  Certain (3+1)-dimensional chiral non-Abelian gauge theories have been shown
to exhibit a new type of global gauge anomaly, which in the Hamiltonian
formulation is due to the fermion zero-modes of a Z-string-like configuration
of the gauge potential and the corresponding spectral flow. Here, we clarify
the relation between this Z-string global gauge anomaly and other anomalies in
both 3+1 and 2+1 dimensions. We then point out a possible trade-off between the
(3+1)-dimensional Z-string global gauge anomaly and the violation of CPT and
Lorentz invariance.
