Modular flavor symmetry and vector-valued modular forms

Abstract

We revisit the modular flavor symmetry from a more general perspective. The scalar modular forms of principal congruence subgroups are extended to the vector-valued modular forms, then we have more possible finite modular groups including ${\Gamma }_N$ and ${\Gamma }_N^{\prime }$ as the flavor symmetry. The theory of vector-valued modular forms provide a method of differential equation to construct the modular multiplets, and it also reveals the simple structure of the modular invariant mass models. We review the theory of vector-valued modular forms and give general results for the lower dimensional vector-valued modular forms. The general finite modular groups are listed up to order 72. We apply the formalism to construct two new lepton mass models based on the finite modular groups $A_4\times Z_2$ and $GL(2,3)$.

37 pages

References in corpus (11)

• Unification of Flavor, CP, and Modular Symmetries
• Landscape of Modular Symmetric Flavor Models
• Eclectic flavor scheme from ten-dimensional string theory -- I. Basic results
• Spontaneous CP violation by modulus $\tau$ in $A_4$ model of lepton flavors
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Adjoint SU(5) GUT model with Modular $S_4$ Symmetry
• Top-Down Anatomy of Flavor Symmetry Breakdown
• First direct neutrino-mass measurement with sub-eV sensitivity
• Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP
• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Classification of Vector-Valued modular Forms of Dimension less than Six

Cited by in corpus (1)

• Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry