Reduced modular symmetries of threshold corrections and gauge coupling unification

TL;DR

This paper investigates how reduced modular symmetries in threshold corrections influence gauge coupling unification in heterotic string orbifold models, showing that unification at the observed scale is achievable with specific moduli values.

Contribution

It introduces the concept of reduced modular symmetries in threshold corrections and demonstrates their role in achieving gauge coupling unification in certain orbifold compactifications.

Findings

Reduced modular symmetries can occur in threshold corrections.

Unification at the observed scale is possible with Kahler moduli T around one.

Sums of Dedekind eta functions can simulate these threshold effects.

Abstract

We revisit the question of gauge coupling unification at the string scale in orbifold compactifications of the heterotic string for the supersymmetric Standard Model. In the presence of discrete Wilson lines threshold corrections with modular symmetry that is a subgroup of the full modular group arise. We find that reduced modular symmetries not previously reported are possible. We conjecture that the effects of such threshold corrections can be simulated using sums of terms built from Dedekind eta functions to obtain the appropriate modular symmetry. For the cases of the Z_8-I orbifold and the Z_3 x Z_6 orbifold it is easily possible to obtain gauge coupling unification at the "observed" scale with Kahler moduli T of approximately one.