Pocket Formulae for Non-Abelian Discrete Anomaly Freedom

TL;DR

This paper derives simplified formulae to quickly check for gauge and gravitational anomalies in models with non-Abelian discrete symmetries, aiding beyond-the-Standard-Model research.

Contribution

It introduces a classification of anomaly constraints and provides practical formulae for anomaly cancellation checks in various theoretical models.

Findings

Discrete anomaly constraints divide into two classes.

Simplified formulae enable rapid anomaly checks.

Results have implications for GUT and dark matter models.

Abstract

We show that the discrete anomaly constraints governing popular non-Abelian symmetries of use in (e.g.) flavoured, supersymmetric, and dark matter model building typically subdivide into two classes differentiated by the simple restrictions they impose on the number of fields transforming under certain irreducible representations of the relevant groups. These constraints lead us both to generic conclusions for common Beyond-the-Standard-Model constructions (including rather powerful statements for Grand Unified theories) as well as to simplified formulae that can be rapidly applied to determine whether a given field and symmetry content suffers from gauge and gravitational anomalies.