2,747 research outputs found
Exact Chiral Symmetry on the Lattice
Developments during the last eight years have refuted the folklore that
chiral symmetries cannot be preserved on the lattice. The mechanism that
permits chiral symmetry to coexist with the lattice is quite general and may
work in Nature as well. The reconciliation between chiral symmetry and the
lattice is likely to revolutionize the field of numerical QCD.Comment: 30 pages, LaTeX, reference adde
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
Topological Phases in Neuberger-Dirac operator
The response of the Neuberger-Dirac fermion operator D=\Id + V in the
topologically nontrivial background gauge field depends on the negative mass
parameter in the Wilson-Dirac fermion operator which enters
through the unitary operator . We classify
the topological phases of by comparing its index to the topological charge
of the smooth background gauge field. An exact discrete symmetry in the
topological phase diagram is proved for any gauge configurations. A formula for
the index of D in each topological phase is derived by obtaining the total
chiral charge of the zero modes in the exact solution of the free fermion
propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise
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
Improving meson two-point functions by low-mode averaging
Some meson correlation functions have a large contribution from the low lying
eigenmodes of the Dirac operator. The contribution of these eigenmodes can be
averaged over all positions of the source. This can improve the signal in these
channels significantly. We test the method for meson two-point functions.Comment: Talk given at Lattice2004(spectrum), Fermilab, June 21-26, 200
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
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
Finite size effects on in QCD from Chiral Perturbation Theory
We present a determination of the shift due to the finite
spatial box size by means of Chiral Perturbation Theory and
L\"uscher's formula. The range of applicability of the chiral prediction is
discussed.Comment: 3 pages, 3 figures, Lattice2002(spectrum
Numerical simulation of dynamical gluinos: experience with a multi-bosonic algorithm and first results
We report on our experience with the two-step multi-bosonic algorithm in a
large scale Monte Carlo simulation of the SU(2) Yang-Mills theory with
dynamical gluinos. First results are described on the low lying spectrum of
bound states, the string tension and the gluino condensate.Comment: LATTICE98(algorithms), latex using espcrc2.sty, 6 pages, 7 figure
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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