Global gauge anomalies for simple Lie algebras.

Abstract

We generalize the formula by Elitzur and Nair on the global-anomaly coefficients in even (D = 2n)-dimensional space and analyze global anomalies for Sp(2N), SO(N), and SU(N) groups. In particular, we show that any irreducible representation of any Sp(N) and SU(2) group has no global anomalies in D = 8k dimensions. In D = 8k+4 dimensions, SU(2) has Z/sub 2/-type global anomalies only if the spin J of an irreducible representation has the form J = (12(1+4l) = 1)2, (52,9)2,... For any SU(N) group in D = 2n, the global-anomaly coefficients can be expressed in terms of so-called unstable James numbers of Stiefel manifold SU(n+1)SU(n-k) and generalized Dynkin indices Q/sub n/..mu../sub 1/(..omega..) for SU(n+1)