On the Overlap Prescription for Lattice Regularization of Chiral Fermions

TL;DR

This paper derives Feynman rules for a lattice model of chiral fermions, showing it correctly reproduces continuum chiral anomalies and serves as a valid regularization method for such theories.

Contribution

It provides a clear derivation of Feynman rules for domain wall lattice fermions and demonstrates their continuum limit reproduces chiral anomalies.

Findings

Lattice Feynman rules correspond to 1-loop vacuum graphs.

Continuum limit reproduces chiral anomalies.

Lattice model acts as a valid regularization for chiral fermions.

Abstract

Feynman rules for the vacuum amplitude of fermions coupled to external gauge and Higgs fields in a domain wall lattice model are derived using time--dependent perturbation theory. They have a clear and simple structure corresponding to 1--loop vacuum graphs. Their continuum approximations are extracted by isolating the infrared singularities and it is shown that, in each order, they reduce to vacuum contributions for chiral fermions. In this sense the lattice model is seen to constitute a valid regularization of the continuum theory of chiral fermions coupled to weak and slowly varying gauge and Higgs fields. The overlap amplitude, while not gauge invariant, exhibits a well defined (modulo phase conventions) response to gauge transformations of the background fields. This response reduces in the continuum limit to the expected chiral anomaly, independently of the phase conventions.