# Domain-wall fermions with U(1) dynamical gauge fields in (4+1)-dimensions

## TL;DR

This paper presents a numerical simulation of a (4+1)-dimensional domain-wall model with a quenched U(1) gauge field, revealing challenges in realizing lattice chiral gauge theories due to the absence of zero modes in the symmetric phase.

## Contribution

It introduces a numerical approach to study domain-wall fermions with U(1) gauge fields in higher dimensions, highlighting difficulties in achieving chiral symmetry on the lattice.

## Key findings

- Zero mode appears absent in the symmetric phase
- Challenges in constructing lattice chiral gauge theories
- Simulation results suggest limitations in continuum limit

## Abstract

We carry out a numerical simulation of a domain-wall model in (4+1) dimensions, in the presence of a quenched U(1) dynamical gauge field only in an extra dimension, corresponding to the weak coupling limit of a (4-dimensional) physical gauge coupling. Our numerical data suggest that the zero mode seems absent in the symmetric phase, so that it is difficult to construct a lattice chiral gauge theory in the continuum limit.