Some comments on 6D global gauge anomalies

Abstract

Abstract Global gauge anomalies in six dimensions associated with non-trivial homotopy groups $\pi_6(G)$ for $G=SU(2)$, $SU(3)$, and $G_2$ have been computed and utilized in the past. From the modern bordism point of view of anomalies, however, they come from the bordism groups $\Omega^\text{spin}_7(BG)$, which are in fact trivial and therefore preclude their existence. Instead, it was noticed that a proper treatment of the 6D Green–Schwarz mechanism reproduces the same anomaly cancellation conditions derived from $\pi_6(G)$. In this paper, we revisit and clarify the relation between these two different approaches.