Gauge extension of non-Abelian discrete flavor symmetry

TL;DR

This paper explores how non-Abelian discrete flavor symmetries can be realized through gauge theories, specifically using a $U(1)$ gauge theory with permutation symmetry, and constructs a model for leptons based on a $U(1)^2 \rtimes S_3$ symmetry.

Contribution

It demonstrates a gauge-theoretic realization of non-Abelian discrete flavor symmetries and applies gauge enhancement mechanisms from heterotic orbifold models to field theory.

Findings

Effective realization of non-Abelian discrete symmetries from $U(1)$ gauge theories

Construction of a lepton sector model with $U(1)^2 \rtimes S_3$ symmetry

Application of gauge enhancement mechanism in model building

Abstract

We investigate a gauge theory realization of non-Abelian discrete flavor symmetries and apply the gauge enhancement mechanism in heterotic orbifold models to field-theoretical model building. Several phenomenologically interesting non-Abelian discrete symmetries are realized effectively from a $U(1)$ gauge theory with a permutation symmetry. We also construct a concrete model for the lepton sector based on a $U(1)^2 \rtimes S_3$ symmetry.