  The free energy of U(N) and SU(N) gauge theory was recently found to be of
order N^0 to all orders of a perturbative expansion about a center-symmetric
orbit of vanishing curvature. Here I consider extended models for which this
expansion is perturbatively stable. The extreme case of an SU(2) gauge theory
whose configuration space is restricted to center-symmetric orbits has recently
been investigated on the lattice hep-lat/0509156. In extension of my talk, a
discussion and possible interpretation of the observed finite temperature phase
transition is given. The transfer matrix of constrained SU(N) lattice gauge
theory is constructed for any finite temperature.
