Renormalizable extra-dimensional models

Non-Abelian gauge theories may have continuum limits in more than fourdimensions, supported by non-trivial ultra-violet fixed points. Moreover, suchtheories can be expected to be accessible to Wilson's epsilon expansion. Weinvestigate this series for SU(N) Yang-Mills, in particular for the fixed pointcoupling and critical exponent nu, up to four loops. From the model-buildingpoint of view, such theories would be effectively perturbatively renormalizablein the normal way. A particularly attractive possibility is the construction ofrenormalizable extra-dimensional models of the weak interactions, which havethe potential to address the full hierarchy problem. The simplest suchgauge-Higgs unification model is however ruled out by a combination oftheoretical and phenomenological constraints.Comment: 29 pages, 2 eps figures; extra refs adde