Generalized Matter Parities from Finite Modular Symmetries

Abstract

We classify a supersymmetric extension of the Standard Model by discrete symmetries originating from finite modular symmetries ${\Gamma }_N$. Since all the couplings in supersymmetric theories of finite modular symmetries ${\Gamma }_N$ are described by holomorphic modular forms with even modular weights, renormalizable and non-renormalizable operators such as baryon- and/or lepton-number violating operators are severely constrained. From the modular transformation of matter multiplets with modular weight $1/M$, we find ${\mathbb{Z}}_{2M}$ symmetries, including the generalized baryon and lepton parities, $R$-parity, ${\mathbb{Z}}_3$ baryon triality and ${\mathbb{Z}}_6$ proton hexality. Such ${\mathbb{Z}}_{2M}$ symmetries are enlarged to ${\mathbb{Z}}_{2M}⋊{\mathbb{Z}}_2^{\text{CP}}$ symmetries together with the CP transformation.

23 pagess, v2: published version

References in corpus (19)

• Unification of Flavor, CP, and Modular Symmetries
• (Non-)Abelian discrete anomalies
• Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau =i$
• Landscape of Modular Symmetric Flavor Models
• 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
• $SU(5)$ GUTs with $A_4$ modular symmetry
• Twin Modular $S_4$ with $SU(5)$ GUT
• Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Symplectic modular symmetry in heterotic string vacua: flavor, CP, and $R$-symmetries
• Adjoint SU(5) GUT model with Modular $S_4$ Symmetry
• Modular symmetry in the SMEFT
• Flipped SU(5) with modular $A_4$ symmetry
• On Stringy Origin of Minimal Flavor Violation
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models