Dimensional reduction from five-dimensional gauge theories

We study the phase diagram of five-dimensional SU(2) gauge theories on anisotropic lattices with periodic boundary conditions. We locate a line of first order bulk phase transitions and second order phase transitions related to breaking of the center along one direction. A reduction to four dimensions occurs through compactification of one dimension but not only. By choosing a lattice spacing in the extra dimension larger than in the other dimensions, we find hints that the hyperplanes orthogonal to the extra dimension decouple from each other. Our analysis is based on measurements of Polyakov loops, the static potential extracted from Wilson loops and renormalized couplings defined through the static force and its derivative.