The domain wall fermion chiral condensate in quenched QCD

It is a common assertion that quenched lattice QCD qualitatively produces many of the features found in continuum full QCD. However, a quenched simulation is expected to include topological gauge configurations which produce exact fermion zero modes. Not suppressed by the missing fermion determinant, such modes will cause divergent behavior in the small mass limit of the chiral condensate. Surprisingly, the standard lattice fermion formulations do not demonstrate divergent behavior for the quenched chiral condensate at current lattice spacings and quark masses. One may imagine that the small eigenvalue spectrum of those lattice Dirac operators bears little resemblance to the continuum Dirac spectrum until the lattice spacing is substantially smaller. See the introduction of [1] for further discussion and references. Starting from Kaplan’s initial ideas for domain wall fermions (DWF) [2], several fermion formulations have been developed which use an infinite number of massive fermion flavors to produce an effective chiral-invariant action for a single massless fermion flavor. Using the overlap formalism [4], which describes the infinite flavor case, Narayanan and Neuberger demonstrated that these theories have a unique, integer valued index for the associated Dirac operator. Stud-