title:
Duality of gauge field singularities and the structure of the flux tube
  in Abelian-projected SU(2) gauge theory and the dual Abelian Higgs model

abstract:
  The structure of the flux-tube profile in Abelian-projected (AP) SU(2) gauge
theory in the maximally Abelian gauge is studied. The connection between the AP
flux tube and the classical flux-tube solution of the U(1) dual Abelian Higgs
(DAH) model is clarified in terms of the path-integral duality transformation.
This connection suggests that the electric photon and the magnetic monopole
parts of the Abelian Wilson loop can act as separate sources creating the
Coulombic and the solenoidal electric field inside a flux tube. The conjecture
is confirmed by a lattice simulation which shows that the AP flux tube is
composed of these two contributions.


title:
Field theoretical approach to the study of theta dependence in
  Yang-Mills theories on the lattice

abstract:
  We discuss the extension of the field theoretical approach, already used in
the lattice determination of the topological susceptibility, to the computation
of further terms in the expansion of the ground state energy $F(\theta)$ around
$\theta = 0$ in SU(N) Yang-Mills theories. In particular we determine the
fourth order term in the expansion for SU(3) pure gauge theory and compare our
results with previous cooling determinations. In the last part of the paper we
make some considerations about the nature of the ultraviolet fluctuations
responsible for the renormalization of the lattice topological charge
correlation functions; in particular we propose and test an ansatz which leads
to improved estimates of the fourth and higher order terms in the expansion of
F(\theta).


title: Delta Baryon Magnetic Moments From Lattice QCD

abstract:
  Theoretical predictions for the magnetic moments of the physical Delta
baryons are extracted from lattice QCD calculations. We utilize finite-range
regulated effective field theory that is constructed to have the correct Dirac
moment mass dependence in the region where the up and down quark masses are
heavy. Of particular interest is the chiral nonanalytic behaviour encountered
as the nucleon-pion decay channel opens. We find a Delta^++ magnetic moment (at
the Delta pole) of 4.99 \pm 0.56 \mu_N. This result is within the Particle Data
Group range of 3.7-7.5 \mu_N and compares well with the experimental result of
Bosshard et al. of 4.52 \pm 0.51 \pm 0.45 \mu_N. The interplay between the
different pion-loop contributions to the Delta^+ magnetic moment leads to the
surprising result that the proton moment may exceed that of the Delta^+,
contrary to conventional expectations.


title:
Low-Dimensional Long-Range Topological Charge Structure in the QCD
  Vacuum

abstract:
  While sign-coherent 4-dimensional structures cannot dominate topological
charge fluctuations in the QCD vacuum at all scales due to reflection
positivity, it is possible that enhanced coherence exists over extended
space-time regions of lower dimension. Using the overlap Dirac operator to
calculate topological charge density, we present evidence for such structure in
pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium
configuration is dominated by two oppositely-charged sign-coherent connected
structures (``sheets'') covering about 80% of space-time. Each sheet is built
from elementary 3-d cubes connected through 2-d faces, and approximates a
low-dimensional curved manifold (or possibly a fractal structure) embedded in
the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18%
of the most intense space-time points organized into a global long-range
structure, involving connected parts spreading over maximal possible distances.
We find that the skeleton is locally 1-dimensional and propose that its
geometrical properties might be relevant for understanding the possible role of
topological charge fluctuations in the physics of chiral symmetry breaking.


title:
Critical parameters and universal amplitude ratios of two-dimensional
  spin-S Ising models using high- and low-temperature expansions

abstract:
  For the study of Ising models of general spin S on the square lattice, we
have combined our recently extended high-temperature expansions with the
low-temperature expansions derived some time ago by Enting, Guttmann and
Jensen. We have computed for the first time various critical parameters and
improved the estimates of others.
  Moreover the properties of hyperscaling and of universality (spin S
independence) of exponents and of various dimensionless amplitude combinations
have been verified accurately. Assuming the validity of the lattice-lattice
scaling, from our estimates of critical amplitudes for the square lattice we
have also obtained estimates of the corresponding amplitudes for the spin S
Ising model on the triangular, honeycomb, and kagome` lattices.


title: Partially quenched chiral perturbation theory and numerical simulations

abstract:
  The dependence of the pseudoscalar meson mass and decay constant is compared
to one-loop Partially Quenched Chiral Perturbation Theory (PQChPT) in a
numerical simulation with two light dynamical quarks. The characteristic
behaviour with chiral logarithms is observed. The values of the fitted
PQChPT-parameters are in a range close to the expectation in continuum in spite
of the fact that the lattice spacing is still large, namely a=0.28 fm.


title: Anisotropic lattice actions for heavy quark

abstract:
  The anisotropic lattice fermion actions are investigated with the one-loop
perturbative calculations aiming at constructing a formulation for heavy quark
with controlled systematic uncertainties. For the heavy-light systems at rest
the anisotropic lattice with small temporal lattice spacing $a_t$ suppresses
the discretization error by a power of $a_t m_Q$ for a heavy quark of mass
$m_Q$. We discuss the issue of large discretization errors, which scales as
$a_s m_Q$ with $a_s$ the spatial lattice spacing. By performing one-loop
calculations of the speed-of-light renormalization for several possible lattice
actions in the limit of $a_t\to 0$, we show that one can eliminate the large
systematic error on the anisotropic lattice.


title: Negative-parity baryon spectra in quenched anisotropic lattice QCD

abstract:
  We investigate the negative-parity baryon spectra in quenched lattice QCD. We
employ the anisotropic lattice with standard Wilson gauge and O(a) improved
Wilson quark actions at three values of lattice spacings with renormalized
anisotropy xi=a_sigma/a_tau=4, where a_sigma and a_tau are spatial and temporal
lattice spacings, respectively. The negative-parity baryons are measured with
the parity projection. In particular, we pay much attention to the lowest SU(3)
flavor-singlet negative-parity baryon, which is assigned as the Lambda(1405) in
the quark model. For the flavor octet and decuplet negative-parity baryons, the
calculated masses are close to the experimental values of corresponding
lowest-lying negative-parity baryons. In contrast, the flavor-singlet baryon is
found to be about 1.7 GeV, which is much heavier than the Lambda(1405).
Therefore, it is difficult to identify the Lambda(1405) to be the
flavor-singlet three-quark state, which seems to support an interesting picture
of the penta-quark (uds qbar q) state or the N-Kbar molecule for the
Lambda(1405).


title: The self-energy of improved staggered quarks

abstract:
  We calculate the fermion self-energy at O(alpha_s) for the Symanzik improved
staggered fermion action used in recent lattice simulations by the MILC
collaboration. We demonstrate that the algebraic approach to lattice
perturbation theory, suggested by us recently, is a powerful tool also for
improved lattice actions.


title: A model for string-breaking in QCD

abstract:
  We present a model for string breaking based on the existence of
chromoelectric flux tubes. We predict the form of the long-range potential, and
obtain an estimate of the string breaking length. A prediction is also obtained
for the behaviour with temperature of the string breaking length near the
deconfinement phase transition. We plan to use this model as a guide for a
program of study of string breaking on the lattice.


title:
A precise determination of the decay constant of the Ds-meson in
  quenched QCD

abstract:
  We present a lattice determination of the leptonic decay constant F_Ds of the
Ds-meson using its mass and F_K as experimental input. Setting the scale with
F_K=160 MeV, our final result is F_Ds = 252(9) MeV. The error contains all
uncertainties apart from the quenched approximation. Setting the scale with the
nucleon mass instead leads to an increase of 3(1) MeV of the leptonic decay
constant which might indicate a small quenching error.


title:
Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with
  Four Supercharges

abstract:
  We formulate a Euclidean spacetime lattice whose continuum limit is (2,2)
supersymmetric Yang-Mills theory in two dimensions, a theory which possesses
four supercharges and an anomalous global chiral symmetry. The lattice action
respects one exact supersymmetry, which allows the target theory to emerge in
the continuum limit without fine-tuning. Our method exploits an orbifold
construction described previously for spatial lattices in Minkowski space, and
can be generalized to more complicated theories with additional supersymmetry
and more spacetime dimensions.


title: Coulomb Energy, Vortices, and Confinement

abstract:
  We estimate the Coulomb energy of static quarks from a Monte Carlo
calculation of the correlator of timelike link variables in Coulomb gauge. We
find, in agreement with Cucchieri and Zwanziger, that this energy grows
linearly with distance at large quark separations. The corresponding string
tension, however, is several times greater than the accepted asymptotic string
tension, indicating that a state containing only static sources, with no
constituent gluons, is not the lowest energy flux tube state. The Coulomb
energy is also measured on thermalized lattices with center vortices removed by
the de Forcrand-D'Elia procedure. We find that when vortices are removed, the
Coulomb string tension vanishes.


