1,455 research outputs found
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 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, , coupling Dirac
fermions. When 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 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
where stands for a non-negative integer.
The choice 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.
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