Anomaly-safe discrete groups

TL;DR

This paper demonstrates that perfect finite groups, including all non-Abelian finite simple groups, are inherently free of anomalies, while non-perfect groups typically exhibit anomalies, providing two methods to understand these phenomena.

Contribution

It establishes a fundamental link between group perfection and anomaly-freedom, offering new insights into the structure of finite groups in relation to anomalies.

Findings

All non-Abelian finite simple groups are anomaly-free.

Non-perfect groups generally suffer from anomalies.

Two methods are presented to understand the anomaly properties of groups.

Abstract

We show that there is a class of finite groups, the so-called perfect groups, which cannot exhibit anomalies. This implies that all non-Abelian finite simple groups are anomaly-free. On the other hand, non-perfect groups generically suffer from anomalies. We present two different ways that allow one to understand these statements.