Abstract
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 4D massless spectra emerging from supersymmetric Abelian orbifold compactifications, including roto-translations and non-factorizable compact spaces, for generic moduli values. Although these symmetries are valid in all string theories, we focus on the E8 x E8 heterotic string. We perform the widest known search of E8 x E8 Abelian orbifold compactifications, yielding over 121,000 models with MSSM-like features. About 75.4% of these models exhibit flavor symmetries containing D4 factors and only nearly 1.2% have Delta(54) factors. The remaining models are furnished with purely Abelian flavor symmetries. Our findings suggest that, should particle phenomenology arise from a heterotic orbifold, it could accommodate only one of these flavor symmetries.
Highlights
The reason for the number of families in the standard model (SM) as well as the origin of fermion mixings may be clarified in extensions of the SM
These symmetries are valid in all string theories, we focus on the E8 × E8 heterotic string
The general structure of the quark-mixing matrix motivated the bottom-up introduction of ad hoc discrete flavor symmetries that, together with a number of extra fields transforming in nontrivial flavor representations, yield new phenomenology that may be contrasted with observations
Summary
The reason for the number of families in the standard model (SM) as well as the origin of fermion mixings may be clarified in extensions of the SM. Choosing the correct flavor symmetry among the different scenarios that render similar physics requires a selection principle that is not found in this field-theoretic approach It is in this sense that, given the constraints of string theory and its potential to provide an ultraviolet completion of the SM, we can try to identify a mechanism in string theory to restrict the admissible flavor symmetries, providing thereby their origin. We present first a systematic classification of flavor symmetries in Abelian toroidal orbifolds, whose moduli have no special values, avoiding possible enhancements These symmetries are completely determined by the orbifold space group, whose nature is purely geometric, and are independent of the string theory to be compactified.
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