Z-string global gauge anomaly and Lorentz non-invariance

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 how 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. (C) 1998 Elsevier Science B.V.