Domain Wall Fermions and Chiral Gauge Theories

TL;DR

This paper reviews the domain wall fermion approach for constructing chiral gauge theories on the lattice, highlighting its anomaly structure, methods for including dynamical gauge fields, and potential for QCD simulations.

Contribution

It presents a comprehensive review of domain wall fermions, including new methods for maintaining an infinite lattice and incorporating dynamical gauge fields for chiral gauge theories.

Findings

Correct anomaly structure with external gauge fields

Proposed methods for adding dynamical gauge fields

Potential application to lattice QCD simulations

Abstract

We review the status of the domain wall fermion approach to construct chiral gauge theories on the lattice. In this model an extra, fifth dimension is added and our 4-dimensional world lives on a domainwall induced by a soliton shaped mass defect that depends on the extra dimension only. We demonstrate that the domain wall model gives the correct anomaly structure when external gauge fields are used. We discuss two ways of adding dynamical gauge fields aiming at a lattice regularized chiral gauge theory. An approach is presented to keep the lattice infinite by regarding the fifth direction as the time-axis of a 4-dimensional Hamiltonian. Finally, a prospect to use domain wall fermions for simulating QCD is given.