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 Γ N . Since all the couplings in supersymmetric theories of finite modular symmetries Γ 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 Z 2M symmetries, including the generalized baryon and lepton parities, R-parity, Z 3 baryon triality and Z 6 proton hexality. Such Z M symmetries are enlarged to Z M Z CP 2 symmetries together with the CP transformation.

Subcritical regime of hybrid inflation with modular A4 symmetry

“…For other phenomenological applications, for example, the application of modular symmetry to grand-unified theories is discussed in refs. [70][71][72][73][74][75][76][77][78]. Moreover, in cosmology, models with dark matter candidates [79][80][81][82][83][84][85][86] have been considered and refs.…”

Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models

“…In addition to the above aspects, the modular flavor symmetries were recently extended to models for dark matter [84,85], soft supersymmetry breaking terms [86][87][88], matter parity [89], the strong CP problem [90], etc.…”