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 zeromodes 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. PACS : 11.15.-q; 03.65.Bz; 11.30.Er; 11.30.Cp