Running and Matching from 5 to 4 Dimensions

We study 5 dimensional grand-unified theories in an orbifold geometry by the method of effective field theory: we match the low and high energy theories by integrating out at 1-loop the massive Kaluza-Klein states. In the supersymmetric case the radius dependence of threshold effects is fixed by the rescaling anomalies of the low energy theory. We focus on a recently proposed SU(5) model on $M^4 \times S^1/(Z_2\times Z_2^\prime)$. Even though the spectrum of the heavy modes is completely known, there still are corrections to gauge unification originating from boundary couplings. In order to control these effects one has to rely on extra assumptions. We argue that, as far as gauge couplings are concerned, the predictive power of these models is similar to conventional GUTs.