Effect of Extra Dimensions on Gauge Coupling Unification

The effects of extra dimensions on gauge coupling unification is studied. We start with a comparison between power law running of the gauge couplings in models with extra dimensions and logarithmic running that happens in many realistic cases. We then discuss the effect of extra dimensions on various classes of unification models. We identify products of evolution coefficients that dictate the profile of unification in different models. We use them to study under what conditions unification of couplings can occur in both one and two step unification models. We find that Kaluza-Klein modes can help generate interesting intermediate scale models with gauge coupling unification such as the minimal left-right models with the seesaw mechanism with a $M_{W_R}\sim 10^{13}$ GeV intermediate scale, useful in understanding neutrino oscillations. We also obtain several examples where the presence of noncanonical normalization of couplings enables us to obtain unification scales around $10^{11}$ GeV. This fits very well into a class of models proposed recently where the string scale is advocated to be at this value from physical arguments.