Higher loop effects on unification via Kaluza-Klein thresholds

We discuss higher loop corrections to gauge coupling renormalization in the context of gauge coupling unification via Kaluza-Klein thresholds. We show that in the case of N = 1 supersymmetric compactifications the one-loop threshold contributions are dominant, while the higher loop correction are subleading. This is due to the fact that at heavy Kaluza-Klein levels the spectrum as well as the interactions are N = 2 supersymmetric. In particular, we give two different arguments leading to this result - one is field theoretic, while the second one utilizes the power of string perturbation techniques. To illustrate our discussions we perform explicit two-loop computations of various corrections to gauge couplings within this framework, We also remark on phenomenological applications of our discussions in the context of TeV-scale brane world. (C) 1999 Elsevier Science B.V. All rights reserved.