Gauge Threshold Corrections and Field Redefinitions

TL;DR

This paper reviews threshold corrections and field redefinitions in string theories, clarifies issues in type IIB moduli mixing, and estimates the effective cutoff scale near the Kaluza-Klein scale.

Contribution

It provides a detailed analysis of gauge threshold corrections, clarifies the role of field redefinitions, and estimates the effective cutoff in string compactifications.

Findings

Field redefinitions are justified by threshold corrections in heterotic strings.

Moduli mixing at one loop in type IIB is not definitively established.

The effective cutoff scale is around the Kaluza-Klein scale.

Abstract

We review the argument for field redefinitions arising from threshold corrections to heterotic string gauge couplings, and the relation between the linear and the chiral multiplet. In the type IIB case we argue that the necessity for moduli mixing at one loop order has not been clearly established, since this is based on extending the background field expansion way beyond its regime of validity. We also resolve some issues related to the form of non-perturbative terms resulting from gaugino condensation. This enables us to estimate the effective cutoff in the field theory by evaluating the non-perturbative superpotential by two different methods, and find that it is around the Kaluza-Klein scale, as one might have expected on general grounds of self-consistency.