1,010 research outputs found
A note on the practical feasibility of domain-wall fermions
Domain-wall fermions preserve chiral symmetry up to terms that decrease
exponentially when the lattice size in the fifth dimension is taken to
infinity. The associated rates of convergence are given by the low-lying
eigenvalues of a simple local operator in four dimensions. These can be
computed using the Ritz functional technique and it turns out that the
convergence tends to be extremely slow in the range of lattice spacings
relevant to large-volume numerical simulations of lattice QCD. Two methods to
improve on this situation are discussed.Comment: 14 pages, talk given by P. H. at the workshop on {\em Current
theoretical problems in lattice field theory}, Ringberg, German
Perturbative calculation of improvement coefficients to O(g^2a) for bilinear quark operators in lattice QCD
We calculate the O(g^2 a) mixing coefficients of bilinear quark operators in
lattice QCD using a standard perturbative evaluation of on-shell Green's
functions. Our results for the plaquette gluon action are in agreement with
those previously obtained with the Schr\"odinger functional method. The
coefficients are also calculated for a class of improved gluon actions having
six-link terms.Comment: 14 pages, REVTe
Quark confinement and the bosonic string
Using a new type of simulation algorithm for the standard SU(3) lattice gauge
theory that yields results with unprecedented precision, we confirm the
presence of a correction to the static quark potential at large
distances , with a coefficient as predicted by the bosonic string
theory. In both three and four dimensions, the transition from perturbative to
string behaviour is evident from the data and takes place at surprisingly small
distances.Comment: TeX source, 21 pages, figures include
Lattice chirality and the decoupling of mirror fermions
We show, using exact lattice chirality, that partition functions of lattice
gauge theories with vectorlike fermion representations can be split into
"light" and "mirror" parts, such that the "light" and "mirror" representations
are chiral. The splitting of the full partition function into "light" and
"mirror" is well defined only if the two sectors are separately anomaly free.
We show that only then is the generating functional, and hence the spectrum, of
the mirror theory a smooth function of the gauge field background. This
explains how ideas to use additional non-gauge, high-scale mirror-sector
dynamics to decouple the mirror fermions without breaking the gauge
symmetry--for example, in symmetric phases at strong mirror Yukawa
coupling--are forced to respect the anomaly-free condition when combined with
the exact lattice chiral symmetry. Our results also explain a paradox posed by
a recent numerical study of the mirror-fermion spectrum in a toy
would-be-anomalous two-dimensional theory. In passing, we prove some general
properties of the partition functions of arbitrary chiral theories on the
lattice that should be of interest for further studies in this field.Comment: 29 pages, 2 figures; published version, new addendu
Towards Weyl fermions on the lattice without artefacts
In spite of the breakthrough in non-perturbative chiral gauge theories during
the last decade, the present formulation has stubborn artefacts. Independently
of the fermion representation one is confronted with unwanted CP violation and
infinitely many undetermined weight factors. Renormalization group identifies
the culprit. We demonstrate the procedure on Weyl fermions in a real
representation
The gradient flow running coupling with twisted boundary conditions
We study the gradient flow for Yang-Mills theories with twisted boundary
conditions. The perturbative behavior of the energy density is used to define a running coupling at a scale given by the
linear size of the finite volume box. We compute the non-perturbative running
of the pure gauge coupling constant and conclude that the technique is
well suited for further applications due to the relatively mild cutoff effects
of the step scaling function and the high numerical precision that can be
achieved in lattice simulations. We also comment on the inclusion of matter
fields.Comment: 27 pages. LaTe
Linear broadening of the confining string in Yang-Mills theory at low temperature
The logarithmic broadening predicted by the systematic low-energy effective
field theory for the confining string has recently been verified in numerical
simulations of (2+1)-d SU(2) lattice Yang-Mills theory at zero temperature. The
same effective theory predicts linear broadening of the string at low non-zero
temperature. In this paper, we verify this prediction by comparison with very
precise Monte Carlo data. The comparison involves no additional adjustable
parameters, because the low-energy constants of the effective theory have
already been fixed at zero temperature. It yields very good agreement between
the underlying Yang-Mills theory and the effective string theory.Comment: 10 pages, 3 figures. Version published in JHEP; improved figures 1
and
Tip-surface forces, amplitude, and energy dissipation in amplitude-modulation (tapping mode) force microscopy
Amplitude-modulation (tapping mode) atomic force microscopy is a technique for high resolution imaging of a wide variety of surfaces in air and liquid environments. Here by using the virial theorem and energy conservation principles we have derived analytical relationships between the oscillation amplitude, phase shift, and average tip-surface forces. We find that the average value of the interaction force and oscillation and the average power dissipated by the tip-surface interaction are the quantities that control the amplitude reduction. The agreement obtained between analytical and numerical results supports the analytical method.This work has been supported by the Dirección General de Investigación Científica y Técnica (PB98-0471) and the
European Union (BICEPS, BIO4-CT-2112). A. S. P. acknowledges financial support from the Comunidad Autónoma de Madrid.Peer reviewe
Topological Lattice Actions
We consider lattice field theories with topological actions, which are
invariant against small deformations of the fields. Some of these actions have
infinite barriers separating different topological sectors. Topological actions
do not have the correct classical continuum limit and they cannot be treated
using perturbation theory, but they still yield the correct quantum continuum
limit. To show this, we present analytic studies of the 1-d O(2) and O(3)
model, as well as Monte Carlo simulations of the 2-d O(3) model using
topological lattice actions. Some topological actions obey and others violate a
lattice Schwarz inequality between the action and the topological charge Q.
Irrespective of this, in the 2-d O(3) model the topological susceptibility
\chi_t = \l/V is logarithmically divergent in the continuum limit.
Still, at non-zero distance the correlator of the topological charge density
has a finite continuum limit which is consistent with analytic predictions. Our
study shows explicitly that some classically important features of an action
are irrelevant for reaching the correct quantum continuum limit.Comment: 38 pages, 12 figure
A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
We present a gauge-invariant and non-perturbative construction of the
Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac
operator satisfying the Ginsparg-Wilson relation. Our construction covers all
SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable
for a description of the baryon number non-conservation. In infinite volume, it
provides a gauge-invariant regularization of the electroweak theory to all
orders of perturbation theory. First we formulate the reconstruction theorem
which asserts that if there exists a set of local currents satisfying cetain
properties, it is possible to reconstruct the fermion measure which depends
smoothly on the gauge fields and fulfills the fundamental requirements such as
locality, gauge-invariance and lattice symmetries. Then we give a closed
formula of the local currents required for the reconstruction theorem.Comment: 32 pages, uses JHEP3.cls, the version to appear in JHE
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