A lattice implementation of the eta-invariant and effective action for chiral fermions on the lattice

TL;DR

This paper presents a lattice-based approach to implement the eta-invariant and effective action for chiral fermions, connecting domain-wall fermions with Ginsparg-Wilson fermions and deriving a lattice Chern-Simons term.

Contribution

It introduces a lattice formulation of the eta-invariant using domain-wall fermions and clarifies its relation to Ginsparg-Wilson fermions, including a lattice expression for the Chern-Simons term.

Findings

Provides a lattice expression for the eta-invariant.

Clarifies the relation between domain-wall and Ginsparg-Wilson fermions.

Derives a lattice version of the Chern-Simons term.

Abstract

We consider a lattice implementation of the eta-invariant, using the complex phase of the determinant of the simplified domain-wall fermion, which couples to an interpolating five-dimensional gauge field. We clarify the relation to the effective action for chiral Ginsparg-Wilson fermions. The integrability, which holds true for anomaly-free theories in the classical continuum limit, is not assured on the lattice with a finite spacing. A lattice expression for the five-dimensional Chern-Simons term is obtained.