290 research outputs found
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
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
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.
Domain wall fermion and CP symmetry breaking
We examine the CP properties of chiral gauge theory defined by a formulation
of the domain wall fermion, where the light field variables and
together with Pauli-Villars fields and are utilized. It is shown
that this domain wall representation in the infinite flavor limit is
valid only in the topologically trivial sector, and that the conflict among
lattice chiral symmetry, strict locality and CP symmetry still persists for
finite lattice spacing . The CP transformation generally sends one
representation of lattice chiral gauge theory into another representation of
lattice chiral gauge theory, resulting in the inevitable change of propagators.
A modified form of lattice CP transformation motivated by the domain wall
fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion
invariant, is analyzed in detail; this provides an alternative way to
understand the breaking of CP symmetry at least in the topologically trivial
sector. We note that the conflict with CP symmetry could be regarded as a
topological obstruction. We also discuss the issues related to the definition
of Majorana fermions in connection with the supersymmetric Wess-Zumino model on
the lattice.Comment: 33 pages. Note added and a new reference were added. Phys. Rev.D (in
press
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
Neutron electric dipole moment from lattice QCD
We carry out a feasibility study for the lattice QCD calculation of the
neutron electric dipole moment (NEDM) in the presence of the term. We
develop the strategy to obtain the nucleon EDM from the CP-odd electromagnetic
form factor at small , in which NEDM is given by where is the momentum transfer and is the
nucleon mass. We first derive a formula which relates , a matrix element
of the electromagnetic current between nucleon states, with vacuum expectation
values of nucleons and/or the current. In the expansion of , the
parity-odd part of the nucleon-current-nucleon three-point function contains
contributions not only from the parity-odd form factors but also from the
parity-even form factors multiplied by the parity-odd part of the nucleon
two-point function, and therefore the latter contribution must be subtracted to
extract . We then perform an explicit lattice calculation employing the
domain-wall quark action with the RG improved gauge action in quenched QCD at
GeV on a lattice. At the quark mass
, corresponding to , we accumulate 730
configurations, which allow us to extract the parity-odd part in both two- and
three-point functions. Employing two different Dirac matrix
projections, we show that a consistent value for cannot be obtained
without the subtraction described above. We obtain 0.024(5) fm for the neutron and
0.021(6) fm for the
proton.Comment: LaTeX2e, 43 pages, 42 eps figures, uses revtex4 and graphicx,
comments added and typos corrected, final version to appear in Phys. Rev.
Ginsparg-Wilson Fermions: A study in the Schwinger Model
Qualitative features of Ginsparg-Wilson fermions, as formulated by Neuberger,
coupled to two dimensional U(1) gauge theory are studied. The role of the
Wilson mass parameter in changing the number of massless flavors in the theory
and its connection with the index of the Dirac operator is studied. Although
the index of the Dirac operator is not related to the geometric definition of
the topological charge for strong couplings, the two start to agree as soon as
one goes to moderately weak couplings. This produces the desired singularity in
the quenched chiral condensate which appears to be very difficult to reproduce
with staggered fermions. The fermion determinant removes the singularity and
reproduces the known chiral condensate and the meson mass within understandable
errors.Comment: Corrected a few typos and changed some references. Minor changes to
the conten
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
Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator
A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac
operator does not possess any topological zero modes in
topologically-nontrivial gauge backgrounds, it can reproduce correct axial
anomaly for sufficiently smooth gauge configurations, provided that it is
exponentially-local, doublers-free, and has correct continuum behavior. In this
paper, we calculate the axial anomaly of this lattice Dirac operator in weak
coupling perturbation theory, and show that it recovers the topological charge
density in the continuum limit.Comment: 25 pages, v2: calculation up to O(g^4) for nonabelian gauge
backgroun
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