A String Theory of Flavor and CP

Abstract

Modular transformations of string theory (including the well-known stringy dualities) play a crucial role in the discussion of discrete flavor symmetries in the Standard Model. They are at the origin of CP transformations and provide a unification of CP with traditional flavor symmetries. Here, we present a novel, fully systematic method to reliably compute the unified flavor symmetry of the low-energy effective theory, including enhancements from the modular transformations of string theory. The unified flavor group is non-universal in moduli space and exhibits the phenomenon of "Local Flavor Unification" where different sectors of the theory can be subject to different flavor structures.

arXiv comment38 pages, 2 figures

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• A note on the predictions of models with modular flavor symmetries
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• Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau =i$
• Lessons from eclectic flavor symmetries
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• Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group
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• Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries
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• Automorphic Forms and Fermion Masses
• Fermion Masses and Mixing from Double Cover and Metaplectic Cover of $A_5$ Modular Group
• Half-integral weight modular forms and application to neutrino mass models
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• CP Symmetry and Symplectic Modular Invariance
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• The first string-derived eclectic flavor model with realistic phenomenology
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• Residual flavor symmetry breaking in the landscape of modular flavor models
• Modular $S_4\times SU(5)$ GUT
• $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau =\omega$
• The symmetry approach to quark and lepton masses and mixing
• Fermion masses, critical behavior and universality
• A minimal modular invariant neutrino model
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• Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models
• Neutrino Mass and Mixing Models with Eclectic Flavor Symmetry $\Delta (27)⋊T^{\prime }$
• Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry
• Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP
• Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism
• Classification of three generation models by orbifolding magnetized $T^2\times T^2$
• Contrast data mining for the MSSM from strings
• Modular flavor symmetry and vector-valued modular forms
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• Neutrino Mass Sum Rules from Modular ${\mathcal{A}}_4$ Symmetry
• Moduli trapping mechanism in modular flavor symmetric models
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• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
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• Higgs-portal dark matter from non-supersymmetric strings
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• Froggatt-Nielsen Meets the SMEFT
• Reconstructing Effective Lagrangians Embedding Residual Family Symmetries
• Completing the eclectic flavor scheme of the ${\mathbb{Z}}_2$ orbifold
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• Flavor's Delight
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• Modular flavored dark matter
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• Flavor and CP from String Theory