Lessons from eclectic flavor symmetries

Abstract

A top-down approach to the flavor problem motivated from string theory leads to the concept of eclectic flavor groups that combine traditional and modular flavor symmetries. To make contact with models constructed in the bottom-up approach, we analyze a specific example based on the eclectic flavor group Omega(1) (a nontrivial combination of the traditional flavor group Delta(54) and the finite modular group T') in order to extract general lessons from the eclectic scheme. We observe that this scheme is highly predictive since it severely restricts the possible group representations and modular weights of matter fields. Thereby, it controls the structure of the Kaehler potential and the superpotential, which we discuss explicitly. In particular, both Kaehler potential and superpotential are shown to transform nontrivially, but combine to an invariant action. Finally, we find that discrete R-symmetries are intrinsic to eclectic flavor groups.

30 pages, 2 tables, 1 figure; v2: assumptions clarified, references added and updated, matches version published in NPB

References in corpus (13)

• Stringy origin of non-Abelian discrete flavor symmetries
• The Heterotic Road to the MSSM with R parity
• Unification of Flavor, CP, and Modular Symmetries
• Modular Flavor Symmetry on Magnetized Torus
• Eclectic flavor scheme from ten-dimensional string theory -- I. Basic results
• From strings to the MSSM
• A radiative seesaw model with three Higgs doublets in modular $A_4$ symmetry
• Geography of Fields in Extra Dimensions: String Theory Lessons for Particle Physics
• An Inverse Seesaw model with $A_4$-modular symmetry
• Delta(54) flavor phenomenology and strings
• Contrast data mining for the MSSM from strings
• Predicting the orbifold origin of the MSSM
• Neutrino Mass and Mixing with Modular Symmetry

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