Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds

Abstract

We study the modular symmetry on magnetized toroidal orbifolds with Scherk-Schwarz phases. In particular, we investigate finite modular flavor groups for three-generation modes on magnetized orbifolds. The three-generation modes can be the three-dimensional irreducible representations of covering groups and central extended groups of ${\Gamma }_N$ for $N=3,4,5,7,8,16$, that is, covering groups of $\Delta (6(N/2{)}^2)$ for $N=$ even and central extensions of $PSL(2,{\mathbb{Z}}_N)$ for $N=$odd with Scherk-Schwarz phases. We also study anomaly behaviors.

34 pages

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• Quark and lepton hierarchies from $S_4^{\prime }$ modular flavor symmetry
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• Top-Down Anatomy of Flavor Symmetry Breakdown
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• Flavor, CP and Metaplectic Modular Symmetries in Type IIB Chiral Flux Vacua
• 4D effective action from non-Abelian DBI action with magnetic flux background
• Generalized Matter Parities from Finite Modular Symmetries
• Modular flavored dark matter
• Orbifolds from $\mathrm{Sp}(4,\mathbb{Z})$ and their modular symmetries
• Neutrino Oscillations in the Three Flavor Paradigm