7,118 research outputs found
Two dimensional fermions in three dimensional YM
Dirac fermions in the fundamental representation of SU(N) live on the surface
of a cylinder embedded in and interact with a three dimensional SU(N)
Yang Mills vector potential preserving a global chiral symmetry at finite .
As the circumference of the cylinder is varied from small to large, the chiral
symmetry gets spontaneously broken in the infinite limit at a typical bulk
scale. Replacing three dimensional YM by four dimensional YM introduces
non-trivial renormalization effects.Comment: 21 pages, 7 figures, 5 table
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
Stellar Mixing and the Primordial Lithium Abundance
We compare the properties of recent samples of the lithium abundances in halo
stars to one another and to the predictions of theoretical models including
rotational mixing, and we examine the data for trends with metal abundance. We
find from a KS test that in the absence of any correction for chemical
evolution, the Ryan, Norris, & Beers (1999} sample is fully consistent with
mild rotational mixing induced depletion and, therefore, with an initial
lithium abundance higher than the observed value. Tests for outliers depend
sensitively on the threshold for defining their presence, but we find a
1045% probability that the RNB sample is drawn from the rotationally mixed
models with a 0.2 dex median depletion (with lower probabilities corresponding
to higher depletion factors). When chemical evolution trends (Li/H versus Fe/H)
are treated in the linear plane we find that the dispersion in the RNB sample
is not explained by chemical evolution; the inferred bounds on lithium
depletion from rotational mixing are similar to those derived from models
without chemical evolution. We find that differences in the equivalent width
measurements are primarily responsible for different observational conclusions
concerning the lithium dispersion in halo stars. The standard Big Bang
Nucleosynthesis predicted lithium abundance which corresponds to the deuterium
abundance inferred from observations of high-redshift, low-metallicity QSO
absorbers requires halo star lithium depletion in an amount consistent with
that from our models of rotational mixing, but inconsistent with no depletion.Comment: 39 pages, 9 figures; submitted Ap
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.
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
A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator
We compute fermionic observables relevant to the study of chiral symmetry in
quenched QCD using the Overlap-Dirac operator for a wide range of the fermion
mass. We use analytical results to disentangle the contribution from exact zero
modes and simplify our numerical computations. Details concerning the numerical
implementation of the Overlap-Dirac operator are presented.Comment: 24 pages revtex with 5 postscript figures included by eps
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
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