The euclidean spectrum of Kaplan's lattice chiral fermions

Abstract

We consider the (2 n + 1)-dimensional euclidean Dirac operator with a mass term that looks like a domain wall, recently proposed by Kaplan to describe chiral fermions in 2 n dimensions. In the continuum case we show that the euclidean spectrum contains no bound states with non-zero momentum. On the lattice, a bound state spectrum without energy gap exists only if m is fine tuned to some special values, and the dispersion relation does not describe a relativistic fermion. In spite of these peculiarities, the fermionic propagator has the expected 1/ p̵ pole on the domain wall. But there may be a problem with the phase of the fermionic determinant at the non-perturbative level.