Eclectic flavor groups

Nilles, Hans Peter; Ramos‐Sánchez, Saúl; Vaudrevange, Patrick K.S.

doi:10.1007/jhep02(2020)045

Cited by 91 publications

(107 citation statements)

References 92 publications

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“…This idea has already been discussed in Refs. [29,[48][49][50], in which a possible extension of the conventional flavor groups by finite modular groups has been studied in the heterotic orbifold. In this paper, we develop a similar idea for magnetized torus.…”

Section: Introductionmentioning

confidence: 99%

Modular flavor symmetry on a magnetized torus

2020

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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 modes transform under the modular group, the above modular subgroup (referred to as modular flavor symmetry) provides a new type of modular invariant flavor models with D 4 × Z 2 , ðZ 4 × Z 2 Þ ⋊ Z 2 , and ðZ 8 × Z 2 Þ ⋊ Z 2. We also find that conventional discrete flavor symmetries which arise in magnetized torus model are noncommutative with the modular flavor symmetry. Combining both symmetries, we obtain a larger flavor symmetry, which is the semidirect product of the conventional flavor symmetry and the modular flavor symmetry for the nonvanishing Wilson line. For the vanishing Wilson line, we have additional Z 2 symmetry, i.e., parity, which is the unique common element between the conventional flavor symmetry and the modular flavor symmetry.

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Section: Introductionmentioning

confidence: 99%

Modular flavor symmetry on a magnetized torus

2020

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“…do not depend on the complex structure modulus U i if K i ∈ {3, 4, 6}. In contrast, for K i = 2 they do depend on U i but are invariant under the "rotational" modular transformation γ (2) . Hence, we can set n Y = 0 and ρ s Y (γ (2) ) = 1.…”

Section: Sublattice Rotations From Sl(2 Z) U Of the Complex Structurmentioning

confidence: 94%

“…Consequently, one can show that the finite modular group T ∼ = SL(2, 3) gets enhanced by CP to GL (2,3). Simultaneously, the eclectic flavor group Ω(2) is enhanced by CP to a group of order 3,888 (while the Ω(1) subgroup of Ω(2) is enhanced to [1296, 2891] by CP).…”

Section: Cp As a Modular Symmetrymentioning

confidence: 98%

“…where we have ρ s (K * ) = 1 in our basis of GL(2, 3) modular forms. Consequently, T ∼ = SL (2,3) modular forms naturally become modular forms of the CP-extended finite modular group GL(2, 3).…”

Section: Cp As a Modular Symmetrymentioning

confidence: 99%

“…The consideration of finite modular flavor groups has been suggested in the pioneering work of Feruglio [1]. A combination of these modular symmetries and traditional flavor symmetries leads to the eclectic flavor scheme [2,3]. Here, we present a study of the eclectic flavor approach towards ten-dimensional string theory with D = 6 compactified spatial dimensions 1 .…”

Section: Introductionmentioning

confidence: 99%

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Eclectic flavor scheme from ten-dimensional string theory – I. Basic results

2020

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String theory leads to a flavor scheme where modular symmetries play a crucial role. Together with the traditional flavor symmetries they combine to an eclectic flavor group, which we determine via outer automorphisms of the Narain space group. Unbroken flavor symmetries are subgroups of this eclectic group and their size depends on the location in moduli space. This mechanism of local flavor unification allows a different flavor structure for different sectors of the theory (such as quarks and leptons) and also explains the spontaneous breakdown of flavor-and CP-symmetries (via a motion in moduli space). We derive the modular groups, including CP and R-symmetries, for different sub-sectors of sixdimensional string compactifications and determine the general properties of the allowed flavor groups from this top-down perspective. It leads to a very predictive flavor scheme that should be confronted with the variety of existing bottom-up constructions of flavor symmetry in order to clarify which of them could have a consistent top-down completion.

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Automorphic forms and fermion masses

Ding

Feruglio

Liu

2021

J. High Energ. Phys.

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We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups Γ, that allow the presence of several moduli and make connection with the theory of automorphic forms. Moduli span a coset space G/K, where G is a Lie group and K is a compact subgroup of G, modded out by Γ. For a general choice of G, K, Γ and a generic matter content, we explicitly construct a minimal Kähler potential and a general superpotential, for both rigid and local $$ \mathcal{N} $$ N = 1 supersymmetric theories. We also specialize our construction to the case G = Sp(2g, ℝ), K = U(g) and Γ = Sp(2g, ℤ), whose automorphic forms are Siegel modular forms. We show how our general theory can be consistently restricted to multi-dimensional regions of the moduli space enjoying residual symmetries. After choosing g = 2, we present several examples of models for lepton and quark masses where Yukawa couplings are Siegel modular forms of level 2.

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Eclectic flavor groups

Cited by 91 publications

References 92 publications

Modular flavor symmetry on a magnetized torus

Modular flavor symmetry on a magnetized torus

Eclectic flavor scheme from ten-dimensional string theory – I. Basic results

Automorphic forms and fermion masses

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