Generalized Matter Parities from Finite Modular Symmetries

TL;DR

This paper classifies supersymmetric extensions of the Standard Model based on finite modular symmetries, revealing new generalized matter parities and discrete symmetries that constrain dangerous operators and include CP transformations.

Contribution

It introduces a systematic classification of matter parities derived from finite modular symmetries, expanding the understanding of discrete symmetries in supersymmetric models.

Findings

Identification of $ ext{Z}_{2M}$ symmetries from modular transformations

Inclusion of CP transformations enlarging the symmetry group to $ ext{Z}_{2M} times ext{Z}_2^{ ext{CP}}$

Constraints on baryon- and lepton-number violating operators

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 $\mathbb{Z}_{2M} \rtimes \mathbb{Z}_2^{\text{CP}}$ symmetries together with the CP transformation.