On Gauge Couplings in String Theory

TL;DR

This paper analyzes how gauge couplings depend on fields in N=1 string vacua, revealing universal one-loop dilaton dependence and constrained moduli effects, with detailed examples from orbifold and Calabi-Yau compactifications.

Contribution

It demonstrates that low-energy effective field theory imposes strong constraints on string loop corrections to gauge couplings, especially on their dilaton and moduli dependence.

Findings

Dilaton dependence of gauge couplings is universal at one-loop.

String threshold corrections are heavily constrained by field theory considerations.

Explicit examples from orbifold and Calabi-Yau vacua illustrate these constraints.

Abstract

We investigate the field dependence of the gauge couplings of $N=1$ string vacua from the point of view of the low energy effective quantum field theory. We find that field-theoretical considerations severely constrain the form of the string loop corrections; in particular, the dilaton dependence of the gauge couplings is completely universal at the one-loop level. The moduli dependence of the string threshold corrections is also constrained, and we illustrate the power of such constraints with a detailed discussion of the orbifold vacua and the $(2,2)$ (Calabi-Yau) vacua of the heterotic string.