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

TL;DR

This paper investigates how fermion number conservation is violated in certain regularization schemes of chiral gauge theories, highlighting the role of gauge field configurations with non-zero winding number and comparing different regularizations.

Contribution

It demonstrates that fermion number is carried by gauge configurations with non-zero winding number in some schemes and shows fermion number conservation in lattice theories with Wilson-Yukawa coupling.

Findings

Fermion number is carried by gauge configurations with non-zero winding number.

Fermion number is not conserved in instanton backgrounds within certain regularizations.

Fermion number is conserved in lattice chiral gauge theories with Wilson-Yukawa coupling.

Abstract

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.