The Free Energy Of Hot Gauge Theories

The total perturbative contribution to the free-energy of hot SU(3) gauge theory is argued to lie significantly higher than the full result obtained by lattice simulations. This then suggests the existence of large non-perturbative corrections even at temperatures a few times above the critical temperature. Some speculations are then made on the nature and origin of the non-perturbative corrections. The analysis is then carried out for quantum chromodynamics, $SU(N_c)$ gauge theories, and quantum electrodynamics, leading to a conjecture and one more speculation.