Reduced modular symmetries of threshold corrections and gauge coupling unification

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 × ℤ 6 orbifold it is easily possible to obtain gauge coupling unification at the “observed” scale with Kähler moduli T of approximately one