Stringy origin of non-Abelian discrete flavor symmetries

Abstract

We study the origin of non-Abelian discrete flavor symmetries in superstring theory. We classify all possible non-Abelian discrete flavor symmetries which can appear in heterotic orbifold models. These symmetries include D_4 and Delta(54). We find that the symmetries of the couplings are always larger than the symmetries of the compact space. This is because they are a consequence of the geometry of the orbifold combined with the space group selection rules of the string. We also study possible breaking patterns. Our analysis yields a simple geometric understanding of the realization of non-Abelian flavor symmetries.

27 pages, 4 figures, v2: matches version published in Nuclear Physics B

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• Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry
• Z_2 x Z_2 Heterotic Orbifold Models of Non Factorisable Six Dimensional Toroidal Manifolds
• The discrete flavor symmetry D5
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