2,232 research outputs found
The Schr\"odinger functional running coupling with staggered fermions and its application to many flavor QCD
We discuss the Schr\"odinger functional in lattice QCD with staggered
fermions and relate it, in the classical continuum limit, to the Schr\"odinger
functional regularized with Wilson fermions. We compute the strong coupling
constant defined via the Schr\"odinger functional with staggered fermions at
one loop and show that it agrees with the continuum running coupling constant
in the Schr\"odinger functional formalism. We compute this running coupling in
the ``weak coupling phase'' of many flavor QCD numerically at several values of
the bare coupling and for several system sizes from to 12. The results
indicate that the -function for 16 flavors has the opposite sign than
for few flavor QCD, in agreement with a recent claim, and with the perturbative
prediction.Comment: 3 pages with 2 ps figures; to appear in the proceedings of Lattice
'97, Edinburgh, Scotland, July 22--26, 199
Wilson chiral perturbation theory, Wilson-Dirac operator eigenvalues and clover improvement
Chiral perturbation theory for eigenvalue distributions, and equivalently
random matrix theory, has recently been extended to include lattice effects for
Wilson fermions. We test the predictions by comparison to eigenvalue
distributions of the Hermitian Wilson-Dirac operator from pure gauge (quenched)
ensembles. We show that the lattice effects are diminished when using clover
improvement for the Dirac operator. We demonstrate that the leading Wilson
low-energy constants associated with Wilson (clover) fermions can be determined
using spectral information of the respective Dirac operator at finite volume.Comment: Presented at "Xth Quark Confinement and the Hadron Spectrum," October
2012, Garching, Germany. To appear as PoS (Confinement X) 07
The zeros of the QCD partition function
We establish a relationship between the zeros of the partition function in
the complex mass plane and the spectral properties of the Dirac operator in
QCD. This relation is derived within the context of chiral Random Matrix Theory
and applies to QCD when chiral symmetry is spontaneously broken. Further, we
introduce and examine the concept of normal modes in chiral spectra. Using this
formalism we study the consequences of a finite Thouless energy for the zeros
of the partition function. This leads to the demonstration that certain
features of the QCD partition function are universal.Comment: 13 page
Microscopic Spectrum of the Wilson Dirac Operator
We calculate the leading contribution to the spectral density of the Wilson
Dirac operator using chiral perturbation theory where volume and lattice
spacing corrections are given by universal scaling functions. We find
analytical expressions for the spectral density on the scale of the average
level spacing, and introduce a chiral Random Matrix Theory that reproduces
these results. Our work opens up a novel approach to the infinite volume limit
of lattice gauge theory at finite lattice spacing and new ways to extract
coefficients of Wilson chiral perturbation theory.Comment: 4 pages, 3 figures, refs added, version to appear in Phys. Rev. Let
Screening and Deconfinement of Sources in Finite Temperature SU(2) Lattice Gauge Theory
Deconfinement and screening of higher-representation sources in
finite-temperature lattice gauge theory is investigated by both
analytical and numerical means. The effective Polyakov-line action at strong
coupling is simulated by an efficient cluster-updating Monte Carlo algorithm
for the case of dimensions. The results compare very favourably with
an improved mean-field solution. The limit of the
theory is shown to be highly singular as far as critical behaviour is
concerned. In that limit the leading amplitudes of higher representation
Polyakov lines vanish at strong coupling, and subleading exponents become
dominant. Each of the higher-representation sources then effectively carry with
them their own critical exponents.Comment: 13pages+7figures, CERN-TH-7222/94 One reference added, else unchange
Finite-Volume Scaling of the Quenched Chiral Condensate
In the large-volume limit with the
mass-dependent chiral condensate is predicted to satisfy exact finite-volume
scaling laws that fall into three major universality classes. We test these
analytical predictions with staggered fermions and overlap fermions in gauge
field sectors of fixed topological charge .Comment: Talk at Lattice99(topology), 3 page
Exact Vacuum Energy of Orbifold Lattice Theories
We investigate the orbifold lattice theories constructed from supersymmetric
Yang-Mills matrix theories (mother theories) with four and eight supercharges.
We show that the vacuum energy of these theories does not receive any quantum
correction perturbatively.Comment: 14 pages, no figure, LaTeX2e, typos corrected, errors in references
corrected, comments adde
Effects of dynamical quarks on the spectrum of the Wilson Dirac operator
Effects of dynamical quarks on the microscopic spectrum of the Wilson Dirac
operator are analyzed by means of effective field theory. We consider the
distributions of the real modes of the Wilson Dirac operator as well as the
spectrum of the Hermitian Wilson Dirac operator, and work out the case of one
flavor in all detail. In contrast to the quenched case, the theory has a mild
sign problem that manifests itself by giving a spectral density that is not
positive definite as the spectral gap closes.Comment: 7 pages 3 figures. Talk given at the XXVIII International Symposium
on Lattice Field Theory (Lattice 2010), Villasimius, Italy, June 201
Individual Eigenvalue Distributions for the Wilson Dirac Operator
We derive the distributions of individual eigenvalues for the Hermitian
Wilson Dirac Operator D5 as well as for real eigenvalues of the Wilson Dirac
Operator DW. The framework we provide is valid in the epsilon regime of chiral
perturbation theory for any number of flavours Nf and for non-zero low energy
constants W6, W7, W8. It is given as a perturbative expansion in terms of the
k-point spectral density correlation functions and integrals thereof, which in
some cases reduces to a Fredholm Pfaffian. For the real eigenvalues of DW at
fixed chirality nu this expansion truncates after at most nu terms for small
lattice spacing "a". Explicit examples for the distribution of the first and
second eigenvalue are given in the microscopic domain as a truncated expansion
of the Fredholm Pfaffian for quenched D5, where all k-point densities are
explicitly known from random matrix theory. For the real eigenvalues of
quenched DW at small "a" we illustrate our method by the finite expansion of
the corresponding Fredholm determinant of size nu.Comment: 20 pages, 5 figures; v2: typos corrected, refs added and discussion
of W6 and W7 extende
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