Number of Fermion Generations Derived from Anomaly Cancellation

TL;DR

It is proved that global anomaly cancellation requires more than one generation of quarks and leptons, provided that the standard model fields propagate in two universal extra dimensions.

Abstract

We prove that global anomaly cancellation requires more than one generation of quarks and leptons, provided that the standard model fields propagate in two universal extra dimensions. Furthermore, if the fermions of different generations have the same gauge charges and chiralities, then global anomaly cancellation implies that there must be three generations.