title:
Non-perturbative renormalization of the static axial current in quenched
  QCD

abstract:
  We non-perturbatively calculate the scale dependence of the static axial
current in the Schroedinger functional scheme by means of a recursive
finite-size scaling technique, taking the continuum limit in each step. The
bare current in the O(a) improved theory as well as in the original Wilson
regularization is thus connected to the renormalization group invariant one.
The latter may then be related to the current at the B-scale defined such that
its matrix elements differ from the physical (QCD) ones by O(1/M). At present,
a (probably small) perturbative uncertainty enters in this step. As an
application, we renormalize existing unimproved data on F_B^{bare} and
extrapolate to the continuum limit. We also study an interesting function
h(d/L,u) derived from the Schroedinger functional amplitude describing the
propagation of a static quark-antiquark pair.


title: Physical Nucleon Properties from Lattice QCD

abstract:
  We demonstrate that the extremely accurate lattice QCD data for the mass of
the nucleon recently obtained by CP-PACS, combined with modern chiral
extrapolation techniques, leads to a value for the mass of the physical nucleon
which has a systematic error of less than one percent.


title: Fermi Surface Phenomena in the (2+1)d Four-Fermi Model

abstract:
  We study the Gross-Neveu model in 2+1 dimensions with a baryon chemical
potential mu using both analytical and numerical methods. For mu greater than a
critical value the model is chirally symmetric and has a Fermi surface with
Fermi momentum ~mu. We have calculated the particle interaction in medium due
to scalar meson exchange to leading order in 1/N, where N is the number of
flavors, in the hard dense loop approach. The result has been used to calculate
the relation between mu and the Fermi momentum and velocity in the resulting
Fermi liquid to O(1/N). Simulation results from a 32^2x48 lattice for fermion
and meson dispersion relations and meson wavefunctions are then presented,
showing qualitative and in some cases quantitative agreement with analytic
predictions. In particular, the simulations show clear evidence for the
in-medium modification of the scalar propagator, oscillatory behaviour in the
wavefunction consistent with a sharp Fermi surface, and tentative evidence for
a massless pole in the vector meson channel resembling zero sound.


title: SU(2) Landau gluon propagator on a 140^3 lattice

abstract:
  We present a numerical study of the gluon propagator in lattice Landau gauge
for three-dimensional pure-SU(2) lattice gauge theory at couplings beta = 4.2,
5.0, 6.0 and for lattice volumes V = 40^3, 80^3, 140^3. In the limit of large V
we observe a decreasing gluon propagator for momenta smaller than p_{dec} =
350^{+ 100}_{- 50} MeV. Data are well fitted by Gribov-like formulae and seem
to indicate an infra-red critical exponent kappa slightly above 0.6, in
agreement with recent analytic results.


title: Exceptional Confinement in G(2) Gauge Theory

abstract:
  We study theories with the exceptional gauge group G(2). The 14 adjoint
"gluons" of a G(2) gauge theory transform as {3}, {3bar} and {8} under the
subgroup SU(3), and hence have the color quantum numbers of ordinary quarks,
anti-quarks and gluons in QCD. Since G(2) has a trivial center, a "quark" in
the {7} representation of G(2) can be screened by "gluons". As a result, in
G(2) Yang-Mills theory the string between a pair of static "quarks" can break.
In G(2) QCD there is a hybrid consisting of one "quark" and three "gluons". In
supersymmetric G(2) Yang-Mills theory with a {14} Majorana "gluino" the chiral
symmetry is Z(4)_\chi. Chiral symmetry breaking gives rise to distinct confined
phases separated by confined-confined domain walls. A scalar Higgs field in the
{7} representation breaks G(2) to SU(3) and allows us to interpolate between
theories with exceptional and ordinary confinement. We also present strong
coupling lattice calculations that reveal basic features of G(2) confinement.
Just as in QCD, where dynamical quarks break the Z(3) symmetry explicitly, G(2)
gauge theories confine even without a center. However, there is not necessarily
a deconfinement phase transition at finite temperature.


title: Two flavors of dynamical quarks on anisotropic lattices

abstract:
  We report on our study of two-flavor full QCD on anisotropic lattices using
$O(a)$-improved Wilson quarks coupled with an RG-improved glue. The bare gauge
and quark anisotropies corresponding to the renormalized anisotropy
$\xi=a_s/a_t = 2$ are determined as functions of $\beta$ and $\kappa$, which
covers the region of spatial lattice spacings $a_s\approx 0.28$--0.16 fm and
$m_{PS}/m_V\approx 0.6$--0.9. The calibrations of the bare anisotropies are
performed with the Wilson loop and the meson dispersion relation at 4 lattice
cutoffs and 5--6 quark masses. Using the calibration results we calculate the
meson mass spectrum and the Sommer scale $r_0$. We confirm that the values of
$r_0$ calculated for the calibration using pseudo scalar and vector meson
energy momentum dispersion relation coincide in the continuum limit within
errors. This work serves to lay ground toward studies of heavy quark systems
and thermodynamics of QCD including the extraction of the equation of state in
the continuum limit using Wilson-type quark actions.


title: A recurrence scheme for least-square optimized polynomials

abstract:
  A recurrence scheme is defined for the numerical determination of high degree
polynomial approximations to functions as, for instance, inverse powers near
zero. As an example, polynomials needed in the two-step multi-boson (TSMB)
algorithm for fermion simulations are considered. For the polynomials needed in
TSMB a code in C is provided which is easily applicable to polynomial degrees
of several thousands.


title: Dynamical fermions as a global correction

abstract:
  In the simplified setting of the Schwinger model we present a systematic
study on the simulation of dynamical fermions by global accept/reject steps
that take into account the fermion determinant. A family of exact algorithms is
developed, which combine stochastic estimates of the determinant ratio with the
exploitation of some exact extremal eigenvalues of the generalized problem
defined by the `old' and the `new' Dirac operator. In this way an acceptable
acceptance rate is achieved with large proposed steps and over a wide range of
couplings and masses.


title: Quark mass dependence of the nucleon axial-vector coupling constant

abstract:
  We study the quark mass expansion of the axial-vector coupling constant g_A
of the nucleon. The aim is to explore the feasibility of chiral effective field
theory methods for extrapolation of lattice QCD results - so far determined at
relatively large quark masses corresponding to pion masses larger than 0.6 GeV
- down to the physical value of the pion mass. We compare two versions of
non-relativistic chiral effective field theory: One scheme restricted to pion
and nucleon degrees of freedom only, and an alternative approach which
incorporates explicit Delta(1230) resonance degrees of freedom. It turns out
that, in order to approach the physical value of g_A in a leading-one-loop
calculation, the inclusion of the explicit Delta(1230) degrees of freedom is
crucial. With information on important higher order couplings constrained from
analyses of inelastic pion production processes, a chiral extrapolation
function for g_A is obtained, which works well from the chiral limit across the
physical point into the region of present lattice data. The resulting
enhancement of our extrapolation function near the physical pion mass is found
to arise from an interplay between long- and short- distance physics.


title: Chiral Limit of Strongly Coupled Lattice Gauge Theories

abstract:
  We construct a new and efficient cluster algorithm for updating strongly
coupled U(N) lattice gauge theories with staggered fermions in the chiral
limit. The algorithm uses the constrained monomer-dimer representation of the
theory and should also be of interest to researchers working on other models
with similar constraints. Using the new algorithm we address questions related
to the chiral limit of strongly coupled U(N) gauge theories beyond the mean
field approximation. We show that the infinite volume chiral condensate is
non-zero in three and four dimensions. However, on a square lattice of size $L$
we find $\sum_x < \bar\psi\psi(x) \bar\psi\psi(0) > \sim L^{2-\eta}$ for large
$L$ where $\eta = 0.420(3)/N + 0.078(4)/N^2$. These results differ from an
earlier conclusion obtained using a different algorithm. Here we argue that the
earlier calculations were misleading due to uncontrolled autocorrelation times
encountered by the previous algorithm.


title: Spectroscopy using the Anisotropic Clover Action

abstract:
  The calculation of the light-hadron spectrum in the quenched approximation to
QCD using an anisotropic clover fermion action is presented. The tuning of the
parameters of the action is discussed, using the pion and rho dispersion
relation. The adoption of an anisotropic lattice provides clear advantages in
the determination of the baryonic resonances, and in particular that of the
so-called Roper resonance, the lightest radial excitation of the nucleon.


