Background Symmetries In Orbifolds With Discrete Wilson Lines

TL;DR

This paper investigates how background Wilson lines influence the symmetries of orbifold compactifications in string theory, revealing subgroup structures of the modular group that depend on Wilson line choices and lattice geometry.

Contribution

It characterizes the target space symmetries in orbifold string theories with Wilson lines, identifying their subgroup structures within the modular group based on background configurations.

Findings

Symmetry groups are subgroups of PSL(2, Z).

Symmetries depend on Wilson line choices.

Results impact understanding of gauge coupling corrections.

Abstract

Target space symmetries are studied for orbifold compactified string theories containing Wilson line background fields. The symmetries determined are for those moduli which contribute to the string loop threshold corrections of the gauge coupling constants. The groups found are subgroups of the modular group $PSL(2, Z)$ and depend on the choice of discrete Wilson lines and the shape of the underlying six-dimensional lattice.