at fourth order in the coupling. Possible contributions to this function are collected, seen to be gauge-fixing independent subsets and shown to vanish all, except those which are either regulators or constituents of the self-energy of Euklidean 3D Yang-Mills theory at zero temperature. The latter self-energy, in turn, is known from the non-perturbative analysis by Karabali and Nair.