DOMAIN-WALL FERMIONS AND THE ETA-INVARIANT

We extend work by Callan and Harvey and show how the phase of the chir al fermion determinant in four dimensions is reproduced by zero modes bound to a domain wall in five dimensions. The analysis could shed lig ht on the applicability of zero mode fermions and the vacuum overlap f ormulation of Narayanan and Neuberger for chiral gauge theories on the lattice.