The {cal O}(g⁶) coefficient in the thermodynamic potential of hot SU(N) Gauge Theories and MQCD

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.