Multiple modular symmetries as the origin of flavour

Abstract

We develop a general formalism for multiple moduli and their associated modular symmetries. We apply this formalism to an example based on three moduli with finite modular symmetries $S_4^A$, $S_4^B$ and $S_4^C$, associated with two right-handed neutrinos and the charged lepton sector, respectively. The symmetry is broken by two bi-triplet scalars to the diagonal $S_4$ subgroup. The low energy effective theory involves the three independent moduli fields ${\tau }_A$, ${\tau }_B$ and ${\tau }_C$, which preserve the residual modular subgroups $Z_3^A$, $Z_2^B$ and $Z_3^C$, in their respective sectors, leading to trimaximal TM${}_1$ lepton mixing, consistent with current data, without flavons.

arXiv comment31 pages, 1 figure, 6 tables, refs and comments added

References in corpus (65)

• Symmetries and Strings in Field Theory and Gravity
• Neutrino Mass and Mixing with Discrete Symmetry
• Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of theta_23, delta_CP, and the mass ordering
• Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry
• A SUSY SU(5) Grand Unified Model of Tri-Bimaximal Mixing from A4
• Finite Modular Groups and Lepton Mixing
• Large Mixing Angle MSW and Atmospheric Neutrinos from Single Right-Handed Neutrino Dominance and U(1) Family Symmetry
• Stringy origin of non-Abelian discrete flavor symmetries
• Lepton Masses and Mixing from Modular $S_4$ Symmetry
• Unified Models of Neutrinos, Flavour and CP Violation
• Neutrino mixing from finite modular groups
• Possible Alternatives to Tri-bimaximal Mixing
• Tri-bimaximal Neutrino Mixing from Orbifolding
• Unification of Flavor, CP, and Modular Symmetries
• Constructing the large mixing angle MNS matrix in see-saw models with right-handed neutrino dominance
• Gauge Unification In Six Dimensions
• Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries
• Tri-bimaximal neutrino mixing from discrete subgroups of SU(3) and SO(3) family symmetry
• Modular Invariance Faces Precision Neutrino Data
• Modular $A_4$ invariance and neutrino mixing
• Stringy corrections to Kahler potentials, SUSY breaking, and the cosmological constant problem
• Comparing Trimaximal Mixing and Its Variants with Deviations from Tri-bimaximal Mixing
• Modular $A_5$ Symmetry for Flavour Model Building
• CP violation of quarks in $A_4$ modular invariance
• Generalised CP Symmetry in Modular-Invariant Models of Flavour
• Modular $S_4$ Models of Lepton Masses and Mixing
• Finite modular subgroups for fermion mass matrices and baryon/lepton number violation
• Neutrino Mass and Mixing with $A_5$ Modular Symmetry
• $SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry
• Soft scalar masses in supergravity with horizontal U(1)_X gauge symmetry
• Modular symmetry and non-Abelian discrete flavor symmetries in string compactification
• Tri-bimaximal Neutrino Mixing and Flavor-dependent Resonant Leptogenesis
• Modular forms of finite modular subgroups from magnetized D-brane models
• The Flavor Group Delta(6n^2)
• Discrete dark matter
• Trimaximal TM1 neutrino mixing in S4 with spontaneous CP violation
• Mass Independent Textures and Symmetry
• S_4 Flavor Symmetry Embedded into SU(3) and Lepton Masses and Mixing
• Complete structure of Z_n Yukawa couplings
• $A_4$ Family Symmetry from SU(5) SUSY GUTs in 6d
• Littlest Seesaw
• CP violation and modular symmetries
• Flavour models for TM1 lepton mixing
• A_4xSU(5) SUSY GUT of Flavour in 8d
• Explicit and spontaneous breaking of SU(3) into its finite subgroups
• Deep learning in the heterotic orbifold landscape
• Towards unification of quark and lepton flavors in $A_4$ modular invariance
• Flavor Symmetry Breaking and Vacuum Alignment on Orbifolds
• Spontaneous breaking of SU(3) to finite family symmetries: a pedestrian's approach
• Non-Abelian Discrete Flavor Symmetries from T^2/Z_N Orbifolds
• Kahler corrections and softly broken family symmetries
• Heterotic Yukawa couplings and continuous Wilson lines
• Charting the flavor landscape of MSSM-like Abelian heterotic orbifolds
• Flavored Orbifold GUT - an SO(10) x S4 model
• Modular Weights, U(1)'s and Mass Matrices
• The CKM Phase in Heterotic Orbifold Models
• An $S_4\times SU(5)$ SUSY GUT of flavour in 6d
• Dynamical mass matrices from effective superstring theories
• SU(3) Gauge Family Symmetry and Prediction for the Lepton-Flavor Mixing and Neutrino Masses with Maximal Spontaneous CP Violation
• Spontaneous breaking of $SO(3)$ to finite family symmetries with supersymmetry - an $A_4$ model
• Flavor changing neutral current constraints on standard-like orbifold models
• On the modular invariance of mass eigenstates and CP violation
• Lepton Mixing Predictions from $S_4$ in the Tri-Direct CP approach to Two Right-handed Neutrino Models
• Tri-Direct CP in the Littlest Seesaw Playground
• Spontaneous Breaking of Gauge Groups to Discrete Symmetries

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