Charting the flavor landscape of MSSM-like Abelian heterotic orbifolds

Discovering a selection principle and the origin of flavor symmetries from an ultraviolet completion of particle physics is an interesting open task. As a step in this direction, we classify all possible flavor symmetries of four-dimensional massless spectra emerging from supersymmetric Abelian orbifold compactifications, including roto-translations and nonfactorizable tori, for generic moduli values. Although these symmetries are valid in all string theories, we focus on the E₈E₈ heterotic string. We perform the widest known search of E₈E₈ Abelian orbifold compactifications, yielding over 94, 000 models with MSSM-like features. About 70. 5% of these models exhibit flavor symmetries containing D₄ factors and only nearly 1. 5% have (54) factors. The remaining models are furnished with purely Abelian flavor symmetries. Our findings suggest that should particle phenomenology arise from such a heterotic orbifold, it could accommodate only one of these flavor symmetries.