  Field theories with extra dimensions live in a limbo. While their classical
solutions have been the subject of considerable study, their quantum aspects
are difficult to control. A special class of such theories are anisotropic
gauge theories. The anisotropy was originally introduced to localize chiral
fermions. Their continuum limit is of practical interest and it will be shown
that the anisotropy of the gauge couplings plays a crucial role in opening the
phase diagram of the theory to a new phase, that is separated from the others
by a second order phase transition. The mechanism behind this is generic for a
certain class of models, that can be studied with lattice techniques. This
leads to new perspectives for the study of quantum effects of extra dimensions.
