String–Unification, Universal One–Loop Corrections and Strongly Coupled Heterotic String Theory

We derive the universal threshold corrections in heterotic string theory including a continuous Wilson line. Unification of gauge and gravitational couplings is shown to be possible even within perturbative string theory. The relative importance of gauge group dependent and independent thresholds on unification is clarified. Equipped with these results we can then attempt an extrapolation to the strongly coupled heterotic string — M–theory. We argue that such an extrapolation might be meaningful because of the holomorphic structure of the gauge coupling function and the close connection of the threshold corrections to the anomaly cancelation mechanism. ∗ Supported by the Swiss National Science Foundation, the European Commission TMR programmes ERBFMRX–CT96–0045 and ERBFMRX–CT96–0090 as well as a grant from Deutsche Forschungsgemeinschaft SFB-375-95. ∗∗ On leave from: Physik Department, Technische Universität München, D–85747 Garching, FRG.