Regularizations, Anomalies and Fermion Number Non-Conservation in Chiral Gauge Theories

We study how fermion number conservation fails in fermion number preserving regularization schemes. We show that the fermion number have to be carried by the gauge field configurations with non-zero winding number in this scheme and this fermion number is not conserved in the presence of instantons. We also consider other types of regularization scheme which have different global symmetries. In particular, we point out that the fermion number is conserved in the lattice chiral gauge theories with the Wilson-Yukawa coupling.