The computation of one-loop heterotic string threshold corrections for general orbifold models with discrete Wilson lines

TL;DR

This paper computes one-loop gauge coupling corrections in heterotic string orbifold models with Wilson lines, providing a method to evaluate these corrections through integral solutions and modular symmetry analysis.

Contribution

It introduces a novel approach to calculate threshold corrections for general orbifold models with Wilson lines by solving specific integrals and mapping models via fractional linear transformations.

Findings

Derived explicit integral solutions for threshold corrections.

Established a mapping technique for different models using modular transformations.

Discussed the modular symmetry properties of the corrections.

Abstract

We calculate the moduli dependent part of string one-loop threshold corrections to gauge couplings for the heterotic string theory compactified on abelian toroidal orbifolds, allowing for arbitrary discrete Wilson lines. We show that the knowledge of threshold corrections for any such compactification is equivalent to solving a class of integrals. We solve a sub-class of these integrals and show how any model can be mapped onto this class by fractional linear transformations of its fixed plane moduli. Modular symmetries of the final expression are discussed.