Higher Loop Effects on Unification via Kaluza-Klein Thresholds

TL;DR

This paper analyzes higher loop corrections to gauge coupling unification in models with Kaluza-Klein thresholds, showing one-loop dominance in N=1 supersymmetric compactifications and exploring implications for TeV-scale brane worlds.

Contribution

It demonstrates that higher loop corrections are subleading in N=1 supersymmetric Kaluza-Klein models and provides explicit two-loop calculations supporting this.

Findings

One-loop threshold effects dominate in N=1 supersymmetric compactifications.

Higher loop corrections are subleading due to N=2 supersymmetry at heavy Kaluza-Klein levels.

Explicit two-loop computations confirm the theoretical predictions.

Abstract

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 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.