SU(N) global gauge anomalies in even dimensions.

Abstract

Assuming that the representations of the SU(N) (N=n,n-1) gauge groups in (D=2n)-dimensional space are chosen to be free of local (perturbative) anomalies, i.e., Tr ${F}^{n+1}$=0, the following is proved by group theory: (1) For SU(n), there will be no global (nonperturbative) gauge anomalies in D=4k+2 and at most ${Z}_{2}$ global anomalies in D=4k and (2) for SU(n-1), there exist no global gauge anomalies if D=2n\ensuremath{\ge}6. The topological argument is given for why, for any gauge group, the global anomaly is at most ${Z}_{2}$ and in D=4k+2 no global gauge anomalies exist for a self-contragredient representation.