Chiral Fermions Coupled to Lattice Gauge Fields

TL;DR

This paper develops two Euclidean formulations for effective actions involving continuum fermions coupled to lattice gauge fields, addressing chiral symmetry issues and providing explicit counter-terms for chiral gauge invariance.

Contribution

It introduces novel formulations for effective actions with continuum fermions on the lattice, including explicit counter-terms and finite-mode regulators for practical computations.

Findings

Effective actions can be evaluated with finite regulators.

Counter-terms explicitly maintain chiral gauge invariance.

Coupling-constant renormalization and anomaly structures are consistent with expectations.

Abstract

Lattice fermions have well-known difficulties with chiral symmetry. To evade them it is possible to couple continuum fermions to lattice gauge fields, by introducing an interpolation of the latter. Following this line of thinking, this paper presents two Euclidean formulations of the effective action that appears after functional integration over fermion fields, one for vector-like and the other for chiral couplings. With suitable finite-mode regulators both effective actions can be evaluated in a finite computation. The prescriptions provided here contain some details not found in previous work marrying continuum fermions to the lattice via an interpolation. For example, the counter-terms needed to maintain chiral gauge invariance are explicitly given. By construction coupling-constant renormalization, anomaly structure, and (in the chiral gauge theory) fermion nonconserving amplitudes all satisfy one's expectations from perturbative and semi-classical analyses.