Gauge anomalies of finite groups

TL;DR

This paper uses character theory to analyze gauge anomalies in theories with finite gauge groups, providing a method applicable to models relevant for quark and lepton physics.

Contribution

It introduces a character-based approach to detect anomalies in finite gauge groups, extending anomaly analysis beyond continuous groups.

Findings

Character theory effectively identifies anomalies in finite gauge groups

Application to groups relevant for quark and lepton models demonstrates practical utility

Provides a new tool for anomaly analysis in finite gauge theories

Abstract

We show how the theory of characters can be used to analyse an anomaly corresponding to chiral fermions carrying an arbitrary representation of a gauge group that is finite, but otherwise arbitrary. By way of example, we do this for some groups of relevance for the study of quark and lepton masses and mixings.