Abstract
AbstractWe classify a supersymmetric extension of the Standard Model by discrete symmetries originating from finite modular symmetries ΓN. Since all the couplings in supersymmetric theories of finite modular symmetries ΓN 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.
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