title: Gauge Theories on a 2+2 Anisotropic Lattice

abstract:
  The implementation of gauge theories on a four-dimensional anisotropic
lattice with two distinct lattice spacings is discussed, with special attention
to the case where two axes are finely and two axes are coarsely discretized.
Feynman rules for the Wilson gauge action are derived and the renormalizability
of the theory and the recovery of the continuum limit are analyzed. The
calculation of the gluon propagator and the restoration of Lorentz invariance
in on-shell states is presented to one-loop order in lattice perturbation
theory for $SU(N_c)$ on both 2+2 and 3+1 lattices.


title: The pion form factor in improved lattice QCD

abstract:
  We calculate the electromagnetic form factor of the pion in lattice gauge
theory. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is
used together with the O(a) improved current. The form factor is compared to
results for other choices for the current and features of the structure of the
pion deduced from the 'Bethe-Salpeter wave function' are discussed.


title:
An Application of Feynman-Kleinert Approximants to the Massive Schwinger
  Model on a Lattice

abstract:
  A trial application of the method of Feynman-Kleinert approximants is made to
perturbation series arising in connection with the lattice Schwinger model. In
extrapolating the lattice strong-coupling series to the weak-coupling continuum
limit, the approximants do not converge well. In interpolating between the
continuum perturbation series at large fermion mass and small fermion mass,
however, the approximants do give good results. In the course of the
calculations, we picked up and rectified an error in an earlier derivation of
the continuum series coefficients.


title: Aspects of Domain-Wall Fermion on the Lattice

abstract:
  Two transparent layers are introduced at the boundaries of the fifth
dimension for the optimal domain-wall fermions. For the quark fields defined in
terms of these two transparent layers, they obey the usual chiral projection
rule in the continuum, independent of the gauge fields. Consequently, any
observable constructed with the quark fields manifests the symmetries exactly
as those of its counterpart in the continuum.


title: Lattice chiral fermions from continuum defects

abstract:
  We consider whether defects of co-dimension two could produce new lattice
chiral fermions.


title: Status of B_K from Lattice QCD

abstract:
  A brief review of lattice calculations of the bag parameter B_K relevant for
understanding indirect CP violation in the neutral kaon sector is given. A
status report on current state-of-the-art calculations is presented as well as
a discussion of the value of B_K exported to phenomenologists. This is a
condensed and updated version of the review presented at the CKM Unitarity
Triangle Workshop held at CERN during Feburary 13-16, 2002
(http://ckm-workshop.web.cern.ch/ckm-workshop/).


title:
Renormalization of Anisotropy and Glueball Masses on Tadpole Improved
  Lattice Gauge Action

abstract:
  The Numerical calculations for tadpole-improved U(1) lattice gauge theory in
three-dimensions on anisotropic lattices have been performed using standard
path integral Monte Carlo techniques. Using average plaquette tadpole
renormalization scheme, simulations were done with temporal lattice spacings
much smaller than the spatial ones and results were obtained for the string
tension, the renormalized anisotropy and scalar glueball masses. We find, by
comparing the `regular' and `sideways' potentials, that tadpole improvement
results in very little renormalization of the bare anisotropy and reduces the
discretization errors in the static quark potential and in the glueball masses.


title:
Continuous external momenta in non-perturbative lattice simulations: a
  computation of renormalization factors

abstract:
  We discuss the usage of continuous external momenta for computing
renormalization factors as needed to renormalize operator matrix elements.
These kind of external momenta are encoded in special boundary conditions for
the fermion fields. The method allows to compute certain renormalization
factors on the lattice that would have been very difficult, if not impossible,
to compute with standard methods. As a result we give the renormalization group
invariant step scaling function for a twist-2 operator corresponding to the
average momentum of non-singlet quark densities.


title:
Pressure and non-linear susceptibilities in QCD at finite chemical
  potentials

abstract:
  When the free energy density of QCD is expanded in a series in the chemical
potential, mu, the Taylor coefficients are the non-linear quark number
susceptibilities. We show that these depend on the prescription for putting
chemical potential on the lattice, making all extrapolations in chemical
potential prescription dependent at finite lattice spacing. To put bounds on
the prescription dependence, we investigate the magnitude of the non-linear
susceptibilities over a range of temperature, T, in QCD with two degenerate
flavours of light dynamical quarks at lattice spacing 1/4T. The prescription
dependence is removed in quenched QCD through a continuum extrapolation, and
the dependence of the pressure, P, on mu is obtained.


title:
The Determination of the Quark-Gluon Mixed Condensate (anti-Q sigma G Q)
  from Lattice QCD

abstract:
  We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, using the
SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. We
generate 100 gauge configurations on the 16^4 lattice with \beta = 6.0, and
perform the measurement of the mixed condensate at 16 points in each gauge
configuration for each current quark mass of m_q=21, 36, 52 MeV. Using the 1600
data for each m_q, we find the ratio between the mixed condensate and the quark
condensate, m_0^2 = g<\bar{q} sigma G q> / <\bar{q}q> \simeq 2.5 GeV^2 at the
lattice scale of 1/a \simeq 2 GeV in the chiral limit. The large value of the
mixed condensate suggests its importance in the operator product expansions in
QCD. We study also chiral restoration at finite temperature in terms of the
mixed condensate, which is another chiral order parameter. We present the
lattice QCD results of the mixed condensate at finite temperature.


title: Parton distribution functions in the pion from lattice QCD

abstract:
  We analyze the moments of parton distribution functions in the pion
calculated in lattice QCD, paying particular attention to their chiral
extrapolation. Using the lowest three non-trivial moments calculated on the
lattice, we assess the accuracy with which the x dependence of both the valence
and sea quark distributions in the pion can be extracted. The resulting valence
quark distributions at the physical pion mass are in fair agreement with
existing Drell-Yan data, but the statistical errors are such that one cannot
yet confirm (or rule out) the large-x behavior expected from hadron helicity
conservation in perturbative QCD. However, one can expect that the next
generation of calculations in lattice QCD will allow one to extract parton
distributions with a level of accuracy comparable with current experiments.


title: SU(N) Glueball Masses in 2+1 Dimensions

abstract:
  We calculate the masses of the lowest lying eigenstates of improved SU(2),
SU(3), SU(4) and SU(5) Hamiltonian lattice gauge theory (LGT) in 2+1 dimensions
using an analytic variational approach. The ground state is approximated by a
one plaquette trial state and mass gaps are calculated in the symmetric and
antisymmetric sectors by minimising over a suitable basis of rectangular
states. Analytic techniques are developed to handle the group integrals arising
in the calculation.


title:
Infinite temperature limit of meson spectral functions calculated on the
  lattice

abstract:
  We analyze the cut-off dependence of mesonic spectral functions calculated at
finite temperature on Euclidean lattices with finite temporal extent. In the
infinite temperature limit we present analytic results for lattice spectral
functions calculated with standard Wilson fermions as well as a truncated
perfect action. We explicitly determine the influence of `Wilson doublers' on
the high momentum structure of the mesonic spectral functions and show that
this cut-off effect is strongly suppressed when using an improved fermion
action.


title: The Large N Glueball Mass Spectrum in 2+1 Dimensions

abstract:
  In this paper we explore the large N limit of the glueball mass spectrum for
2+1 dimensional pure gauge theory. We employ Hamiltonian lattice gauge theory
(LGT) and analytic variational techniques to calculate glueball masses for
finite values of N < 26. The results are then accurately extrapolated to
infinite N. An empirical observation is discussed which links the infinite N
glueball spectrum to a simple oscillator model.


title:
Nucleon electromagnetic form factors on the lattice and in chiral
  effective field theory

abstract:
  We compute the electromagnetic form factors of the nucleon in quenched
lattice QCD, using non-perturbatively improved Wilson fermions, and compare the
results with phenomenology and chiral effective field theory.


title:
Charmonium Spectrum from Quenched Lattice QCD with Tadpole Improvement
  Action

abstract:
  We report here our lattice simulation on the charmonium spectra in the
quenched approximation. Because the full adjustment on the nonperturbative
parameters such as $C_E$, $C_B$, $m_0a_s$ and $r_s$ needs many calculation
time, we only adjust two of them, $m_0a_s$ and $r_s$($\xi_3$ plays this role in
the paper) but with some rescale for mass splitting. After the rescale, we find
that our results are in agreement with the experiment ones.


