One-loop effects in higher-dimensional Yang-Mills theories

I study a model of a compactified Kaluza-Klein theory as an SU(2) gauge theory on a flat n-dimensional Minkowski space Mn in a direct product with a two sphere S2. The gauge and ghost gaussian functional integrals (one loop effective potentials) are explicitly calculated. To this order, SU(2) does indeed breakdown dynamically to U(1) on Mn x S2 as Hosotani previously conjectured. On Mn, there is an infinite tower of massive gauge bosons with m2 proportional to mplanck2 with a massless photon and two tachyons. A renormalization scheme for Mn x S2 for all odd n and for n = 2 is presented. The n = 2 result reproduces the standard four dimensional beta function for a fixed spatial background. In addition, the perturbation theory on M2 is developed. In particular, induced tree level fermion-gauge field and one loop fermion-higgs Yukawa couplings are computed. The latter calculation generates a mass hierarchy for the massless fermions on M2