String thresholds and renormalization group evolution

Abstract

We consider the calculation of threshold effects due to Kaluza–Klein and winding modes in string theory. We show that for a large radius of compactification these effects may be approximated by an effective field theory applicable below the string cut-off scale. Using this formalism we show that the radiative contribution to gauge couplings involving only massive Kaluza–Klein and winding modes may be calculated to all orders in perturbation theory and determine the full two-loop contribution involving light modes and estimate the magnitude of the higher-order contributions. For the case of the weakly coupled heterotic string we also discuss how an improved calculation can be made incorporating the string theory threshold corrections which avoids the limitations of the effective field theory approach. Using this formalism we determine the implications for gauge coupling unification for one representative model including the effects of two-loop corrections above the compactification scale. Finally we discuss the prospects for gauge unification in Type I models with a low string scale and point out potential fine tuning problems in this case.