Residual flavor symmetry breaking in the landscape of modular flavor models

Abstract

We study a symmetry breaking of residual flavor symmetries realized at fixed points of the moduli space. In the supersymmetric modular invariant theories, a small departure of the modulus from fixed points is required to realize fermion mass hierarchies and sizable CP-breaking effects. We investigate whether one can dynamically fix the moduli values in the vicinity of the fixed points in the context of Type IIB string theory. It is found that the string landscape prefers $|\delta \tau |\simeq 10^{-5}$ for the deviation of the complex structure modulus from all fixed points and the CP-breaking vacuum is statistically favored. To illustrate phenomenological implications of distributions of moduli values around fixed points, we analyze the lepton sector on a concrete $A_4$ modular flavor model.

31 pages, 18 figures, v2: published version

References in corpus (29)

• The fate of hints: updated global analysis of three-flavor neutrino oscillations
• Unification of Flavor, CP, and Modular Symmetries
• Double Cover of Modular $S_4$ for Flavour Model Building
• Towards a complete $A_4\times SU(5)$ SUSY GUT
• Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau =i$
• Modular Flavor Symmetry on Magnetized Torus
• Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group
• Revisiting modular symmetry in magnetized torus and orbifold compactifications
• Landscape of Modular Symmetric Flavor Models
• Modular symmetry by orbifolding magnetized $T^2\times T^2$: realization of double cover of ${\Gamma }_N$
• Modular invariant flavor model of ${\mathrm{A}}_4$ and hierarchical structures at nearby fixed points
• Double Covering of the Modular $A_5^{}$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model
• Metaplectic Flavor Symmetries from Magnetized Tori
• Fermion Masses and Mixing from Double Cover and Metaplectic Cover of $A_5$ Modular Group
• Spontaneous CP violation by modulus $\tau$ in $A_4$ model of lepton flavors
• Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds
• Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Classification of discrete modular symmetries in Type IIB flux vacua
• Siegel modular flavor group and CP from string theory
• Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes
• Symplectic modular symmetry in heterotic string vacua: flavor, CP, and $R$-symmetries
• Modular symmetry in the SMEFT
• Predictions from warped flavordynamics based on the $T^{\prime }$ family group
• Remark on integrating out heavy moduli in flux compactification
• Small flux superpotential in F-theory compactifications
• On Stringy Origin of Minimal Flavor Violation
• Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models
• Modular Flavour Symmetries and Modulus Stabilisation

Cited by in corpus (14)

• Matter matters in moduli fixing and modular flavor symmetries
• Fermion masses, critical behavior and universality
• Quark hierarchical structures in modular symmetric flavor models at level 6
• Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models
• A simplest modular $S_3$ model for leptons
• Moduli inflation from modular flavor symmetries
• More about quark Yukawa textures from selection rules without group actions
• Subcritical regime of hybrid inflation with modular $A_4$ symmetry
• Minimal seesaw and leptogenesis with the smallest modular finite group
• Finite modular axion and radiative moduli stabilization
• Moduli trapping mechanism in modular flavor symmetric models
• Flavor, CP and Metaplectic Modular Symmetries in Type IIB Chiral Flux Vacua
• Classification of Modular Symmetries in Type IIB Flux Landscape
• Diffusion-model approach to flavor models: A case study for $S_4^{\prime }$ modular flavor model