title:
World-Line Path Integral Study of Supersymmetry Breaking in the
  Wess-Zumino Model

abstract:
  We study supersymmetry breaking in the lattice N=1 Wess-Zumino model by the
world-line path integral algorithm. The ground state energy and supersymmetric
Ward identities are exploited to support the expected symmetry breaking in
finite volume. Non-Gaussian fluctuations of the topological charge are
discussed and related to the infinite volume transition.


title: SU(N) Lattice Gauge Theory on a Single Cube

abstract:
  In this paper we study the viability of persuing analytic variational
techniques for the calculation of glueball masses in 3+1 dimensional
Hamiltonian lattice gauge theory (LGT) in the pure gauge sector. We discuss the
major problems presented by a move from 2+1 to 3+1 dimensions and develop
analytic techniques to approximate the integrals appearing in 3+1 dimensional
variational glueball mass calculations. We calculate $0^{++}$ and $1^{+-}$
glueball masses on a lattice consisting of a single cube. Despite the use of a
very simplistic model, promising signs of an approach to asymptotic scaling is
displayed by the SU(N) $1^{+-}$ glueball mass as N is increased.


title: Large N reduction in the continuum three dimensional Yang-Mills theory

abstract:
  Numerical and theoretical evidence leads us to propose the following: Three
dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase
transition on a torus of side $l=l_c$. For $l>l_c$ the planar limit is
$l$-independent, as expected of a non-interacting string theory. We expect the
situation in four dimensions to be similar.


title: Color Confinement in Lattice Landau Gauge

abstract:
  The problem of color confinement in lattice Landau gauge QCD is briefly
reviewed in the light of Kugo-Ojima criterion and Gribov-Zwanziger theory. The
infrared properties of the Landau gauge QCD is studied by the measurement of
the gluon propagator, ghost propagator, Kugo-Ojima parameter and the running
coupling via $\beta=6.4,32^4,48^4$ lattice simulation. The data are analyzed in
the principle of minimum sensitivity(PMS) in the $\widetilde{MOM}$ scheme. We
observe the running coupling $\alpha_s(q)$ has a maximum about 1 and decreases
near q=0. The Kugo-Ojima parameter, which is expected to be 1 was about 0.8.


title: Chiral Anomalies in the Reduced (or Matrix) Model

abstract:
  We show that, with an appropriate choice of a Dirac operator, there is a
remnant of chiral anomalies in the reduced model in which there is no
coordinate dependences of the gauge field. This result is obtained by exploring
a topological nature of chiral anomalies associated to Ginsparg-Wilson-type
lattice Dirac operators.


title: Accelerating the Hybrid Monte Carlo algorithm

abstract:
  An algorithm for separating the high- and low-frequency molecular dynamics
modes in Hybrid Monte Carlo simulations of gauge theories with dynamical
fermions is presented. The separation is based on splitting the pseudo-fermion
action into two parts, as was initially proposed by Hasenbusch. We propose to
introduce different evolution time-scales for each part. We test our proposal
in realistic simulations of two-flavor O(a) improved Wilson fermions. A
speed-up of more than a factor of three compared to the standard HMC algorithm
is observed in a typical run.


title:
N=(1,1) Super Yang-Mills on a (2+1) Dimensional Transverse Lattice with
  one Exact Supersymmetry

abstract:
  We present a formulation of N=(1,1), Super Yang-Mills theory in 2+1
dimensions using a transverse lattice methods that exactly preserves one
supersymmetry. First, using a Lagrangian approach we obtain a standard
transverse lattice formulation of the Hamiltonian. We then show that the
Hamiltonian also can be written discretely as the square of a supercharge and
that this produces a different result. Problems associated with the discrete
realization of the full supercharge algebra are discussed. Numerically we solve
for the bound states of the theory in the large N_c approximation and we find
good convergence. We show that the number of fermion and boson massless bound
states are closely related. Also we find that this theory admits winding states
in the transverse direction and that their masses vary inversely with the
winding number.


title: Spin-3/2 Nucleon and Delta Baryons in Lattice QCD

abstract:
  We present first results for masses of spin-3/2 N and Delta baryons in
lattice QCD using Fat-Link Irrelevant Clover (FLIC) fermions. Spin-3/2
interpolating fields providing overlap with both spin-3/2 and spin-1/2 states
are considered. In the isospin-1/2 sector, we observe, after appropriate spin
and parity projection, a strong signal for the J^P=3/2^- state together with a
weak but discernible signal for the 3/2^+ state with a mass splitting near that
observed experimentally. We also find good agreement between the 1/2^+/- masses
and earlier nucleon mass simulations with the standard spin-1/2 interpolating
field. For the isospin-3/2 Delta states, clear mass splittings are observed
between the various 1/2^+/- and 3/2^+/- channels, with the calculated level
orderings in good agreement with those observed empirically.


title: Optimal lattice domain-wall fermions with finite Ns

abstract:
  I review the lattice formulations of vector-like gauge theories (e.g. QCD)
with domain-wall fermions, and discuss how to optimize the chiral symmetry for
any finite N_s (in the fifth dimension), as well as to eliminate its dependence
on a_5.


title: Nonperturbative QCD, gauge-fixing, Gribov copies, and the lattice

abstract:
  Perturbative QCD uses the Faddeev-Popov gauge-fixing procedure, which leads
to ghosts and the local BRST invariance of the gauge-fixed perturbative QCD
action. In the asymptotic regime, where perturbative QCD is relevant, Gribov
copies can be neglected. In the nonperturbative regime, one must adopt either a
nonlocal Gribov-copy free gauge (e.g., Laplacian gauge) or attempt to maintain
local BRST invariance at the expense of admitting Gribov copies. These issues
are explored. In addition, we discuss the relationship between recent
Dyson-Schwinger based model calculations of the infrared behavior of QCD
Green's functions and the lattice calculation of these quantities.


title: High-Precision Lattice QCD Confronts Experiment

abstract:
  We argue that high-precision lattice QCD is now possible, for the first time,
because of a new improved staggered quark discretization. We compare a wide
variety of nonperturbative calculations in QCD with experiment, and find
agreement to within statistical and systematic errors of 3% or less. We also
present a new determination of alpha_msbar(Mz); we obtain 0.121(3). We discuss
the implications of this breakthrough for phenomenology and, in particular, for
heavy-quark physics.


title: Chiral Logs in Quenched QCD

abstract:
  The quenched chiral logs are examined on a $16^3 \times 28$ lattice with
Iwasaki gauge action and overlap fermions. The pion decay constant $f_{\pi}$ is
used to set the lattice spacing, $a = 0.200(3) {\rm fm}$. With pion mass as low
as $\sim 180 {\rm MeV}$, we see the quenched chiral logs clearly in
$m_{\pi}^2/m$ and $f_P$, the pseudoscalar decay constant. We analyze the data
to determine how low the pion mass needs to be in order for the quenched
one-loop chiral perturbation theory ($\chi$PT) to apply. With the constrained
curve-fitting method, we are able to extract the quenched chiral log parameter
$\delta$ together with other low-energy parameters. Only for $m_{\pi} \leq 300
{\rm MeV}$ do we obtain a consistent and stable fit with a constant $\delta$
which we determine to be 0.24(3)(4) (at the chiral scale $\Lambda_{\chi}=0.8
{\rm GeV}$). By comparing to the $12^3 \times 28$ lattice, we estimate the
finite volume effect to be about 2.7% for the smallest pion mass. We also
fitted the pion mass to the form for the re-summed cactus diagrams and found
that its applicable region is extended farther than the range for the one-loop
formula, perhaps up to $m_{\pi} \sim 500-600$ MeV. The scale independent
$\delta$ is determined to be 0.20(3) in this case. We study the quenched
non-analytic terms in the nucleon mass and find that the coefficient $C_{1/2}$
in the nucleon mass is consistent with the prediction of one-loop $\chi$PT\@.
We also obtain the low energy constant $L_5$ from $f_{\pi}$. We conclude from
this study that it is imperative to cover only the range of data with the pion
mass less than $\sim 300 {\rm MeV}$ in order to examine the chiral behavior of
the hadron masses and decay constants in quenched QCD and match them with
quenched one-loop $\chi$PT\@.


