2,562 research outputs found
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
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, , 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
Another determination of the quark condensate from an overlap action
I use the technique of Hernandez, et al (hep-lat/0106011) to convert a recent
calculation of the lattice-regulated quark condensate from an overlap action to
a continuum-regulated number. I find Sigma(MSbar)(mu = 2 GeV) = (282(6)
MeV)-cubed times (a-inverse/1766 MeV)-cubed from a calculation with the Wilson
gauge action at beta=5.9.Comment: 3 pages, Revtex, 1 postscript figure. References added. COLO-HEP-47
Chiral Logs in Quenched QCD
The quenched chiral logs are examined on a lattice with
Iwasaki gauge action and overlap fermions. The pion decay constant is
used to set the lattice spacing, . With pion mass as low
as , we see the quenched chiral logs clearly in
and , 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 (PT) to apply. With the constrained
curve-fitting method, we are able to extract the quenched chiral log parameter
together with other low-energy parameters. Only for do we obtain a consistent and stable fit with a constant
which we determine to be 0.24(3)(4) (at the chiral scale ). By comparing to the 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 MeV. The scale independent
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
in the nucleon mass is consistent with the prediction of one-loop PT\@.
We also obtain the low energy constant from . We conclude from
this study that it is imperative to cover only the range of data with the pion
mass less than in order to examine the chiral behavior of
the hadron masses and decay constants in quenched QCD and match them with
quenched one-loop 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
Proposal for the numerical solution of planar QCD
Using quenched reduction, we propose a method for the numerical calculation
of meson correlation functions in the planar limit of QCD. General features of
the approach are outlined, and an example is given in the context of
two-dimensional QCD.Comment: 31 pages, 10 figures, uses axodraw.sty, To appear in Physical Review
Large N reduction in the continuum three dimensional Yang-Mills theory
Numerical and theoretical evidence leads us to propose the following: Three
dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase
transition on a torus of side . For the planar limit is
-independent, as expected of a non-interacting string theory. We expect the
situation in four dimensions to be similar.Comment: 4 pages, latex file, two figures, version to appear in Phys. Rev.
Let
A practical implementation of the Overlap-Dirac operator
A practical implementation of the Overlap-Dirac operator
is presented. The implementation exploits
the sparseness of 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
Chiral symmetry restoration and axial vector renormalization for Wilson fermions
Lattice gauge theories with Wilson fermions break chiral symmetry. In the
U(1) axial vector current this manifests itself in the anomaly. On the other
hand it is generally expected that the axial vector flavour mixing current is
non-anomalous. We give a short, but strict proof of this to all orders of
perturbation theory, and show that chiral symmetry restauration implies a
unique multiplicative renormalization constant for the current. This constant
is determined entirely from an irrelevant operator in the Ward identity. The
basic ingredients going into the proof are the lattice Ward identity, charge
conjugation symmetry and the power counting theorem. We compute the
renormalization constant to one loop order. It is largely independent of the
particular lattice realization of the current.Comment: 11 pages, Latex2
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
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