2,268 research outputs found
Overlap Fermions on a Lattice
We report results on hadron masses, fitting of the quenched chiral log, and
quark masses from Neuberger's overlap fermion on a quenched lattice with
lattice spacing fm. We used the improved gauge action which is shown
to lower the density of small eigenvalues for as compared to the Wilson
gauge action. This makes the calculation feasible on 64 nodes of CRAY-T3E. Also
presented is the pion mass on a small volume ( with a Wilson
gauge action at ). We find that for configurations that the
topological charge , the pion mass tends to a constant and for
configurations with trivial topology, it approaches zero possibly linearly with
the quark mass.Comment: Lattice 2000 (Chiral Fermion), 4 pages, 4 figure
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
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.
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
Numerical simulation of dynamical gluinos: experience with a multi-bosonic algorithm and first results
We report on our experience with the two-step multi-bosonic algorithm in a
large scale Monte Carlo simulation of the SU(2) Yang-Mills theory with
dynamical gluinos. First results are described on the low lying spectrum of
bound states, the string tension and the gluino condensate.Comment: LATTICE98(algorithms), latex using espcrc2.sty, 6 pages, 7 figure
A Perturbative Study of a General Class of Lattice Dirac Operators
A perturbative study of a general class of lattice Dirac operators is
reported, which is based on an 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. We study one-loop fermion contributions to
the self-energy of the gauge field, which are related to the fermion
contributions to the one-loop function and to the Weyl anomaly. We
first explicitly demonstrate that the Ward identity is satisfied by the
self-energy tensor. By performing careful analyses, we then obtain the correct
self-energy tensor free of infra-red divergences, as a general consideration of
the Weyl anomaly indicates. This demonstrates that our general operators give
correct chiral and Weyl anomalies. In general, however, the Wilsonian effective
action, which is supposed to be free of infra-red complications, is expected to
be essential in the analyses of our general class of Dirac operators for
dynamical gauge field.Comment: 30 pages. Some of the misprints were corrected. Phys. Rev. D (in
press
General bounds on the Wilson-Dirac operator
Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac
operator H(m) have previously been derived for 0<m<2 when the lattice gauge
field satisfies a certain smoothness condition. In this paper lower bounds are
derived for 2p-2<m<2p for general p=1,2,...,d where d is the spacetime
dimension. The bounds can alternatively be viewed as localisation bounds on the
real spectrum of the usual Wilson-Dirac operator. They are needed for the
rigorous evaluation of the classical continuum limit of the axial anomaly and
index of the overlap Dirac operator at general values of m, and provide
information on the topological phase structure of overlap fermions. They are
also useful for understanding the instanton size-dependence of the real
spectrum of the Wilson-Dirac operator in an instanton background.Comment: 26 pages, 2 figures. v3: Completely rewritten with new material and
new title; to appear in Phys.Rev.
Testing a Topology Conserving Gauge Action in QCD
We study lattice QCD with a gauge action, which suppresses small plaquette
values. Thus the MC history is confined to a single topological sector over a
significant time, while other observables are decorrelated. This enables the
cumulation of statistics with a specific topological charge, which is needed
for simulations of QCD in the -regime. The same action may also be
useful for simulations with dynamical quarks. The update is performed with a
local HMC algorithm.Comment: 3 pages, 3 figures, poster presented by S. Shcheredin at
Lattice2004(theory
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.
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
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