A Note on ``Anomalous" Chiral Gauge Theories

TL;DR

This paper examines the lattice regularization of chiral gauge theories, revealing that in (2+1) dimensions it yields a (1+1)-dimensional theory regardless of anomaly cancellation, unlike in higher dimensions.

Contribution

It demonstrates a dimensional discrepancy in the behavior of lattice regularized chiral gauge theories, highlighting limitations of the Kaplan approach in certain dimensions.

Findings

In (2+1)D, the regularization leads to a (1+1)D theory regardless of anomaly cancellation.

The behavior differs in higher dimensions, where the same regularization does not produce a lower-dimensional theory.

The results clarify the dimensional dependence of lattice regularization effects on chiral gauge theories.

Abstract

We show that, the lattice regularization of chiral gauge theories proposed by Kaplan, when applied to a (2+1)-dimensional domain wall, produces a (1+1)-dimensional theory at low energy even if gauge anomaly produced by chiral fermions does not cancel. But the corresponding statement is not true in higher dimensions.