194 research outputs found
Topological Charge and the Spectrum of the Fermion Matrix in Lattice-QED_2
We investigate the interplay between topological charge and the spectrum of
the fermion matrix in lattice-QED_2 using analytic methods and Monte Carlo
simulations with dynamical fermions. A new theorem on the spectral
decomposition of the fermion matrix establishes that its real eigenvalues (and
corresponding eigenvectors) play a role similar to the zero eigenvalues (zero
modes) of the Dirac operator in continuous background fields. Using numerical
techniques we concentrate on studying the real part of the spectrum. These
results provide new insights into the behaviour of physical quantities as a
function of the topological charge. In particular we discuss fermion
determinant, effective action and pseudoscalar densities.Comment: 33 pages, 10 eps-figures; reference adde
Discussing the U(1)-problem of QED without instantons
We construct QED_2 with mass and flavor and an extra Thirring term. The vacuum expectation values are carefully decomposed into clustering states using the U(1)-axial symmetry of the considered operators and a limiting procedure. The properties of the emerging expectation functional are compared to the proposed theta-vacuum of QCD. The massive theory is bosonized to a generalized Sine-Gordon model (GSG). The structure of the vacuum of QED_2 manifests itself in symmetry properties of the GSG. We study the U(1)-problem and derive a Witten-Veneziano-type formula for the masses of the pseudoscalars determined from a semiclassical approximation
Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory
We analyze the zero-modes of the Dirac operator in quenched SU(3) gauge
configurations at non-zero temperature and compare periodic and anti-periodic
temporal boundary conditions for the fermions. It is demonstrated that for the
different boundary conditions often the modes are localized at different
space-time points and have different sizes. Our observations are consistent
with patterns expected for Kraan - van Baal solutions of the classical
Yang-Mills equations. These solutions consist of constituent monopoles and the
zero-modes are localized on different constituents for different boundary
conditions. Our findings indicate that the excitations of the QCD vacuum are
more structured than simple instanton-like lumps.Comment: Remarks added. To appear in Phys. Rev.
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
Topology and Duality in Abelian Lattice Theories
We show how to obtain the dual of any lattice model with inhomogeneous local
interactions based on an arbitrary Abelian group in any dimension and on
lattices with arbitrary topology. It is shown that in general the dual theory
contains disorder loops on the generators of the cohomology group of a
particular dimension. An explicit construction for altering the statistical sum
to obtain a self-dual theory, when these obstructions exist, is also given. We
discuss some applications of these results, particularly the existence of
non-trivial self-dual 2-dimensional Z_N theories on the torus. In addition we
explicitly construct the n-point functions of plaquette variables for the U(1)
gauge theory on the 2-dimensional g-tori.Comment: 11 pages, LateX, 1 epsf figure; minor typos corrected and references
update
Chiral symmetry restoration and the Z3 sectors of QCD
Quenched SU(3) lattice gauge theory shows three phase transitions, namely the
chiral, the deconfinement and the Z3 phase transition. Knowing whether or not
the chiral and the deconfinement phase transition occur at the same temperature
for all Z3 sectors could be crucial to understand the underlying microscopic
dynamics. We use the existence of a gap in the Dirac spectrum as an order
parameter for the restoration of chiral symmetry. We find that the spectral gap
opens up at the same critical temperature in all Z3 sectors in contrast to
earlier claims in the literature.Comment: 4 pages, 4 figure
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