Unification of Flavor, CP, and Modular Symmetries

Abstract

Flavor symmetry plays a crucial role in the standard model of particle physics but its origin is still unknown. We develop a new method (based on outer automorphisms of the Narain space group) to determine flavor symmetries within compactified string theory. A picture emerges where traditional (discrete) flavor symmetries, CP-like symmetries and modular symmetries (like T-duality) of string theory combine to unified flavor symmetries. The groups depend on the geometry of compact space and the geographical location of fields in the extra dimensions. We observe a phenomenon of "local flavor groups" with potentially different flavor symmetries for the various sectors of quarks and leptons. This should allow interesting connections to existing bottom-up attempts in flavor model building.

arXiv comment18 pages, 3 figures; v2: minor changes, version accepted by PLB

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• A note on the predictions of models with modular flavor symmetries
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• Loop Fayet-Iliopoulos terms in $T^2/Z_2$ models: instability and moduli stabilization
• Quark and lepton hierarchies from $S_4^{\prime }$ modular flavor symmetry
• The symmetry approach to quark and lepton masses and mixing
• A minimal modular invariant neutrino model
• Fermion masses, critical behavior and universality
• Modulus $\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model
• Top-Down Anatomy of Flavor Symmetry Breakdown
• A simplest modular $S_3$ model for leptons
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• Moduli inflation from modular flavor symmetries
• Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry
• Neutrino Mass and Mixing Models with Eclectic Flavor Symmetry $\Delta (27)⋊T^{\prime }$
• Texture-zero patterns of lepton mass matrices from modular symmetry
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