Can String Theory Predict the Weinberg Angle?

TL;DR

This paper explores whether heterotic string theory models can naturally predict the Weinberg angle, finding that a subset of models aligns with the GUT value of 3/8, especially those with hypercharge in SU(5).

Contribution

It introduces a general method to compute hypercharge in heterotic orbifolds and compares these results to GUT expectations, revealing prevalent hypercharge structures.

Findings

12% of models have sin^2 theta = 3/8

Most models with sin^2 theta = 3/8 have hypercharge in SU(5)

Majority of models allow a non-anomalous, vector-like hypercharge direction

Abstract

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. 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 non-anomalous hypercharge direction can be defined, for which the spectrum is vector-like. For these models, we calculate sin^2 theta to see how well it agrees with the standard GUT value. We find that 12% have sin^2 theta = 3/8, while all others have values which are less. Finally, 89% of the models with sin^2 theta = 3/8 have U(1)_Y in SU(5).