title: Non-positive fermion determinants in lattice supersymmetry

abstract:
  We find that fermion determinants are not generally positive in a recent
class of constructions with explicit lattice supersymmetry. These involve an
orbifold of supersymmetric matrix models, and have as their target (continuum)
theory (2,2) 2-dimensional super-Yang-Mills. The fermion determinant is shown
to be identically zero for all boson configurations due to the existence of a
zeromode fermion inherited from the "mother theory." Once this eigenvalue is
factored out, the fermion determinant generically has arbitrary complex phase.
We discuss the implications of this result for simulation of the models.


title: Lattice QCD and the Schwarz alternating procedure

abstract:
  A numerical simulation algorithm for lattice QCD is described, in which the
short- and long-distance effects of the sea quarks are treated separately. The
algorithm can be regarded, to some extent, as an implementation at the quantum
level of the classical Schwarz alternating procedure for the solution of
elliptic partial differential equations. No numerical tests are reported here,
but theoretical arguments suggest that the algorithm should work well also at
small quark masses.


title: Behind the success of the quark model

abstract:
  The ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the
excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ are studied using SU(3)
lattice QCD at the quenched level. For more than 300 patterns of the 3Q
systems, the ground-state potential $V_{\rm 3Q}^{\rm g.s.}$ is investigated in
detail in lattice QCD with $12^3\times 24$ at $\beta=5.7$ and with $16^3\times
32$ at $\beta=5.8, 6.0$. As a result, the ground-state potential $V_{\rm
3Q}^{\rm g.s.}$ is found to be well described with Y-ansatz within the 1%-level
deviation. From the comparison with the Q-$\rm\bar Q$ potential, we find the
universality of the string tension as $\sigma_{\rm 3Q}\simeq\sigma_{\rm Q\bar
Q}$ and the one-gluon-exchange result as $A_{\rm 3Q}\simeq\frac12 A_{\rm Q\bar
Q}$. The excited-state potential $V_{\rm 3Q}^{\rm e.s.}$ is also studied in
lattice QCD with $16^3\times 32$ at $\beta=5.8$ for 24 patterns of the 3Q
systems.The energy gap between $V_{\rm 3Q}^{\rm g.s.}$ and $V_{\rm 3Q}^{\rm
e.s.}$, which physically means the gluonic excitation energy, is found to be
about 1GeV in the typical hadronic scale, which is relatively large compared
with the excitation energy of the quark origin. This large gluonic excitation
energy justifies the great success of the simple quark model.


title: Static Three-Quark Potential in SU(3) Lattice QCD Monte-Carlo Simulation

abstract:
  The static three-quark(3Q) potential is investigated in the SU(3) lattice QCD
at the quenched level, using the standard Wilson action with $\beta =5.7
(a\simeq 0.2{\rm fm})$ and $12^3\times 24$. With the 3Q Wilson loop, the
ground-state 3Q potential $V_{\rm 3Q}$ is calculated for 16 patterns of the 3Q
configuration, using the smearing technique, which enhances the ground-state
overlap of the 3Q operator. With the accuracy better than a few %, the lattice
QCD data for $V_{\rm 3Q}$ are well described by a sum of the Coulomb term, a
constant and the linear term which is proportional to the minimal length
$L_{\rm min}$ of the flux-tube linking the 3 quarks. Our results seem to
support the Y-type flux picture rather than $\Delta$-type one. From the
comparison of $V_{\rm 3Q}$ with the ${\rm Q}$-${\rm \bar{Q}}$ potential, we
find the universality of the string tension, $\sigma_{\rm 3Q}\simeq \sigma_{\rm
Q\bar{Q}}$ as well as the OGE relation on the Coulomb coefficient, $A_{\rm
3Q}\simeq {1/2}A_{\rm Q\bar{Q}}$.


title: Thermal Width Broadening of the 0++ Glueball Spectrum near Tc

abstract:
  We study the 0++ glueball correlator constructed with SU(3) anisotropic
quenched lattice QCD at various temperature taking into account the possible
existence of the thermal width in the ground-state peak. For this purpose, we
adopt the Breit-Wigner ansatz, analysing the lattice data obtained with
5,500-9,900 gauge configurations at each T. The results indicate the
significant thermal width broadening as Gamma(Tc) \sim 300 MeV with a reduction
in the peak center as Delta omega_0(Tc) \sim 100 MeV in the vicinity of the
critical temperature Tc.


title: Dynamical Regge Calculus as Lattice Quantum Gravity

abstract:
  We propose a hybrid model of simplicial quantum gravity by performing at once
dynamical triangulations and Regge calculus. A motive for the hybridization is
to give a dynamical description of topology-changing processes of Euclidean
spacetime. In addition, lattice diffeomorphisms as invariance of the simplicial
geometry are generated by certain elementary moves in the model. We attempt
also a lattice-theoretic derivation of the black hole entropy using the
symmetry. Furthermore, numerical simulations of 3D pure gravity are carried
out,exhibiting a large hysteresis between two phases. We also measure geometric
properties of Euclidean `time slice' based on a geodesic distance, resulting in
a fractal structure in the strong-coupling phase. Our hybrid model not only
reproduces numerical results consistent with those of dynamical triangulations
and Regge calculus, but also opens a possibility of studying quantum black hole
physics on the lattice.


title: Vortex critical behavior at the de-confinement phase transition

abstract:
  The de-confinement phase transition in SU(2) Yang-Mills theory is revisited
in the vortex picture. Defining the world sheets of the confining vortices by
maximal center projection, the percolation properties of the vortex lines in
the hypercube consisting of the time axis and two spatial axis are studied.
Using the percolation cumulant, the temperature for the percolation transition
is seen to be in good agreement with the critical temperature of the thermal
transition. The finite size scaling function for the cumulant is obtained. The
critical index of the finite size scaling function is consistent with the index
of the 3D Ising model.


title:
A perturbative determination of O(a) boundary improvement coefficients
  for the Schr\"odinger Functional coupling at 1-loop with improved gauge
  actions

abstract:
  We determine O($a$) boundary improvement coefficients up to 1-loop level for
the Schr\"odinger Functional coupling with improved gauge actions including
plaquette and rectangle loops. These coefficients are required to implement
1-loop O($a$) improvement in full QCD simulations for the coupling with the
improved gauge actions. To this order, lattice artifacts of step scaling
function for each improved gauge action are also investigated. In addition,
passing through the SF scheme, we estimate the ratio of $\Lambda$-parameters
between the improved gauge actions and the plaquette action more accurately.


title: Pion and Kaon masses in Staggered Chiral Perturbation Theory

abstract:
  We show how to compute chiral logarithms that take into account both the
$\cO(a^2)$ taste-symmetry breaking of staggered fermions and the fourth-root
trick that produces one taste per flavor. The calculation starts from the
Lee-Sharpe Lagrangian generalized to multiple flavors. An error in a previous
treatment by one of us is explained and corrected. The one loop chiral
logarithm corrections to the pion and kaon masses in the full (unquenched),
partially quenched, and quenched cases are computed as examples.


title: Lattice chiral symmetry with hopping interactions

abstract:
  We formulate Dirac fermions on a (1+1)-dimensional lattice based on a
Hamiltonian formalism. The species doubling problem of the lattice fermion is
resolved by introducing hopping interactions that mix left- and right-handed
fermions around the momentum boundary. Approximate chiral symmetry is realized
on the lattice. The deviation of the fermion propagator from the continuum one
is small.


title:
Advanced Algorithms for the Simulation of Gauge Theories with Dynamical
  Fermionic Degrees of Freedom

abstract:
  This thesis is focused on the implementation and the application of a novel
kind of algorithm which is expected to overcome the limitations of older
schemes. This new algorithm is named Multiboson Method. It allows to simulate
an arbitrary number of dynamical fermion flavors, which can in principle have
different masses. It will be shown that it exhibits better scaling properties
for light fermions than other methods. Therefore, it has the potential to
become the method of choice.


title: Heavy Quark Free Energies and Screening in SU(2) Gauge Theory

abstract:
  We study the properties of the free energy of infinitely heavy quark
anti-quark pair in SU(2) gauge theory. By means of lattice Monte Carlo
simulations we calculated the free energies in the singlet, triplet and color
averaged channels, both in the confinement and in the deconfinement phase. The
singlet and triplet free energies are defined in Coulomb gauge which is
equivalent to their gauge invariant definitions recently introduced by
Philipsen. We analyzed the short and the long distance behavior, making
comparisons with the zero temperature case. The temperature dependence of the
electric screening mass is carefully investigated. The order of the deconfining
transition is manifest in the results near T_c and it allows a reliable test of
a recently proposed method to renormalize the Polyakov loop.


