2020
DOI: 10.1103/physrevd.102.085008
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Modular flavor symmetry on a magnetized torus

Abstract: We study the modular invariance in magnetized torus models. The modular invariant flavor model is a recently proposed hypothesis for solving the flavor puzzle, where the flavor symmetry originates from modular invariance. In this framework, coupling constants such as Yukawa couplings are also transformed under the flavor symmetry. We show that the low-energy effective theory of magnetized torus models is invariant under a specific subgroup of the modular group. Since Yukawa couplings as well as chiral zero mod… Show more

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Cited by 84 publications
(61 citation statements)
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“…It has been stated in the literature [26,27] that the wave functions given by eq. (2.1) do not satisfy the boundary conditions given by the lattice periodicity when transformed under eq.…”
Section: Boundary Conditions For Transformed Wave Functionsmentioning
confidence: 99%
See 1 more Smart Citation
“…It has been stated in the literature [26,27] that the wave functions given by eq. (2.1) do not satisfy the boundary conditions given by the lattice periodicity when transformed under eq.…”
Section: Boundary Conditions For Transformed Wave Functionsmentioning
confidence: 99%
“…symmetry based (SB), i.e. impose the modular flavor symmetry to construct the Lagrange density [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], and 2. torus based (TB), in which one derives the symmetries from an underlying torus or related setup [18][19][20][21][22][23][24][25][26][27][28][29][30].…”
Section: Introductionmentioning
confidence: 99%
“…In the former case, since the representations on the T 2 /Z 2 twist orbifolds satisfy the relation in eq. (3.34), the tensor product of these obeys 15) where m 1 , m 2 denote the Z 2 -twist eigenmodes 0, 1 on T 2 1 and T 2 2 , respectively. Therefore, the products of the same Z 2 -twist eigenmodes (m 1 = m 2 ) correspond to Γ 2lcm(|M 1 |,|M 2 |) , while the different Z 2 -twist eigenmodes (m 1 = m 2 ) correspond to Γ 2lcm(|M 1 |,|M 2 |) .…”
Section: Jhep11(2020)101mentioning
confidence: 99%
“…Zero-modes on such a geometry, corresponding to flavors of the SM quarks or leptons, transform under the modular transformation. It was investigated in magnetized D-brane models [12][13][14][15][16] and heterotic orbifold models [17][18][19][20][21][22][23][24][25]. (See also [26][27][28].)…”
Section: Introductionmentioning
confidence: 99%
“…In more detail, the traditional flavor symmetry of ref. [1] is extended from [32,49] This picture reveals the fact that the top-down discussion of modular flavor symmetry constitutes an extremely restrictive scenario, which is confirmed in other top-down scenarios [38][39][40][41][42]. As in the case of the bottom-up discussion, firstly the role of (otherwise freely chosen) flavons is played by the moduli T and U , and secondly we arrive at a specific finite modular group, being…”
Section: Discussionmentioning
confidence: 60%