8,770 research outputs found

### Alternative to Domain Wall Fermions

An alternative to commonly used domain wall fermions is presented. Some
rigorous bounds on the condition number of the associated linear problem are
derived. On the basis of these bounds and some experimentation it is argued
that domain wall fermions will in general be associated with a condition number
that is of the same order of magnitude as the {\it product} of the condition
number of the linear problem in the physical dimensions by the inverse bare
quark mass. Thus, the computational cost of implementing true domain wall
fermions using a single conjugate gradient algorithm is of the same order of
magnitude as that of implementing the overlap Dirac operator directly using two
nested conjugate gradient algorithms. At a cost of about a factor of two in
operation count it is possible to make the memory usage of direct
implementations of the overlap Dirac operator independent of the accuracy of
the approximation to the sign function and of the same order as that of
standard Wilson fermions.Comment: 7 pages, 1 figure, LaTeX, uses espcrc2, reference adde

### Tricks to implement the overlap Dirac operator

I present several tricks to help implement the overlap Dirac operator
numerically.Comment: 3 pages, latex, espcrc2.st

### Lattice Chirality

The external fermion propagator and the internal fermion propagator in the
overlap are given by different matrices. A generic problem (formulated by
Pelissetto) faced by all chiral, non-local, propagators of Rebbi type is
avoided in this manner. Nussinov-Weingarten-Witten mass inequalities are
exactly preserved. It is sketched how to obtain simple lattice chiral Yukawa
models and simple expressions for covariant currents. Going beyond my oral
presentation, I have added to the write-up several comments on Niedermayer's
talk. His transparencies are available on the internet.Comment: LATTICE98(chiral

### Regularization dependence of the Higgs mass triviality bound

We calculate the triviality bound on the Higgs mass in scalar field theory
models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial}
\approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity.
Limits on observable cutoff effects at four percent in several regularized
models with tunable couplings in the bare action yield triviality bounds
displaying a large degree of universality. Extrapolating from $N=\infty$ to
$N=4$ we conservatively estimate that a Higgs particle with mass up to
$0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff
effects, indicating that strong scalar self interactions in the standard model
are not ruled out. We also present preliminary numerical results of the
physical $N=4$ case for the $F_4$ lattice that are in agreement with the large
$N$ expectations. Note: The full ps file is also available via anonymous ftp to
ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username
"anonymous" and for password your name. The file is in the directory pub/vranas
(to go to that directory type: cd pub/vranas) and is called lat92_proc.ps (to
get it type: get lat92_proc.ps)Comment: 5 pages with 5 ps figures included. LaTex file. Contribution to the
LAT92 proceedings. Preprint, FSU-SCRI-92-150, RU-92-4

### A simple derivation of the Overlap Dirac Operator

We derive the vector-like four dimensional overlap Dirac operator starting
from a five dimensional Dirac action in the presence of a delta-function
space-time defect. The effective operator is obtained by first integrating out
all the fermionic modes in the fixed gauge background, and then identifying the
contribution from the localized modes as the determinant of an operator in one
dimension less. We define physically relevant degrees of freedom on the defect
by introducing an auxiliary defect-bound fermion field and integrating out the
original five dimensional bulk field.Comment: 9 pages, LaTe

### Ginsparg-Wilson relation with R=(a \gamma_5 D)^{2k}

The Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$
with $R = (a \gamma_5 D)^{2k}$ is discussed. An explicit realization of D is
constructed. It is shown that this sequence of topologically-proper lattice
Dirac operators tend to a nonlocal operator in the limit $k \to \infty$. This
suggests that the locality of a lattice Dirac operator is irrelevant to its
index.Comment: 4 pages, 1 EPS figure, talk presented at Lattice'00 (Chiral Fermion

### Chiral fermions on the lattice

Chiral fermions resisted being put on the lattice for twenty years. This
raised the suspicion that asymptotically free chiral gauge theories were not
renormalizable outside perturbation theory and therefore could not be
mathematically extended to infinite energies. During the last several years the
situation has reversed itself. Today we believe that all the essential
ingredients for a full lattice definition of non-anomalous chiral gauge
theories are in place within the overlap construction. This construction is
based on earlier work by Callan and Harvey, by Kaplan and by Frolov and
Slavnov. It can be reinterpreted as coming from the Ginsparg-Wilson relation,
but, at the moment, it is a unique construction and therefore might also be the
way by which Nature itself regularizes chiral fermions. This is yet another
instance in which lattice field theory makes a potentially important
contribution to fundamental particle physics.Comment: 10 pages, latex, espcrc2.st

### Truncated Overlap Fermions

In this talk I propose a new computational scheme with overlap fermions and a
fast algorithm to invert the corresponding Dirac operator.Comment: LATTICE99(algorithms

### Low energy effective action of domain-wall fermion and the Ginsparg-Wilson relation

We derive the effective action of the light fermion field of the domain-wall
fermion, which is referred as $q(x)$ by Furman and Shamir. The inverse of the
effective Dirac operator turns out to be identical to the inverse of the
truncated overlap Dirac operator, except a local contact term which would give
the chiral symmetry breaking in the Ginsparg-Wilson relation. This result
allows us to relate the light fermion field and the fermion field described by
the truncated overlap Dirac operator and to understand the chiral property of
the light fermion through the exact chiral symmetry based on the
Ginsparg-Wilson relation.Comment: 35 pages, LaTeX2e, references added and updated, minor correction

### 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

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