Mean-field gauge interactions in five dimensions I. The torus

We consider the lattice regularization of a five-dimensional SU(2)SU(2) gauge theory with periodic boundary conditions. We determine a consistent mean-field background and perform computations of various observables originating from fluctuations around this background. Our aim is to extract the properties of the system in regimes of its phase diagram where it seems to be in a dimensionally reduced state. Within the mean-field theory we establish the existence of a second order phase transition at finite value of the gauge coupling for anisotropy parameter less than one, where there is evidence for dimensional reduction.