title: Moments of Nucleon Generalized Parton Distributions in Lattice QCD

abstract:
  Calculation of moments of generalized parton distributions in lattice QCD
requires more powerful techniques than those previously used to calculate
moments of structure functions. Hence, we present a novel approach that
exploits the full information content from a given lattice configuration by
measuring an overdetermined set of lattice observables to provide maximal
statistical constraints on the generalized form factors at a given virtuality,
t. In an exploratory investigation using unquenched QCD configurations at
intermediate sea quark masses, we demonstrate that our new technique is
superior to conventional methods and leads to reliable numerical signals for
the n=2 flavor singlet generalized form factors up to 3 GeV^2. The contribution
from connected diagrams in the flavor singlet sector to the total quark angular
momentum is measured to an accuracy of the order of one percent.


title:
B --> pi and B --> K transitions in partially quenched chiral
  perturbation theory

abstract:
  We study the properties of the B-->pi and B-->K transition form factors in
partially quenched QCD by using the approach of partially quenched chiral
perturbation theory combined with the static heavy quark limit. We show that
the form factors change almost linearly when varying the value of the sea quark
mass, whereas the dependence on the valence quark mass contains both the
standard and chirally divergent (quenched) logarithms. A simple strategy for
the chiral extrapolations in the lattice studies with Nsea=2 is suggested. It
consists of the linear extrapolations from the realistically accessible quark
masses, first in the sea and then in the valence quark mass. From the present
approach, we estimate the uncertainty induced by such extrapolations to be
within 5%.


title: A lattice study of the two-dimensional Wess Zumino model

abstract:
  We present results from a numerical simulation of the two-dimensional
Euclidean Wess-Zumino model. In the continuum the theory possesses N=1
supersymmetry. The lattice model we employ was analyzed by Golterman and
Petcher in \cite{susy} where a perturbative proof was given that the continuum
supersymmetric Ward identities are recovered without finite tuning in the limit
of vanishing lattice spacing. Our simulations demonstrate the existence of
important non-perturbative effects in finite volumes which modify these
conclusions. It appears that in certain regions of parameter space the vacuum
state can contain solitons corresponding to field configurations which
interpolate between different classical vacua. In the background of these
solitons supersymmetry is partially broken and a light fermion mode is
observed. At fixed coupling the critical mass separating phases of broken and
unbroken supersymmetry appears to be volume dependent. We discuss the
implications of our results for continuum supersymmetry breaking.


title: The pseudo-Goldstone spectrum of 2-colour QCD at finite density

abstract:
  We examine the spectrum of 2-colour lattice QCD with 4 continuum flavours at
a finite chemical potential ($\mu$) for quark-number, on a $12^3 \times 24$
lattice. First we present evidence that the system undergoes a transition to a
state with a diquark condensate, which spontaneously breaks quark number at
$\mu=m_\pi/2$, and that this transition is mean field in nature. We then
examine the 3 states that would be Goldstone bosons at $\mu=0$ for zero Dirac
and Majorana quark masses. The predictions of chiral effective Lagrangians give
a good description of the behaviour of these masses for $\mu < m_\pi/2$. Except
for the heaviest of these states, these predictions diverge from our
measurements, once $\mu$ is significantly greater than $m_\pi/2$. However, the
qualitative behaviour of these masses, indicates that the physics is very
similar to that predicted by these effective Lagrangians, and there is some
indication that at least part of these discrepancies is due to saturation, a
lattice artifact.


title:
Lattice Study of the Massive Schwinger Model with $\theta$ Term under
  L\"{u}scher's "Admissibility" Condition

abstract:
  L\"uscher's ``admissibility'' condition on the gauge field space plays an
essential role in constructing lattice gauge theories which has exact chiral
symmetries. We apply the gauge action proposed by L\"uscher with the
domain-wall fermion action to the numerical simulation of the massive Schwinger
model. We find this action can generate configurations in each topological
sector separately without any topology changes. By developing a new method to
sum over different topological sectors, we calculate meson masses in
nonzero-$\theta$ vacuum.


title: Theta-vacuum systems via real action simulations

abstract:
  Inspired by the results of the Ising model within an imaginary external
magnetic field, we introduce a transformation in quantum systems with a
theta-vacuum term that amounts to a rescaling of z=cos(theta/2). Making use of
this transformation we are able to determine the order parameter as a function
of theta. The approach is successfully tested in models with both broken and
unbroken CP symmetry at theta=pi.


title: A Ginsparg-Wilson Approach to Lattice Chern-Simons Theory

abstract:
  The concept of lattice modified symmetry formulations is adapted to the
parity symmetry of gauge fields and applied to the pure Abelian Chern-Simons
action in three dimensions. We derive an analogue of the Ginsparg-Wilson
relation for the parity anti-symmetry, which is motivated from the perfect
lattice action, and which we denote as the Chern-Simons-Ginsparg-Wilson
relation (CSGWR). In addition to the overlap type solutions, we construct
explicitly simple and local polynomial solutions to the CSGWR. We show that
these actions are exactly invariant under a lattice modified parity
transformation. That transformation is local as well, and it turns into the
standard parity transformation in the continuum limit.


title: The Equation of State for Two Flavor QCD at Non-zero Chemical Potential

abstract:
  We present results of a simulation of QCD on a 4x16^3 lattice with 2
continuum flavors of p4-improved staggered fermion with mass m/T=0.4.
Derivatives of the thermodynamic grand potential with respect to quark chemical
potential mu_q up to fourth order are calculated, enabling estimates of the
pressure, quark number density and associated susceptibilities as functions of
mu_q via Taylor series expansion. Discretisation effects associated with
various staggered fermion formulations are discussed in some detail. In
addition it is possible to estimate the radius of convergence of the expansion
as a function of temperature. We also discuss the calculation of energy and
entropy densities which are defined via mixed derivatives of the thermodynamic
grand potential with respect to the bare couplings and quark masses.


title: Hybrid configuration content of heavy S-wave mesons

abstract:
  We use the non-relativistic expansion of QCD (NRQCD) on the lattice to study
the lowest hybrid configuration contribution to the ground state of heavy
S-wave mesons. Using lowest-order lattice NRQCD to create the heavy-quark
propagators, we form a basis of ``unperturbed'' S-wave and hybrid states. We
then apply the lowest-order coupling of the quark spin and chromomagnetic field
at an intermediate time slice to create ``mixed'' correlators between the
S-wave and hybrid states. From the resulting amplitudes, we extract the
off-diagonal element of our two-state Hamiltonian. Diagonalizing this
Hamiltonian gives us the admixture of hybrid configuration within the meson
ground state. The present effort represents a continuation of previous work:
the analysis has been extended to include lattices of varying spacings, source
operators having better overlap with the ground states, and the pseudoscalar
(along with the vector) channel. Results are presented for bottomonium
($\Upsilon$, $\eta_b^{}$) using three different sets of quenched lattices. We
also show results for charmonium ($J/\psi$, $\eta_c^{}$) from one lattice set,
although we note that the non-relativistic approximation is not expected to be
very good in this case.


title: Reducing Residual-Mass Effects for Domain-Wall Fermions

abstract:
  It has been suggested to project out a number of low-lying eigenvalues of the
four-dimensional Wilson--Dirac operator that generates the transfer matrix of
domain-wall fermions in order to improve simulations with domain-wall fermions.
We investigate how this projection method reduces the residual chiral
symmetry-breaking effects for a finite extent of the extra dimension. We use
the standard Wilson as well as the renormalization--group--improved gauge
action. In both cases we find a substantially reduced residual mass when the
projection method is employed. In addition, the large fluctuations in this
quantity disappear.


title: Infrared Features of the Landau Gauge QCD

abstract:
  The infrared features of Landau gauge QCD are studied by the lattice
simulation of $\beta=6.0, 16^4, 24^4, 32^4$ and $\beta=6.4, 32^4, 48^4$. We
adopt two definitions of the gauge field; 1) $U-$linear 2) $\log U$ and
measured the gluon propagator and ghost propagator. Infrared singularity of the
gluon propagator is less than that of tree level result but the gluon
propagator at 0 momentum remains finite. The infrared singularity of ghost
propagator is stronger than the tree level. The QCD running coupling measured
by using the gluon propagator and the ghost propagator has a maximum
$\alpha_s(p)\simeq 1$ at around $p=0.5GeV$ and decreases as $p$ approaches 0.
The data are analyzed in use of formula of the principle of minimal
sensitivity(PMS), the effective charge method and the contour-improved
perturbation method, which suggest necessity of the resummation of perturbation
series in the infrared region together with existence of the infrared fixed
point. Kugo-Ojima parameter saturates at about -0.8 in contrast to the
theoretically expected value -1.


