paper

The Euclidean Spectrum of Kaplan's Lattice Chiral Fermions

arXiv:hep-lat/9212010 · doi:10.1016/0370-2693(93)91068-X

Abstract

We consider the (2n+1)-dimensional euclidean Dirac operator with a mass term that looks like a domain wall, recently proposed by Kaplan to describe chiral fermions in dimensions. In the continuum case we show that the euclidean spectrum contains {\it no} bound states with non-zero momentum. On the lattice, a bound state spectrum without energy gap exists only if 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 {\it has} the expected (1/p-slash) pole on the domain wall. But there may be a problem with the phase of the fermionic determinant at the non-perturbative level.

15 pages, LATEX, WIS-92/97/12-PH

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