9,379 research outputs found
The overlap lattice Dirac operator and dynamical fermions
I show how to avoid a two level nested conjugate gradient procedure in the
context of Hybrid Monte Carlo with the overlap fermionic action. The resulting
procedure is quite similar to Hybrid Monte Carlo with domain wall fermions, but
is more flexible and therefore has some potential worth exploring.Comment: Further expanded version. 12 pages, plain Te
Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions
Domain Wall Fermions utilize an extra space time dimension to provide a
method for restoring the regularization induced chiral symmetry breaking in
lattice vector gauge theories even at finite lattice spacing. The breaking is
restored at an exponential rate as the size of the extra dimension increases.
Before this method can be used in dynamical simulations of lattice QCD, the
dependence of the restoration rate to the other parameters of the theory and,
in particular, the lattice spacing must be investigated. In this paper such an
investigation is carried out in the context of the two flavor lattice Schwinger
model.Comment: LaTeX, 37 pages including 18 figures. Added comments regarding power
law fitting in sect 7. Also, few changes were made to elucidate the content
in sect. 5.1 and 5.3. To appear in Phys. Rev.
Domain-wall fermions with dynamical gauge fields
We have carried out a numerical simulation of a domain-wall model in
-dimensions, in the presence of a dynamical gauge field only in an extra
dimension, corresponding to the weak coupling limit of a ( 2-dimensional )
physical gauge coupling. Using a quenched approximation we have investigated
this model at 0.5 ( ``symmetric'' phase),
1.0, and 5.0 (``broken'' phase), where is the gauge coupling constant of
the extra dimension. We have found that there exists a critical value of a
domain-wall mass which separates a region with a fermionic zero
mode on the domain-wall from the one without it, in both symmetric and broken
phases. This result suggests that the domain-wall method may work for the
construction of lattice chiral gauge theories.Comment: 27 pages (11 figures), latex (epsf style-file needed
The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice
We consider the large N limit of four dimensional SU(N) Yang-Mills field
coupled to adjoint fermions on a single site lattice. We use perturbative
techniques to show that the Z^4_N center-symmetries are broken with naive
fermions but they are not broken with overlap fermions. We use numerical
techniques to support this result. Furthermore, we present evidence for a
non-zero chiral condensate for one and two Majorana flavors at one value of the
lattice gauge coupling.Comment: 21 pages, 13 figures; a reference added; version to be published in
JHEP, small clarifications and references adde
Domain wall fermion zero modes on classical topological backgrounds
The domain wall approach to lattice fermions employs an additional dimension,
in which gauge fields are merely replicated, to separate the chiral components
of a Dirac fermion. It is known that in the limit of infinite separation in
this new dimension, domain wall fermions have exact zero modes, even for gauge
fields which are not smooth. We explore the effects of finite extent in the
fifth dimension on the zero modes for both smooth and non-smooth topological
configurations and find that a fifth dimension of around ten sites is
sufficient to clearly show zero mode effects. This small value for the extent
of the fifth dimension indicates the practical utility of this technique for
numerical simulations of QCD.Comment: Updated fig. 3-7, small changes in sect. 3, added fig. 8, added more
reference
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
Perturbative study for domain-wall fermions in 4+1 dimensions
We investigate a U(1) chiral gauge model in 4+1 dimensions formulated on the
lattice via the domain-wall method. We calculate an effective action for smooth
background gauge fields at a fermion one loop level. From this calculation we
discuss properties of the resulting 4 dimensional theory, such as gauge
invariance of 2 point functions, gauge anomalies and an anomaly in the fermion
number current.Comment: 39 pages incl. 9 figures, REVTeX+epsf, uuencoded Z-compressed .tar
fil
Hamiltonian domain wall fermions at strong coupling
We apply strong-coupling perturbation theory to gauge theories containing
domain-wall fermions in Shamir's surface version. We construct the effective
Hamiltonian for the color-singlet degrees of freedom that constitute the
low-lying spectrum at strong coupling. We show that the effective theory is
identical to that derived from naive, doubled fermions with a mass term, and
hence that domain-wall fermions at strong coupling suffer both doubling and
explicit breaking of chiral symmetry. Since we employ a continuous fifth
dimension whose extent tends to infinity, our result applies to overlap
fermions as well.Comment: Revtex, 21 pp. Some changes in Introduction, dealing with consistency
with previous wor
Residual Chiral Symmetry Breaking in Domain-Wall Fermions
We study the effective quark mass induced by the finite separation of the
domain walls in the domain-wall formulation of chiral fermion as the function
of the size of the fifth dimension (), the gauge coupling and the
physical volume . We measure the mass by calculating the small eigenvalues
of the hermitian domain-wall Dirac operator ( in the
topologically-nontrivial quenched SU(3) gauge configurations. We find that the
induced quark mass is nearly independent of the physical volume, decays
exponentially as a function of , and has a strong dependence on the size
of quantum fluctuations controlled by . The effect of the choice of the
lattice gluon action is also studied.Comment: 12 pages, 7 figure
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