CHIRAL FERMIONS AND ANOMALIES ON A FINITE LATTICE

Recently Kaplan proposed a new method to simulate chiral fermions on the lattice by introducing a space dependent mass term that looks like a domain wall. He showed that if one starts with an odd-dimensional lattice theory the lower (even-)dimensional world on the domain will have a chiral zero mode and the corresponding anomaly. I test this proposal by computing the gauge and Goldstone-Wilczek currents and their derivatives on a three-dimensional finite lattice. By determining the spectrum of the finite lattice hamiltonian I demonstrate that the theory one obtains is chiral below a critical momentum. Furthermore I show that one can see the anomaly on the finite lattice and that in the case of the 3-4-5 model the anomalies in the gauge currents cancel as in the continuum.