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Stringy origin of non-Abelian discrete flavor symmetries
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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.
Forward citations
Cited by 5 Pith papers
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Non-Invertible Selection Rules on Heterotic Non-Abelian Orbifolds
Non-Abelian orbifolds in heterotic string theory produce non-invertible coupling selection rules, since twisted sectors are labeled by conjugacy classes whose products contain multiple classes and yield characteristic...
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On discrete gauging and non-invertible selection rules
Fields labeled by conjugacy classes of Z3- and S3-gauged finite groups obey non-invertible fusion selection rules with residual automorphism symmetries.
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Flavor Symmetries and Winding Modes
In the Z3 heterotic orbifold, the modular symmetry of the Kähler modulus is Gamma(3), and the discrete flavor symmetry Delta(27) arises from misaligned U(1) gauge symmetries that become massless at different critical points.
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Matter symmetries in supersymmetric standard models from non-invertible selection rules
Non-invertible fusion rules from Z2-gauged ZM symmetries reproduce the operator selection of R-parity, baryon triality, and proton hexality in the MSSM, but cannot forbid the Weinberg operator.
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Quark and lepton masses
A review of fermion mass and mixing data and of the main theoretical attempts to explain them, from GUTs to string theory, without claiming a new result.
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