String thresholds and Renormalisation Group Evolution

TL;DR

This paper develops a formalism to calculate threshold effects and gauge coupling evolution in string theory, incorporating Kaluza Klein and winding modes, and explores implications for unification in various string models.

Contribution

It introduces an effective field theory approach for threshold effects and provides all-order perturbative calculations for gauge couplings in string compactifications.

Findings

All-order perturbative calculation of gauge couplings involving massive modes.

Implications for gauge coupling unification in heterotic and Type I string models.

Identification of potential fine-tuning issues in low string scale scenarios.

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.