Chiral Fermions, Anomalies and Chern-Simons Currents on the Lattice

TL;DR

This paper investigates the spectrum of lattice chiral fermions in the domain wall model, linking zero modes and anomalies to Chern-Simons currents, and demonstrates finite lattice effects preserve key features of the infinite system.

Contribution

It provides a detailed analysis of the zero mode spectrum and its relation to Chern-Simons currents in lattice chiral fermion models, highlighting finite lattice effects.

Findings

Zero modes cease at critical momenta.

Spectrum related to Chern-Simons current behavior.

Finite lattice results mirror infinite system features.

Abstract

I discuss the zeromode spectrum of lattice chiral fermions in the domain wall model suggested recently. In particular I give the critical momenta where the fermions cease to be chiral and show that the spectrum is directly related to the behaviour of the Chern-Simons current on the lattice. First results for the domain wall model on the finite lattice indicate that the relevant features of the model in the infinite system survive for the finite lattice.