Center-symmetric 1/N expansion

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 subleading 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 [A. Linde, Phys. Lett. B 96, 289 (1980).]. 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.