Some comments on 6D global gauge anomalies

Global gauge anomalies in six dimensions associated with non-trivial homotopy groups ${\pi }_6\left(G\right)$ for $G=SU\left(2\right)$, $SU\left(3\right)$, 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 ${\Omega }_7^{\text{spin}}\left(BG\right)$, 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 ${\pi }_6\left(G\right)$. In this paper, we revisit and clarify the relation between these two different approaches.