Origin of family symmetries

TL;DR

This paper explores how discrete family symmetries originate from the geometry of extra dimensions in string and field theories, emphasizing their role in particle physics models and discussing anomaly constraints.

Contribution

It provides a framework for understanding the origin of discrete family symmetries through geometrical properties of extra dimensions in ultraviolet completions.

Findings

Discrete symmetries can emerge from special geometries of compact dimensions.

Localization of fields influences the emergence of family symmetries.

Anomaly constraints restrict possible discrete symmetry realizations.

Abstract

Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.