Low energy effective action of domain-wall fermion and the Ginsparg-Wilson relation

We derive the effective action of the light fermion field of the domain-wall fermion, which is referred as $q(x)$ by Furman and Shamir. The inverse of the effective Dirac operator turns out to be identical to the inverse of the truncated overlap Dirac operator, except a local contact term which would give the chiral symmetry breaking in the Ginsparg-Wilson relation. This result allows us to relate the light fermion field and the fermion field described by the truncated overlap Dirac operator and to understand the chiral property of the light fermion through the exact chiral symmetry based on the Ginsparg-Wilson relation.Comment: 35 pages, LaTeX2e, references added and updated, minor correction

The overlap lattice Dirac operator and dynamical fermions

I show how to avoid a two level nested conjugate gradient procedure in the context of Hybrid Monte Carlo with the overlap fermionic action. The resulting procedure is quite similar to Hybrid Monte Carlo with domain wall fermions, but is more flexible and therefore has some potential worth exploring.Comment: Further expanded version. 12 pages, plain Te

Symmetry and Symmetry Restoration of Lattice Chiral Fermion in the Overlap Formalism

Three aspects of symmetry structure of lattice chiral fermion in the overlap formalism are discussed. By the weak coupling expansion of the overlap Dirac operator, the axial anomaly associated to the chiral transformation proposed by Luescher is evaluated and is shown to have the correct form of the topological charge density for perturbative backgrounds. Next we discuss the exponential suppression of the self-energy correction of the lightest mode in the domain-wall fermion/truncated overlap. Finally, we consider a supersymmetric extension of the overlap formula in the case of the chiral multiplet and examine the symmetry structure of the action.Comment: LATTICE98(chiral), 3 pages, LaTeX using espcrc2.st

Exact Chiral Symmetry on the Lattice

Developments during the last eight years have refuted the folklore that chiral symmetries cannot be preserved on the lattice. The mechanism that permits chiral symmetry to coexist with the lattice is quite general and may work in Nature as well. The reconciliation between chiral symmetry and the lattice is likely to revolutionize the field of numerical QCD.Comment: 30 pages, LaTeX, reference adde

Remark on lattice BRST invariance

A recently claimed resolution to the lattice Gribov problem in the context of chiral lattice gauge theories is examined. Unfortunately, I find that the old problem remains.Comment: 4 pages, plain TeX, presentation improved (see acknowledgments

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

Bounds on the Wilson Dirac Operator

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations using the overlap Dirac operator. The bounds also apply to the Wilson Dirac operator in odd dimensions and are therefore relevant to domain wall fermions as well.Comment: 16 pages, TeX, 3 eps figures, small corrections and improvement

Chiral Fermions and Multigrid

Lattice regularization of chiral fermions is an important development of the theory of elementary particles. Nontheless, brute force computer simulations are very expensive, if not prohibitive. In this letter I exploit the non-interacting character of the lattice theory in the flavor space and propose a multigrid approach for the simulation of the theory. Already a two-grid algorithm saves an order of magnitude of computer time for fermion propagator calculations.Comment: Latex, 6 pages, 1 figur

Generalized Ginsparg-Wilson algebra and index theorem on the lattice

Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. It is shown that local chiral anomaly and the instanton-related index of all these operators are identical. The locality of all these Dirac operators for vanishing gauge fields is proved on the basis of explicit construction, but the locality with dynamical gauge fields has not been established yet. We suggest that the Wilsonian effective action is essential to avoid infrared singularities encountered in general perturbative analyses.Comment: 11 pages. Talk given at APCTP-Nankai Joint Symposium on Lattice Statistics and Mathematical Physics, Tianjin, China, 8-11 October, 2001. To be published in the Proceedings and in Int. Jour. Mod. Phys.