Borel Resummation of the Perturbative Free Energy of Hot Yang-Mills Theory

The divergent perturbative expansion of the free-energy density of thermal SU(3) gauge theory is resummed into a rapidly convergent series using a novel, variational, implementation of the method of conformal mapping of the corresponding Borel series. The resummed result differs significantly from non-perturbative lattice simulations and the discrepancy is attributed to the presence of a pole on the positive axis of the Borel plane. The position of that pole is determined numerically and the difference between the lattice data and the resummed series is related to a phenomenological bag `constant'.