Discrete Anomalies of Binary Groups

TL;DR

This paper derives anomaly conditions for binary tetrahedral and dihedral groups, clarifies embedding ambiguities, and simplifies the process to check if flavor models are free of discrete anomalies.

Contribution

It provides a comprehensive derivation of anomaly conditions for specific finite groups and resolves embedding ambiguities to streamline anomaly checks in flavor models.

Findings

Derived anomaly conditions for T' and Q_2n groups

Clarified embedding ambiguities into SU(2) and SU(3)

Simplified anomaly-free model verification

Abstract

We derive the discrete anomaly conditions for the binary tetrahedral group T' as well as the binary dihedral groups Q_2n. The ambiguities of embedding these finite groups into SU(2) and SU(3) lead to various possible definitions of the discrete indices which enter the anomaly equations. We scrutinize the different choices and show that it is sufficient to consider one particular assignment for the discrete indices. Thus it is straightforward to determine whether or not a given model of flavor is discrete anomaly free.