Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance

TL;DR

This paper presents a method to construct anomaly-free chiral gauge theories on the lattice with exact gauge invariance using domain wall fermions and a five-dimensional gauge field framework.

Contribution

It introduces a new approach to realize chiral gauge coupling on the lattice with exact gauge invariance by employing a five-dimensional gauge field and a gauge-invariant counter term.

Findings

Constructed anomaly-free chiral gauge theories with exact gauge invariance.

Formulated the cohomology problem in 5+1 dimensions using Chern-Simons current.

Derived formulas for the measure and effective action of Weyl fermions on the lattice.

Abstract

We discuss how to construct anomaly-free chiral gauge theories on the lattice with exact gauge invariance in the framework of domain wall fermion. Chiral gauge coupling is realized by introducing a five-dimensional gauge field which interpolates between two different four-dimensional gauge fields at boundaries. The five-dimensional dependence is compensated by a local and gauge-invariant counter term. The cohomology problem to obtain the counter term is formulated in 5+1 dimensional space, using the Chern-Simons current induced from the five-dimensional Wilson fermion. We clarify the connection to the invariant construction based on the Ginsparg-Wilson relation using overlap Dirac operator. Formula for the measure and the effective action of Weyl fermions are obtained in terms of five-dimensional lattice quantities.