Chiral Gauge Theory on Lattice with Domain Wall Fermions

We investigate a U(1) lattice chiral gauge theory with domain wall fermions and compact gauge fixing. In the reduced model limit, our perturbative and numerical investigations show that there exist no extra mirror chiral modes. The longitudinal gauge degrees of freedom have no effect on the free domain wall fermion spectrum consisting of opposite chiral modes at the domain wall and at the anti-domain wall which have an exponentially damped overlap.