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

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

doi:10.1016/j.physletb.2020.135615

Cited by 63 publications

(68 citation statements)

References 96 publications

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“…Restrictions imposed by such bigger symmetry might result in a more constrained Kähler potential [92]. Examples of this type have been shown to occur in low-energy realizations of string theory [93,94]. It would be interesting to see which eclectic flavour groups arise in the more general context studied here.…”

Section: Discussionmentioning

confidence: 97%

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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Section: Discussionmentioning

confidence: 97%

Automorphic forms and fermion masses

Ding

Feruglio

Liu

2021

J. High Energ. Phys.

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“…Aspects of the embedding of the two-tori into six-dimensional compactified space have been discussed in ref. [12] and have shown to be especially relevant for the discussion of R-symmetries. To capture the full eclectic picture one has to consider also those orbifolded tori, where the complex structure modulus is not fixed.…”

Section: Introductionmentioning

confidence: 99%

The eclectic flavor symmetry of the ℤ2 orbifold

Baur

Kade

Nilles³

et al. 2021

J. High Energ. Phys.

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Modular symmetries naturally combine with traditional flavor symmetries and $$ \mathcal{CP} $$ CP , giving rise to the so-called eclectic flavor symmetry. We apply this scheme to the two-dimensional ℤ2 orbifold, which is equipped with two modular symmetries SL(2, ℤ)T and SL(2, ℤ)U associated with two moduli: the Kähler modulus T and the complex structure modulus U. The resulting finite modular group is ((S3× S3) ⋊ ℤ4) × ℤ2 including mirror symmetry (that exchanges T and U) and a generalized $$ \mathcal{CP} $$ CP -transformation. Together with the traditional flavor symmetry (D8× D8)/ℤ2, this leads to a huge eclectic flavor group with 4608 elements. At specific regions in moduli space we observe enhanced unified flavor symmetries with as many as 1152 elements for the tetrahedral shaped orbifold and $$ \left\langle T\right\rangle =\left\langle U\right\rangle =\exp \left(\frac{\pi \mathrm{i}}{3}\right) $$ T = U = exp π i 3 . This rich eclectic structure implies interesting (modular) flavor groups for particle physics models derived form string theory.

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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%

“…This is not always true for the combined symmetry. For the heterotic orbifold, the group structure is indeed rather complicated[48][49][50].…”

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

Cited by 63 publications

References 96 publications

Automorphic forms and fermion masses

Automorphic forms and fermion masses

The eclectic flavor symmetry of the ℤ2 orbifold

Modular flavor symmetry on a magnetized torus

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