2,658 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
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
Topological Effects in Matrix Models representing Lattice Gauge Theories at Large N
Quenched reduction is revisited from the modern viewpoint of
field-orbifolding. Fermions are included and it is shown how the old problem of
preserving anomalies and field topology after reduction is solved with the help
of the overlap construction.Comment: 11 pages, LaTeX, Contribution to TH200
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
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