paper

Some comments on 6d global gauge anomalies

arXiv:2012.11622

Abstract

Global gauge anomalies in $6 d$ associated with non-trivial homotopy groups $I ¨ _{6} (G)$ for $G = S U (2)$ , $S U (3)$ , and $G_{2}$ were computed and utilized in the past. In the modern bordism point of view of anomalies, however, they come from the bordism groups $I^c ◯_{7}^{spin} (B G)$ , which are in fact trivial and therefore preclude their existence. Instead, it was noticed that a proper treatment of the $6 d$ Green-Schwarz mechanism reproduces the same anomaly cancellation conditions derived from $I ¨ _{6} (G)$ . In this paper, we revisit and clarify the relation between these two different approaches.

35 pages; v2: minor changes and additional references, version to be published