Flipped SU(5) with modular A4 symmetry

We study flipped SU(5) x U(1) grand unified theories (GUTs) with Gamma(3) similar or equal to A(4) modular symmetry. We propose two models with different modular weights assignments, where the fermion mass hierarchy can arise from weighton fields. In order to relax the constraint on the Dirac neutrino Yukawa matrix we appeal to mechanisms which allow incomplete GUT representations, allowing a good fit to quark and charged lepton masses and quark mixing for a single modulus field tau, with the neutrino masses and lepton mixing well determined by the type-I seesaw mechanism, at the expense of some tuning. We also discuss the double seesaw possibility allowed by the extra singlets generically predicted in such string inspired theories.

Automated summary

In this study, two models of flipped SU(5) x U(1) grand unified theories were proposed with different modular weights assigned to fermion mass hierarchy. Constraints on the Dirac neutrino Yukawa matrix were relaxed by mechanisms allowing incomplete GUT representations, leading to a good fit for quark and charged lepton masses. The possibility of a double seesaw mechanism was also discussed, enabled by the extra singlets predicted in such string inspired theories.