Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions

We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude as compared to usual domain wall fermions. Moreover, we present first results for four-dimensional quantum chromodynamics, where we also observe significant reductions of chiral symmetry violations for staggered domain wall fermions.

In order to better understand what to expect from numerical CORE computations for two-dimensional massless QED (the Schwinger model) we wish to obtain some analytic control over the approach to the continuum limit for various choices of fermion derivative. To this end we study the Hamiltonian formulation of the lattice Schwinger model (i.e., the theory defined on the spatial lattice with continuous time) in $A_0=0$ gauge. We begin with a discussion of the solution of the Hami...

I demonstrate that the chiral properties of Domain Wall Fermions (DWF) in the large to intermediate lattice spacing regime of QCD, 1 to 2 GeV, are significantly improved by adding to the action two standard Wilson fermions with supercritical mass equal to the negative DWF five dimensional mass. Using quenched DWF simulations I show that the eigenvalue spectrum of the transfer matrix Hamiltonian develops a substantial gap and that the residual mass decreases appreciatively. Fu...

We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, utilizing both Wilson and staggered kernels. In the process, we generalize the staggered kernels to arbitrary even dimensions and introduce both truncated and optimal staggered domain wall fermions. Some numerical investiga...

The domain wall formulation of lattice fermions is expected to support accurate chiral symmetry, even at finite lattice spacing. Here we attempt to use this new fermion formulation to simulate two-flavor, finite temperature QCD near the chiral phase transition. In this initial study, a variety of quark masses, domain wall heights and domain wall separations are explored using an 8^3 x 4 lattice. Both the expectation value of the Wilson line and the chiral condensate show the ...

Kaplan recently proposed a novel lattice chiral gauge theory in which the bare theory is defined on $(2n+1)$-dimensions, but the continuum theory emerges in $2n$-dimensions. We explore whether the resulting theory reproduces all the features of continuum chiral gauge theory in the case of two-dimensional axial Schwinger model. We find that one can arrange for the two-dimensional perturbation expansion to be reproduced successfully. However, the theory fails to reproduce the 2...

Quenched QCD simulations on three volumes, $8^3 \times$, $12^3 \times$ and $16^3 \times 32$ and three couplings, $\beta=5.7$, 5.85 and 6.0 using domain wall fermions provide a consistent picture of quenched QCD. We demonstrate that the small induced effects of chiral symmetry breaking inherent in this formulation can be described by a residual mass ($\mres$) whose size decreases as the separation between the domain walls ($L_s$) is increased. However, at stronger couplings mu...

Simulations with 2+1 flavors of domain wall fermions provide us with the opportunity to compare the lattice data directly to the predictions of continuum chiral perturbation theory, up to corrections from the residual chiral symmetry breaking, $m_{res}$, and $O(a)$ lattice artefacts, which are relatively small for domain wall fermions. We present preliminary results for the pseudoscalar meson masses and decay constants from partially quenched simulations and examine the next-...

We investigate chiral properties of the domain-wall fermion (DWF) system. After a brief introduction for the DWF, we summarize the recent numerical results on the chiral properties of the domain-wall QCD (DWQCD), which seem mutually inconsistent. We next derive a formula which connects a chiral symmetry breaking term in the five dimensional DWF Ward-Takahashi identity with the four-dimensional hermitian Wilson-Dirac operator. Based on this formula, we propose a solution, whic...

Domain-wall Fermions represent a recent lattice approach to chiral symmetry that is receiving considerable attention. The method is presented in a somewhat unconventional manner, in terms of a ladder molecule subjected to a magnetic field. Speculations are made on extending the formalism to multiple species.