title: Axial anomaly in the reduced model: Higher representations

abstract:
  The axial anomaly arising from the fermion sector of $\U(N)$ or $\SU(N)$
reduced model is studied under a certain restriction of gauge field
configurations (the ``$\U(1)$ embedding'' with $N=L^d$). We use the
overlap-Dirac operator and consider how the anomaly changes as a function of a
gauge-group representation of the fermion. A simple argument shows that the
anomaly vanishes for an irreducible representation expressed by a Young tableau
whose number of boxes is a multiple of $L^2$ (such as the adjoint
representation) and for a tensor-product of them. We also evaluate the anomaly
for general gauge-group representations in the large $N$ limit. The large $N$
limit exhibits expected algebraic properties as the axial anomaly.
Nevertheless, when the gauge group is $\SU(N)$, it does not have a structure
such as the trace of a product of traceless gauge-group generators which is
expected from the corresponding gauge field theory.


title: Thermal dilepton rates and in-medium hadron properties from lattice QCD

abstract:
  Recent progress of lattice investigations in thermal physics is summarized in
this contribution. Hadronic spectral functions can be reconstructed from
correlation functions in Euclidean time based on the Maximum Entropy Method
without a priori assumptions on the spectral shape. The thermal modifications
of hadron properties are investigated in the scalar, pseudo-scalar, vector and
axial-vector channels near and above the deconfinement transition temperature
for charmonium systems as well as for light quarks. Moreover, the reconstructed
vector meson spectral function allows to extract the thermal cross section for
the production of dilepton pairs at vanishing momentum.


title:
Impossibility of spontaneously breaking local symmetries and the sign
  problem

abstract:
  Elitzur's theorem stating the impossibility of spontaneous breaking of local
symmetries in a gauge theory is reexamined. The existing proofs of this theorem
rely on gauge invariance as well as positivity of the weight in the Euclidean
partition function. We examine the validity of Elitzur's theorem in gauge
theories for which the Euclidean measure of the partition function is not
positive definite. We find that Elitzur's theorem does not follow from gauge
invariance alone. We formulate a general criterion under which spontaneous
breaking of local symmetries in a gauge theory is excluded. Finally we
illustrate the results in an exactly solvable two dimensional abelian gauge
theory.


title:
Non-perturbative renormalisation and improvement of the local vector
  current for quenched and unquenched Wilson fermions

abstract:
  By considering the local vector current between nucleon states and imposing
charge conservation, we determine its renormalisation constant and quark mass
improvement coefficient for Symanzik $O(a)$ improved Wilson fermions. The
computation is first performed for quenched fermions (and for completeness also
with unimproved fermions) and compared against known results. The two-flavour
unquenched case is then considered.


title: Factorization Method for Simulating QCD at Finite Density

abstract:
  We propose a new method for simulating QCD at finite density. The method is
based on a general factorization property of distribution functions of
observables, and it is therefore applicable to any system with a complex
action. The so-called overlap problem is completely eliminated by the use of
constrained simulations. We test this method in a Random Matrix Theory for
finite density QCD, where we are able to reproduce the exact results for the
quark number density.


title:
Light quark masses, chiral condensate and quark-gluon condensate in
  quenched lattice QCD with exact chiral symmetry

abstract:
  We determine several quantities in quenched lattice QCD with exact chiral
symmetry. For 100 gauge configurations generated with Wilson gauge action at $
\beta = 6.0 $ on the $ 16^3 \times 32 $ lattice, we compute quenched quark
propagators for 13 bare quark masses. The pion decay constant is extracted from
the pion propagator, and from which the inverse lattice spacing is determined
to be $ a^{-1} = 1.979(6) $ GeV. The parameters ($ C, \delta, B $) in the
pseudoscalar meson mass formula in quenched chiral perturbation theory
(q$\chi$PT) to one-loop order are determined. Further, we measure the index
(topological) susceptibility of these 100 gauge configurations, $ \chi_t = (175
\pm 6 {MeV})^4 $, from which we obtain an estimate of the mass of $ \eta' $ in
q$\chi$PT, and the coefficient of quenched chiral logarithm, both in good
agreement with the values determined from the pion masses, as well as with the
theoretical estimates. With our values of $ C, \delta, B $, the experimental
inputs of pion and kaon masses, and the pion decay constant, we determine the
light quark masses: $ m_{u,d} = 4.1 \pm 0.3 $ MeV, and $ m_s = 92 \pm 9 $ MeV,
in the $ \bar{MS} $ scheme at scale $ \mu = 2 $ GeV. Also, we determine the
quark condensate $<\bar q q > = -(250 \pm 3 {MeV})^3 $, and the quark-gluon
condensate $ g < \bar q \sigma_{\mu\nu} F_{\mu\nu} q > = -(434 \pm 4 {MeV})^5
$, in the $ \bar{MS} $ scheme at scale 2 GeV.


title: QCD meson spectrum in the large $N_C$ limit

abstract:
  The low energy mass spectrum of QCD in the large $N_C$ limit is computed. The
low-lying states in the meson spectrum are explicitly evaluated up to the
fourth order in the strong coupling perturbative expansion. The 't Hooft limit
is smooth and the meson masses are in very good agreement with the experimental
values.


title: Heavy quark masses in the continuum limit of quenched Lattice QCD

abstract:
  We compute charm and bottom quark masses in the quenched approximation and in
the continuum limit of lattice QCD. We make use of a step scaling method,
previously introduced to deal with two scale problems, that allows to take the
continuum limit of the lattice data. We determine the RGI quark masses and make
the connection to the MSbar scheme. The continuum extrapolation gives us a
value m_b^{RGI} = 6.73(16) GeV for the b-quark and m_c^{RGI} = 1.681(36) GeV
for the c-quark, corresponding respectively to m_b^{MSbar}(m_b^{MSbar}) =
4.33(10) GeV and m_c^{MSbar}(m_c^{MSbar}) = 1.319(28) GeV. The latter result,
in agreement with current estimates, is for us a check of the method. Using our
results on the heavy quark masses we compute the mass of the Bc meson, M_{Bc} =
6.46(15) GeV.


title:
Critical behaviour and scaling functions of the three-dimensional O(6)
  model

abstract:
  We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3
lattices within the critical region at zero magnetic field, as well as at
finite magnetic field on the critical isotherm and for several fixed couplings
in the broken and the symmetric phase. We obtain from the Binder cumulant at
vanishing magnetic field the critical coupling J_c=1.42865(3). The universal
value of the Binder cumulant at this point is g_r(J_c)=-1.94456(10). At the
critical coupling, the critical exponents \gamma=1.604(6), \beta=0.425(2) and
\nu=0.818(5) are determined from a finite-size-scaling analysis. Furthermore,
we verify predicted effects induced by massless Goldstone modes in the broken
phase. The results are well described by the perturbative form of the model's
equation of state. Our O(6)-result is compared to the corresponding Ising, O(2)
and O(4) scaling functions. Finally, we study the finite-size-scaling behaviour
of the magnetisation on the pseudocritical line.


title:
The Supersymmetric Ward-Takahashi Identity in 1-Loop Lattice
  Perturbation Theory. I. General Procedure

abstract:
  The one-loop corrections to the lattice supersymmetric Ward-Takahashi
identity (WTi) are investigated in the off-shell regime. In the Wilson
formulation of the N=1 supersymmetric Yang-Mills (SYM) theory, supersymmetry
(SUSY) is broken by the lattice, by the Wilson term and is softly broken by the
presence of the gluino mass. However, the renormalization of the supercurrent
can be realized in a scheme that restores the continuum supersymmetric WTi
(once the on-shell condition is imposed). The general procedure used to
calculate the renormalization constants and mixing coefficients for the local
supercurrent is presented. The supercurrent not only mixes with the gauge
invariant operator $T_\mu$. An extra mixing with other operators coming from
the WTi appears. This extra mixing survives in the continuum limit in the
off-shell regime and cancels out when the on-shell condition is imposed and the
renormalized gluino mass is set to zero. Comparison with numerical results are
also presented.


title: Monopole clusters at short and large distances

abstract:
  We present measurements of various geometrical characteristics of monopole
clusters in SU(2) lattice gauge theory. The maximal Abelian projection is
employed and both infinite, or percolating cluster and finite clusters are
considered. In particular, we observe scaling for average length of segments of
the percolating cluster between self-crossings, correlators of vacuum monopole
currents, angular correlation between links along trajectories. Short clusters
are random walks and their spectrum in length corresponds to free particles. At
the hadronic scale, on the other hand, the monopole trajectories are no longer
random walks. Moreover, we argue that the data on the density of finite
clusters suggest that there are long-range correlations between finite clusters
which can be understood as association of the clusters with two-dimensional
surfaces, whose area scales.


