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Anomaly-safe discrete groups. (English) Zbl 1369.81049

Summary: 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.

MSC:

81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81T50 Anomalies in quantum field theory
20C35 Applications of group representations to physics and other areas of science
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