Modular flavor symmetry on a magnetized torus Article Swipe
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· 2020
· Open Access
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· DOI: https://doi.org/10.1103/physrevd.102.085008
· OA: W3009710320
We study the modular invariance in magnetized torus models. Modular invariant\nflavor model is a recently proposed hypothesis for solving the flavor puzzle,\nwhere the flavor symmetry originates from modular invariance. In this framework\ncoupling constants such as Yukawa couplings are also transformed under the\nflavor symmetry. We show that the low-energy effective theory of magnetized\ntorus models is invariant under a specific subgroup of the modular group. Since\nYukawa couplings as well as chiral zero modes transform under the modular\ngroup, the above modular subgroup (referred to as modular flavor symmetry)\nprovides a new type of modular invariant flavor models with $D_4 \\times\n\\mathbb{Z}_2$, $(\\mathbb{Z}_4 \\times \\mathbb{Z}_2) \\rtimes \\mathbb{Z}_2$, and\n$(\\mathbb{Z}_8 \\times \\mathbb{Z}_2) \\rtimes \\mathbb{Z}_2$. We also find that\nconventional discrete flavor symmetries which arise in magnetized torus model\nare non-commutative with the modular flavor symmetry. Combining both two\nsymmetries we obtain a larger flavor symmetry, where the conventional flavor\nsymmetry is a normal subgroup of the whole group.\n
