# Spontaneous Breaking of Gauge Groups to Discrete Symmetries

## TL;DR

This paper explores how gauge theories can spontaneously break to discrete symmetries, ensuring anomaly freedom and compatibility with quantum gravity, by analyzing Higgs potentials and scalar spectra.

## Contribution

It introduces methods to minimize Higgs potentials for gauge breaking to discrete groups and studies the resulting scalar mass spectra, advancing understanding of symmetry breaking mechanisms.

## Key findings

- Successful minimization of Higgs potentials for specific gauge breakings
- Identification of scalar mass spectra after symmetry breaking
- Framework for connecting gauge theories with discrete symmetries

## Abstract

Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent anomalies. We minimize a number of Higgs potentials that break gauge groups to discrete symmetries of interest, and examine their scalar mass spectra.