Noncompact chiral U(1) gauge theories on the lattice

A new, adiabatic phase choice is adopted for the overlap in the case of an infinite volume, noncompact abelian chiral gauge theory. This gauge choice obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in addition, produces a Wess-Zumino functional that is linear in the gauge variables on the lattice. As a result, there are no gauge violations on the trivial orbit in all theories, consistent and covariant anomalies are simply related and Berry's curvature now appears as a Schwinger term. The adiabatic phase choice can be further improved to produce a perfect phase choice, with a lattice Wess-Zumino functional that is just as simple as the one in continuum. When perturbative anomalies cancel, gauge invariance in the fermionic sector is fully restored. The lattice effective action describing an anomalous abelian gauge theory has an explicit form, close to one analyzed in the past in a perturbative continuum framework.Comment: 35 pages, one figure, plain TeX; minor typos corrected; to appear in PR

An alternative to domain wall fermions

We define a sparse hermitian lattice Dirac matrix, $H$, coupling $2n+1$ Dirac fermions. When $2n$ fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of $H$ and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusion is that overlap fermions should be taken seriously as a practical alternative to domain wall fermions in the context of numerical QCD.Comment: Revtex Latex, 26 pages, 1 figure, a few minor change

Domain Wall Fermions with Exact Chiral Symmetry

We show how the standard domain wall action can be simply modified to allow arbitrarily exact chiral symmetry at finite fifth dimensional extent. We note that the method can be used for both quenched and dynamical calculations. We test the method using smooth and thermalized gauge field configurations. We also make comparisons of the performance (cost) of the domain wall operator for spectroscopy compared to other methods such as the overlap-Dirac operator and find both methods are comparable in cost.Comment: revtex, 37 pages, 11 color postscript figure

Chiral Logs in Quenched QCD

The quenched chiral logs are examined on a $16^3 \times 28$ lattice with Iwasaki gauge action and overlap fermions. The pion decay constant $f_{\pi}$ is used to set the lattice spacing, $a = 0.200(3) {\rm fm}$. With pion mass as low as $\sim 180 {\rm MeV}$, we see the quenched chiral logs clearly in $m_{\pi}^2/m$ and $f_P$, the pseudoscalar decay constant. We analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory ($\chi$PT) to apply. With the constrained curve-fitting method, we are able to extract the quenched chiral log parameter $\delta$ together with other low-energy parameters. Only for $m_{\pi} \leq 300 {\rm MeV}$ do we obtain a consistent and stable fit with a constant $\delta$ which we determine to be 0.24(3)(4) (at the chiral scale $\Lambda_{\chi}=0.8 {\rm GeV}$). By comparing to the $12^3 \times 28$ lattice, we estimate the finite volume effect to be about 2.7% for the smallest pion mass. We also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to $m_{\pi} \sim 500-600$ MeV. The scale independent $\delta$ is determined to be 0.20(3) in this case. We study the quenched non-analytic terms in the nucleon mass and find that the coefficient $C_{1/2}$ in the nucleon mass is consistent with the prediction of one-loop $\chi$PT\@. We also obtain the low energy constant $L_5$ from $f_{\pi}$. We conclude from this study that it is imperative to cover only the range of data with the pion mass less than $\sim 300 {\rm MeV}$ in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop $\chi$PT\@.Comment: 37 pages and 24 figures, pion masses are fitted to the form for the re-summed cactus diagrams, figures added, to appear in PR

Nonperturbative Gauge Fixing and Perturbation Theory

We compare the gauge-fixing approach proposed by Jona-Lasinio and Parrinello, and by Zwanziger (JPLZ) with the standard Fadeev-Popov procedure, and demonstrate perturbative equality of gauge-invariant quantities, up to irrelevant terms induced by the cutoff. We also show how a set of local, renormalizable Feynman rules can be constructed for the JPLZ procedure.Comment: 9 pages, latex, version to appear in Phys. Rev.

One loop calculation in lattice QCD with domain-wall quarks

One loop corrections to the domain-wall quark propagator are calculated in massless QCD. It is shown that no additative counter term to the current quark mass is generated in this theory, and the wave function renormalization factor of the massless quark is explicitly evaluated. We also show that an analysis with a simple mean-field approximation can explain properties of the massless quark in numerical simulations of QCD with domain-wall quarks.Comment: 24 pages, REVTeX, with 3 epsf figure

Chiral properties of domain-wall fermions from eigenvalues of 4 dimensional Wilson-Dirac operator

We investigate chiral properties of the domain-wall fermion (DWF) system by using the four-dimensional hermitian Wilson-Dirac operator. We first derive a formula which connects a chiral symmetry breaking term in the five dimensional DWF Ward-Takahashi identity with the four dimensional Wilson-Dirac operator, and simplify the formula in terms of only the eigenvalues of the operator, using an ansatz for the form of the eigenvectors. For a given distribution of the eigenvalues, we then discuss the behavior of the chiral symmetry breaking term as a function of the fifth dimensional length. We finally argue the chiral property of the DWF formulation in the limit of the infinite fifth dimensional length, in connection with spectra of the hermitian Wilson-Dirac operator in the infinite volume limit as well as in the finite volume.Comment: Added a reference and modified the acknowledgmen

Chiral perturbation theory at O(a^2) for lattice QCD

We construct the chiral effective Lagrangian for two lattice theories: one with Wilson fermions and the other with Wilson sea fermions and Ginsparg-Wilson valence fermions. For each of these theories we construct the Symanzik action through order $a^2$. The chiral Lagrangian is then derived, including terms of order $a^2$, which have not been calculated before. We find that there are only few new terms at this order. Corrections to existing coefficients in the continuum chiral Lagrangian are proportional to $a^2$, and appear in the Lagrangian at order $a^2 p^2$ or higher. Similarly, O(4) symmetry breaking terms enter the Symanzik action at order $a^2$, but contribute to the chiral Lagrangian at order $a^2 p^4$ or higher. We calculate the light meson masses in chiral perturbation theory for both lattice theories. At next-to-leading order, we find that there are no order $a^2$ corrections to the valence-valence meson mass in the mixed theory due to the enhanced chiral symmetry of the valence sector.Comment: 25 pages, LaTeX2e; references adde

Effective Lagrangian for strongly coupled domain wall fermions

We derive the effective Lagrangian for mesons in lattice gauge theory with domain-wall fermions in the strong-coupling and large-N_c limits. We use the formalism of supergroups to deal with the Pauli-Villars fields, needed to regulate the contributions of the heavy fermions. We calculate the spectrum of pseudo-Goldstone bosons and show that domain wall fermions are doubled and massive in this regime. Since we take the extent and lattice spacing of the fifth dimension to infinity and zero respectively, our conclusions apply also to overlap fermions.Comment: 26 pp. RevTeX and 3 figures; corrected error in symmetry breaking scheme and added comments to discussio

A practical implementation of the Overlap-Dirac operator

A practical implementation of the Overlap-Dirac operator ${{1+\gamma_5\epsilon(H)}\over 2}$ is presented. The implementation exploits the sparseness of $H$ and does not require full storage. A simple application to parity invariant three dimensional SU(2) gauge theory is carried out to establish that zero modes related to topology are exactly reproduced on the lattice.Comment: Y-axis label in figure correcte