# The ${\cal O}(g^6)$ coefficient in the thermodynamic potential of hot SU(N) Gauge Theories and MQCD

## TL;DR

This paper estimates the non-perturbative contribution to the ${
m O}(g^6)$ term in the free energy density of hot SU(N) gauge theories, emphasizing the role of magnetic fluctuations dominated by screened magnetic gluons.

## Contribution

It provides the first non-perturbative estimate of the ${
m O}(g^6)$ coefficient in the thermodynamic potential for SU(N) gauge theories, highlighting magnetic gluon dominance.

## Key findings

- Non-perturbative input estimated for ${
m O}(g^6)$ term.
- Magnetic fluctuations dominated by screened magnetic gluons.
- Results applicable to SU(2) and SU(3) gauge theories.

## Abstract

The non-perturbative input necessary for the determination of the ${\cal O}(g^6)$ part of the weak coupling expansion of the free energy density for SU(2) and SU(3) gauge theories is estimated. Although the perturbative information completing the contribution to this order is missing, we give arguments that the magnetic fluctuations are dominated by screened elementary magnetic gluons.