Gauge couplings in four-dimensional Type I string orbifolds

TL;DR

Threshold corrections to gauge couplings in four-dimensional ${\\cal N}=2$ and ${\\cal N}=1$ Type I orientifolds are computed using a background-field method, revealing moduli-dependent contributions from ${\\cal N}=2$ sectors (via KK modes) and moduli-independent but nonuniversal pieces from ${\\cal N}=1$ sectors. Twisted NS-NS moduli couple at tree level to gauge fields with coefficients tied to beta-functions, potentially altering unification scales; anomalous U(1) dynamics further constrain moduli VEVs, often restoring unification at the string scale at points of maximal symmetry. The work compares string results with effective supergravity, finding compatibility only with specific moduli dualities and highlighting tensions with heterotic–Type I duality in ${\\cal N}=1$ vacua. Overall, the paper clarifies how geometric and twisted moduli shape gauge coupling unification in Type I orbifolds and informs model-building, especially in low-string-scale scenarios.

Abstract

We compute threshold effects to gauge couplings in four-dimensional $Z_N$ orientifold models of type I strings with ${\cal N}=2$ and ${\cal N}=1$ supersymmetry, and study their dependence on the geometric moduli. We also compute the tree-level (disk) couplings of the open sector gauge fields to the twisted closed string moduli of the orbifold in various models and study their effects and that of the one-loop threshold corrections on gauge coupling unification. We interpret the results from the (supergravity) effective theory point of view and comment on the conjectured heterotic-type I duality