One-Loop Threshold Effects in String Unification

TL;DR

This paper develops a method to compute one-loop corrections to gauge coupling relations in string theory, enabling more precise predictions of fundamental constants like the weak mixing angle and QCD scale.

Contribution

It provides a general framework for calculating one-loop threshold effects in heterotic string models, improving the accuracy of unification predictions.

Findings

Derived formulas for one-loop corrections to gauge couplings.

Applied method to predict $ heta_W$ and $ m ext{QCD}$ scale.

Clarified previous computational errors in early string unification models.

Abstract

Like grand unification of old, string unification predicts simple tree-level relations between the couplings of all unbroken gauge groups such as $SU(3)_C$ or $SU(2)_W\)$. I show here how to compute one-loop corrections to these relations for any four-dimensional model based on a classical vacuum of the heterotic string. The result can be used to calculate both $\sin^2\theta_W$ and $\Lambda_{\rm QCD}$ in terms of $\alpha_{\rm QED}$ and $\mpl\)$. The original version of this paper was written in 1987 and published in Nuclear Physics in 1988. That version had a few factor-of-two errors, which lead some people into confusion. To avoid future confusion, I've written Errata; they are submitted separately to hep-th (article #9205068). This submission is the complete revised version of the paper.