Can string theory predict the Weinberg angle?

We investigate whether the hypercharge assignments in the standard model can be interpreted as a hint at grand unification in the context of heterotic string theory. Our analysis is a follow-up to the recent mini-landscape analysis of the Z6-II orbifold of the E8xE8' heterotic string. In that analysis, an intermediate grand unified theory (GUT) was a requirement for finding MSSM-like theories. Nevertheless, about 1% of the models in this mini-landscape were MSSM-like. In this paper we remove this GUT restriction. To this end, we introduce a general method to calculate U(1)Y for any heterotic orbifold and compare our findings to the cases where hypercharge arises from a GUT. Surprisingly, in the overwhelming majority of 3-2 standard models, a nonanomalous hypercharge direction can be defined, for which the spectrum is vectorlike. For these models, we calculate sin2θw to see how well it agrees with the standard GUT value. We find that 12% have sin2θw=3/8, while all others have values which are less. Finally, 89% of the models with sin2θw=3/8 have U(1)Y subset of SU(5)