536 research outputs found
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
Absence of vortex condensation in a two dimensional fermionic XY model
Motivated by a puzzle in the study of two dimensional lattice Quantum
Electrodynamics with staggered fermions, we construct a two dimensional
fermionic model with a global U(1) symmetry. Our model can be mapped into a
model of closed packed dimers and plaquettes. Although the model has the same
symmetries as the XY model, we show numerically that the model lacks the well
known Kosterlitz-Thouless phase transition. The model is always in the gapless
phase showing the absence of a phase with vortex condensation. In other words
the low energy physics is described by a non-compact U(1) field theory. We show
that by introducing an even number of layers one can introduce vortex
condensation within the model and thus also induce a KT transition.Comment: 5 pages, 5 figure
Ising exponents from the functional renormalisation group
We study the 3d Ising universality class using the functional renormalisation
group. With the help of background fields and a derivative expansion up to
fourth order we compute the leading index, the subleading symmetric and
anti-symmetric corrections to scaling, the anomalous dimension, the scaling
solution, and the eigenperturbations at criticality. We also study the
cross-correlations of scaling exponents, and their dependence on
dimensionality. We find a very good numerical convergence of the derivative
expansion, also in comparison with earlier findings. Evaluating the data from
all functional renormalisation group studies to date, we estimate the
systematic error which is found to be small and in good agreement with findings
from Monte Carlo simulations, \epsilon-expansion techniques, and resummed
perturbation theory.Comment: 24 pages, 3 figures, 7 table
High density QCD with static quarks
We study lattice QCD in the limit that the quark mass and chemical potential
are simultaneously made large, resulting in a controllable density of quarks
which do not move. This is similar in spirit to the quenched approximation for
zero density QCD. In this approximation we find that the deconfinement
transition seen at zero density becomes a smooth crossover at any nonzero
density, and that at low enough temperature chiral symmetry remains broken at
all densities.Comment: LaTeX, 18 pages, uses epsf.sty, postscript figures include
Testing the self-duality of topological lumps in SU(3) lattice gauge theory
We discuss a simple formula which connects the field-strength tensor to a
spectral sum over certain quadratic forms of the eigenvectors of the lattice
Dirac operator. We analyze these terms for the near zero-modes and find that
they give rise to contributions which are essentially either self-dual or anti
self-dual. Modes with larger eigenvalues in the bulk of the spectrum are more
dominated by quantum fluctuations and are less (anti) self-dual. In the high
temperature phase of QCD we find considerably reduced (anti) self-duality for
the modes near the edge of the spectral gap.Comment: Remarks added, to appear in Phys. Rev. Let
D-Theory: Field Theory via Dimensional Reduction of Discrete Variables
A new non-perturbative approach to quantum field theory --- D-theory --- is
proposed, in which continuous classical fields are replaced by discrete
quantized variables which undergo dimensional reduction. The 2-d classical O(3)
model emerges from the (2+1)-d quantum Heisenberg model formulated in terms of
quantum spins. Dimensional reduction is demonstrated explicitly by simulating
correlation lengths up to 350,000 lattice spacings using a loop cluster
algorithm. In the framework of D-theory, gauge theories are formulated in terms
of quantum links --- the gauge analogs of quantum spins. Quantum links are
parallel transporter matrices whose elements are non-commuting operators. They
can be expressed as bilinears of anticommuting fermion constituents. In quantum
link models dimensional reduction to four dimensions occurs, due to the
presence of a 5-d Coulomb phase, whose existence is confirmed by detailed
simulations using standard lattice gauge theory. Using Shamir's variant of
Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of
a 5-d slab. This naturally protects their chiral symmetries without
fine-tuning. The first efficient cluster algorithm for a gauge theory with a
continuous gauge group is formulated for the U(1) quantum link model. Improved
estimators for Wilson loops are constructed, and dimensional reduction to
ordinary lattice QED is verified numerically.Comment: 15 pages, LaTeX, including 9 encapsulated postscript figures.
Contribution to Lattice 97 by 5 authors, to appear in Nuclear Physics B
(Proceeding Supplements). Requires psfig.tex and espcrc2.st
Comparison between Theoretical Four-Loop Predictions and Monte Carlo Calculations in the Two-Dimensional -Vector Model for
We have computed the four-loop contribution to the beta-function and to the
anomalous dimension of the field for the two-dimensional lattice -vector
model. This allows the determination of the second perturbative correction to
various long-distance quantities like the correlation lengths and the
susceptibilities. We compare these predictions with new Monte Carlo data for . From these data we also extract the values of various universal
nonperturbative constants, which we compare with the predictions of the
expansion.Comment: 68456 bytes uuencoded gzip'ed (expands to 155611 bytes Postscript); 4
pages including all figures; contribution to Lattice '9
Locality and topology with fat link overlap actions
We study the locality and topological properties of fat link clover overlap
(FCO) actions. We find that a small amount of fattening (2-4 steps of APE or 1
step of HYP) already results in greatly improved properties compared to the
Wilson overlap (WO). We present a detailed study of the localisation of the FCO
and its connection to the density of low modes of . In contrast to
the Wilson overlap, on quenched gauge backgrounds we do not find any dependence
of the localization of the FCO on the gauge coupling. This suggests that the
FCO remains local in the continuum limit. The FCO also faithfully reproduces
the zero mode wave functions of typical lattice instantons, not like the Wilson
overlap. After a general discussion of different lattice definitions of the
topological charge we also show that the FCO together with the Boulder charge
are likely to satisfy the index theorem in the continuum limit. Finally, we
present a high statistics computation of the quenched topological
susceptibility with the FCO action.Comment: 19 pages, LaTe
Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?
This is a review of the status and outstanding issues in attempts to
construct chiral lattice gauge theories by decoupling the mirror fermions from
a vectorlike theory. In the first half, we explain why studying nonperturbative
chiral gauge dynamics may be of interest, enumerate the problems that a lattice
formulation of chiral gauge theories must overcome, and briefly review our
current knowledge. We then discuss the motivation and idea of mirror-fermion
decoupling and illustrate the desired features of the decoupling dynamics by a
simple solvable toy model. The role of exact chiral symmetries and matching of
't Hooft anomalies on the lattice is also explained. The second, more
technical, half of the article is devoted to a discussion of the known and
unknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilson
fermions. We end by pointing out possible directions for future studies.Comment: 53 pp; 6 figs; added table of contents, references, fixed typo
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