Aspects of Modular Flavor Symmetries

TL;DR

This paper discusses the role of modular flavor symmetries in fermion mass models, highlighting their mathematical properties and realization in string theory, to advance understanding of flavor structures.

Contribution

It provides a detailed analysis of modular flavor symmetries, emphasizing their mathematical framework and potential string theory realizations, offering new insights into fermion mass modeling.

Findings

Modular forms have unique properties useful for flavor symmetry models.

String theory can explicitly realize modular flavor symmetries.

These symmetries can constrain fermion mass matrices.

Abstract

Modular flavor symmetries refers to scenarios in which fermion masses respect modular symmetries. Such scenarios have been studied in the bottom-up approach and have an explicit realization in string theory. They rely on the remarkable properties of vector-valued modular forms.