# The Non-Perturbative ${\cal O}(g^6)$ Contribution to the Free Energy of Hot SU(N) Gauge Theory

## TL;DR

This paper estimates the non-perturbative contribution to the free energy of hot SU(N) gauge theories at order g^6, highlighting the role of magnetic fluctuations dominated by screened magnetic gluons.

## Contribution

It provides the first non-perturbative estimate for the g^6 contribution to the free energy in hot SU(N) gauge theories, focusing on magnetic fluctuations.

## Key findings

- Magnetic fluctuations are dominated by screened magnetic gluons.
- Non-perturbative input is essential for g^6 order calculations.
- Perturbative data alone is insufficient for complete results.

## 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.