The free energy of U(N) gauge theory is expanded about a center-symmetric
topological background configuration with vanishing action and vanishing
Polyakov loops. We construct this background for SU(N) lattice gauge theory and
show that it uniquely describes center-symmetric minimal action orbits in the
limit of infinite lattice volume. The leading contribution to the free energy
in the 1/N expansion about this background is of O(N^0) rather than O(N^2) as
one finds when the center symmetry is spontaneously broken. The contribution of
planar 't Hooft diagrams to the free energy is O(1/N^2) and sub-leading in this
case. The change in behavior of the diagrammatic expansion is traced to Linde's
observation that the usual perturbation series of non-Abelian gauge theories
suffers from severe infrared divergences. This infrared problem does not arise
in a center-symmetric expansion. The 't Hooft coupling \lambda=g^2 N is found
to decrease proportional to 1/\ln(N) for large N. There is evidence of a
vector-ghost in the planar truncation of the model.Comment: 27 pages, 2 figures; extended and corrected version with additional
material and reference