Modular Symmetries of Threshold Corrections for Abelian Orbifolds with Discrete Wilson Lines

TL;DR

This paper investigates the modular symmetries of string loop threshold corrections in abelian orbifolds with discrete Wilson lines, focusing on their mathematical structure and implications for gauge couplings.

Contribution

It provides a comprehensive analysis of modular symmetries in the context of abelian orbifolds with discrete Wilson lines, including cases with Coxeter and generalized Coxeter elements.

Findings

Modular symmetries depend on the structure of the orbifold and Wilson lines.

Threshold corrections exhibit specific transformation properties under these symmetries.

The results unify various cases of abelian orbifolds under a common framework.

Abstract

The modular symmetries of string loop threshold corrections for gauge coupling constants are studied in the presence of discrete Wilson lines for all examples of abelian orbifolds, where the point group is realised by the action of Coxeter elements or generalised Coxeter elements on the root lattices of the Lie groups.