Anomalies and chiral defect fermions

TL;DR

This paper investigates anomalies and chiral defect fermions in higher-dimensional gauge backgrounds, calculating axial and consistent anomalies, and exploring the relation between finite and infinite lattice models with implications for dynamical gauge fields.

Contribution

It provides a detailed calculation of axial and consistent anomalies for chiral defect fermions in various models, extending understanding of lattice and continuum formulations.

Findings

Calculated axial anomaly for arbitrary dimensions with finite extra dimension.

Derived consistent anomaly in 2+1 dimensions for gauge-variant models.

Showed the infinite lattice model as a limit of the gauge-variant model.

Abstract

Chiral defect fermions in the background of an external, $2n$ dimensional gauge field are considered. Assuming first a finite extra dimension, we calculate the axial anomaly in a vector-like, gauge invariant model for arbitrary $n$, and the consistent anomaly in a gauge {\it variant} model with a chiral spectrum. For technical reasons, the latter calculation is limited to the $2+1$ dimensional case. We also show that the infinite lattice chiral model, when properly defined, is in fact a limiting case of the above gauge-variant model. The behaviour of this model with a dynamical gauge field is discussed.