The eclectic flavor symmetry of the ${\mathbb{Z}}_2$ orbifold

Abstract

Modular symmetries naturally combine with traditional flavor symmetries and $\mathcal{C}\mathcal{P}$, giving rise to the so-called eclectic flavor symmetry. We apply this scheme to the two-dimensional ${\mathbb{Z}}_2$ orbifold, which is equipped with two modular symmetries $\mathrm{SL}(2,\mathbb{Z}{)}_T$ and $\mathrm{SL}(2,\mathbb{Z}{)}_U$ associated with two moduli: the Kähler modulus $T$ and the complex structure modulus $U$. The resulting finite modular group is $((S_3\times S_3)⋊{\mathbb{Z}}_4)\times {\mathbb{Z}}_2$ including mirror symmetry (that exchanges $T$ and $U$) and a generalized $\mathcal{C}\mathcal{P}$-transformation. Together with the traditional flavor symmetry $(D_8\times D_8)/{\mathbb{Z}}_2$, 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 $⟨T⟩=⟨U⟩=\exp (\pi \mathrm{i}/3)$. This rich eclectic structure implies interesting (modular) flavor groups for particle physics models derived form string theory.

28 pages, 7 figures, 1 table; v2: matches version published in JHEP

References in corpus (8)

• Stringy origin of non-Abelian discrete flavor symmetries
• Unification of Flavor, CP, and Modular Symmetries
• Lessons from eclectic flavor symmetries
• Modular Flavor Symmetry on Magnetized Torus
• Revisiting modular symmetry in magnetized torus and orbifold compactifications
• Eclectic flavor scheme from ten-dimensional string theory -- I. Basic results
• Half-integral weight modular forms and application to neutrino mass models
• Loop Fayet-Iliopoulos terms in $T^2/Z_2$ models: instability and moduli stabilization

Cited by in corpus (30)

• Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau =i$
• Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries
• Double Covering of the Modular $A_5^{}$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model
• Metaplectic Flavor Symmetries from Magnetized Tori
• Eclectic flavor scheme from ten-dimensional string theory -- II. Detailed technical analysis
• Fermion Masses and Mixing from Double Cover and Metaplectic Cover of $A_5$ Modular Group
• Modular Invariant $A_4$ Models for Quarks and Leptons with Generalized CP Symmetry
• CP Symmetry and Symplectic Modular Invariance
• Siegel modular flavor group and CP from string theory
• The first string-derived eclectic flavor model with realistic phenomenology
• $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau =\omega$
• Modular symmetry at level 6 and a new route towards finite modular groups
• A minimal modular invariant neutrino model
• Fermion masses, critical behavior and universality
• Modulus $\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model
• Quark hierarchical structures in modular symmetric flavor models at level 6
• Top-Down Anatomy of Flavor Symmetry Breakdown
• Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models
• Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism
• The landscape of promising non-supersymmetric string models
• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Modular flavour symmetry and orbifolds
• 4D modular flavor symmetric models inspired by higher dimensional theory
• Remark on modular weights in low-energy effective field theory from type II string theory
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• Flavor, CP and Metaplectic Modular Symmetries in Type IIB Chiral Flux Vacua
• Higgs-portal dark matter from non-supersymmetric strings
• Completing the eclectic flavor scheme of the ${\mathbb{Z}}_2$ orbifold
• Quark-lepton mass relations from modular flavor symmetry
• Modular flavored dark matter