Speaker
Description
Properties of fermions like their masses and their mixings with other generations are determined by the Yukawa sector. The lack of an organizing principle in the Yukawa sector and of a robust model for neutrino masses accounts for the proliferation of the 20 to 22 free parameters needed to account for the flavor structure of the SM. We present a model for neutrino masses in which they are given by modular forms. The lepton sector is governed by a modular symmetry which captures lepton masses and mixings. Chiral anomalies arising from modular transformations should be cancelled since they are reparametrizations (gauge transformations) of a background field called the modulus τ. We consider chiral anomalies in various models based on the modular symmetry Γ3 ≅ A4 and argue for different anomaly cancellation mechanisms based on the bottom-up vs top-down assumptions for those models.