3,172 research outputs found
Large N reduction with overlap fermions
We revisit quenched reduction with fermions and explain how some old problems
can be avoided using the overlap Dirac operator.Comment: Lattice2002(chiral) 3 pages, no figure
Overlap Fermions on a Lattice
We report results on hadron masses, fitting of the quenched chiral log, and
quark masses from Neuberger's overlap fermion on a quenched lattice with
lattice spacing fm. We used the improved gauge action which is shown
to lower the density of small eigenvalues for as compared to the Wilson
gauge action. This makes the calculation feasible on 64 nodes of CRAY-T3E. Also
presented is the pion mass on a small volume ( with a Wilson
gauge action at ). We find that for configurations that the
topological charge , the pion mass tends to a constant and for
configurations with trivial topology, it approaches zero possibly linearly with
the quark mass.Comment: Lattice 2000 (Chiral Fermion), 4 pages, 4 figure
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Pricing Liquidity Risk with Heterogeneous Investment Horizons
We develop an asset pricing model with stochastic transaction costs and investors with heterogeneous horizons. Depending on their horizon, investors hold different sets of assets in equilibrium. This generates segmentation and spillover effects for expected returns, where the liquidity (risk) premium of illiquid assets is determined by investor horizons and the correlation between liquid and illiquid asset returns. We estimate our model for the cross-section of U.S. stock returns and find that it generates a good fit, mainly due to a combination of a substantial expected liquidity premium and segmentation effects, while the liquidity risk premium is small
Bounds on the Wilson Dirac Operator
New exact upper and lower bounds are derived on the spectrum of the square of
the hermitian Wilson Dirac operator. It is hoped that the derivations and the
results will be of help in the search for ways to reduce the cost of
simulations using the overlap Dirac operator. The bounds also apply to the
Wilson Dirac operator in odd dimensions and are therefore relevant to domain
wall fermions as well.Comment: 16 pages, TeX, 3 eps figures, small corrections and improvement
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
An alternative to domain wall fermions
We define a sparse hermitian lattice Dirac matrix, , coupling Dirac
fermions. When fermions are integrated out the induced action for the last
fermion is a rational approximation to the hermitian overlap Dirac operator. We
provide rigorous bounds on the condition number of and compare them to
bounds for the higher dimensional Dirac operator of domain wall fermions. Our
main conclusion is that overlap fermions should be taken seriously as a
practical alternative to domain wall fermions in the context of numerical QCD.Comment: Revtex Latex, 26 pages, 1 figure, a few minor change
Energy minimization using Sobolev gradients: application to phase separation and ordering
A common problem in physics and engineering is the calculation of the minima
of energy functionals. The theory of Sobolev gradients provides an efficient
method for seeking the critical points of such a functional. We apply the
method to functionals describing coarse-grained Ginzburg-Landau models commonly
used in pattern formation and ordering processes.Comment: To appear J. Computational Physic
Two dimensional fermions in three dimensional YM
Dirac fermions in the fundamental representation of SU(N) live on the surface
of a cylinder embedded in and interact with a three dimensional SU(N)
Yang Mills vector potential preserving a global chiral symmetry at finite .
As the circumference of the cylinder is varied from small to large, the chiral
symmetry gets spontaneously broken in the infinite limit at a typical bulk
scale. Replacing three dimensional YM by four dimensional YM introduces
non-trivial renormalization effects.Comment: 21 pages, 7 figures, 5 table
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