Domain Wall Fermions and Chiral Gauge Theories

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.