Infinite Classes of Cases with Non-trivial Anomaly Cancellation

TL;DR

This paper identifies infinite classes of gauge group configurations where anomalies cancel non-trivially, providing new possibilities for model building with extra symmetries and fermions in particle physics.

Contribution

It demonstrates the existence of infinite anomaly-free classes with specific gauge groups involving symmetric tensor representations, not explained by simple group embeddings.

Findings

Infinite classes of anomaly cancellation with SU(p)×SU(q)×U(1)

Potential for models with extra leptons and U(1) interactions

Applications as family symmetries in particle physics

Abstract

It is pointed out that there are infinite classes of cases based on gauge groups of the form SU(p)xSU(q)xU(1) in which gauge anomalies cancel non-trivially for small sets of fermion multiplets that include symmetric tensor representations. These cancellations are non-trivial in the sense that no group-theoretic explanation in terms of embedding in a larger simple group is apparent. The cases presented here could be useful for model building and lead to models with extra leptons and an extra U(1) gauge interaction under which the Standard Model fermions have distinctive charges. In many cases the SU(q)xU(1) groups act as family symmetries.