title: Theta dependence of CP^9 model

abstract:
  We apply to the $CP^9$ model two recently proposed numerical techniques for
simulation of systems with a theta term. The algorithms, successfully tested in
the strong coupling limit, are applied to the weak coupling region. The results
agree and errors have been evaluated and are at % level. The results scale well
with the renormalization group equation and show that, for $CP^9$ in presence
of a theta term, CP symmetry is spontaneously broken at $\theta=\pi$ in the
continuum limit.


title: Beyond Quantum Field Theory: Chaotic Lattices?

abstract:
  We review the idea of chaotic quantization, based on the dynamics of
classical lattice gauge systems as well as on non-abelian plasma physics in the
infrared limit. The basic conjecture between Planck constant and properties of
the five dimensional classical theory (h=aT) is demonstrated numerically for
the U(1) lattice gauge group.


title: Heavy quark expansion parameters from lattice NRQCD

abstract:
  We present a lattice QCD calculation of the heavy quark expansion parameters
$\mu_{\pi}^2$ and $\mu_G^2$ for heavy-light mesons and heavy-light-light
baryons. The calculation is carried out on a 20$^3\times$48 lattice at $\beta$
= 6.0 in the quenched approximation, using the lattice NRQCD action for heavy
quarks. We obtain the parameters $\mu_{\pi}^2$ and $\mu_G^2$ in two different
methods: a direct calculation of the matrix elements and an indirect
calculation through the mass spectrum, and confirm that the both methods give
consistent results. We also discuss an application to the lifetime ratios.


title: Thermodynamics and in-medium hadron properties from lattice QCD

abstract:
  Non-perturbative studies of the thermodynamics of strongly interacting
elementary particles within the context of lattice regularized QCD are being
reviewed. After a short introduction into thermal QCD on the lattice we report
on the present status of investigations of bulk properties. In particular, we
discuss the present knowledge of the phase diagram including recent
developments of QCD at non-zero baryon number density. We continue with the
results obtained so far for the transition temperature as well as the
temperature dependence of energy and pressure and comment on screening and the
heavy quark free energies. A major section is devoted to the discussion of
thermal modifications of hadron properties, taking special account of recent
progress through the use of the maximum entropy method.


title:
Gauge Theories with Nonunitary Parallel Transporters: A soluble Higgs
  model

abstract:
  It has been proposed to abandon the requirement that parallel transporters in
gauge theories are unitary (or pseudoorthogonal). This leads to a geometric
interpretation of Vierbein fields as parts of gauge fields, and nonunitary
parallel transport in extra directions yields Higgs fields. In such theories,
the holonomy group H is larger than the gauge group G. Here we study a
1-dimensional model with fermions which retains only the extra dimension, and
which is soluble in the sense that its renormalization group flow may be
exactly computed, with G=SU(2) and noncompact subgroup H of GL(2,C), or G=U(2),
H=GL(2,C). In all cases the asymptotic behavior of the Higgs potential is
computed, and with one possible exception for G=SU(2), H=GL(2,C), there is a
flow of the action from an UV-fix point which describes a SU(2)-gauge theory
with unitary parallel transporters, to a IR-fixpoint. We explain how a
splitting of the masses of fermions of different flavor can arise through
spontaneous symmetry breaking.


title: Numerical determination of monopole entropy in pure SU(2) QCD

abstract:
  We study numerically the length distributions of the infrared monopole
clusters in pure SU(2) QCD. These distributions are Gaussian for all studied
blocking steps of monopoles, lattice volumes and lattice coupling constant. We
also investigate the monopole action for the infrared monopole clusters. The
knowledge of both the length distribution and the monopole action allows us to
determine the effective entropy of the monopole currents. The entropy is a
descending function of blocking scale, indicating that the effective degrees of
freedom of the extended monopoles are getting smaller as the blocking scale
increases.


title: Localization in Lattice QCD

abstract:
  In this paper, we examine the phase diagram of quenched QCD with two flavors
of Wilson fermions, proposing the following microscopic picture. The
super-critical regions inside and outside the Aoki phase are characterized by
the existence of a density of near-zero modes of the (hermitian) Wilson-Dirac
operator, and thus by a non-vanishing pion condensate. Inside the Aoki phase,
this density is built up from extended near-zero modes, while outside the Aoki
phase, there is a non-vanishing density of exponentially localized near-zero
modes, which occur in "exceptional" gauge-field configurations. Nevertheless,
no Goldstone excitations appear outside the Aoki phase, and the existence of
Goldstone excitations may therefore be used to define the Aoki phase in both
the quenched and unquenched theories. We show that the density of localized
near-zero modes gives rise to a divergent pion two-point function, thus
providing an alternative mechanism for satisfying the relevant Ward identity in
the presence of a non-zero order parameter. This divergence occurs when we take
a "twisted" quark mass to zero, and we conclude that quenched QCD with Wilson
fermions is well-defined only with a non-vanishing twisted mass. We show that
this peculiar behavior of the near-zero-mode density is special to the quenched
theory by demonstrating that this density vanishes in the unquenched theory
outside the Aoki phase. We discuss the implications for domain-wall and overlap
fermions constructed from a Wilson-Dirac kernel. We argue that both methods
work outside the Aoki phase, but fail inside because of problems with locality
and/or chiral symmetry, in both the quenched and unquenched theories.


title: Five-dimensional Lattice Gauge Theory as Multi-Layer World

abstract:
  A five-dimensional lattice space can be decomposed into a number of
four-dimens ional lattices called as layers. The five-dimensional gauge theory
on the lattice can be interpreted as four-dimensional gauge theories on the
multi-layer with interactions between neighboring layers. In the theory, there
exist two independent coupling constants; $\beta_4$ controls the dynamics
inside a layer and $\beta_5$ does the strength of the inter-layer
interaction.We propose the new possibility to realize the continuum limit of a
five-dimensional theory using four-dimensional dynamics with large $\beta_4$
and small $\beta_5$. Our result is also related to the higher dimensional
theory by deconstruction approach.


title: Low-lying meson spectrum of large $N_C$ strongly coupled lattice QCD

abstract:
  We compute the low energy mass spectrum of lattice QCD in the large $N_C$
limit. Expanding around a gauge-invariant ground state, which spontaneously
breaks the discrete chiral symmetry, we derive an improved strong-coupling
expansion and evaluate, for any value of $N_C$, the masses of the low-lying
states in the unflavored meson spectrum. We then take the 't Hooft limit by
rescaling $g^2 N_C\to g^2$; the 't Hooft limit is smooth and no arbitrary
parameters are needed. We find, already at the fourth order of the strong
coupling perturbation theory, a very good agreement between the results of our
lattice computation and the known continuum values.


title:
The static quark potential and scaling behavior of SU(3) l attice
  Yang-Mills theory

abstract:
  The potential between a static quark and antiquark in pure SU(3) Yang-Mills
theory is evaluated non-perturbatively through computations on the lattice in
the region from short to intermediate distances (0.05 fm < r < 0.8 fm). In the
high energy regime the results are compared with the parameter-free prediction
of perturbation theory obtained by solving the Renormalization Group equation
at two and three loops. The choice of the renormalization scheme to define a
running coupling turns out to be important for the accuracy of the perturbative
prediction: by obtaining the running coupling through the force, perturbation
theory is applicable up to alpha ~ 0.3, while from the static potential only up
to alpha ~ 0.15. In the region where perturbation is supposed to be reliable,
no large unexpected non-perturbative term is observed.
  In the second part of this work, universality and scaling behavior of
different formulations of Yang-Mills theory on the lattice are discussed, in
particular the Iwasaki and DBW2 actions. The deconfinement temperature T_c*r0
and the glueball masses (m_0++)*r0, (m_2++)*r0 are analyzed. Particular
attention is dedicated to the violation of physical positivity which occur in
these actions and the consequences in the extraction of physical quantities
from Euclidean correlation functions.


title:
A lattice calculation of vector meson couplings to the vector and tensor
  currents using chirally improved fermions

abstract:
  We present a quenched lattice calculation of $f_V^\perp/f_V$, the coupling of
vector mesons to the tensor current normalized by the vector meson decay
constant. The chirally improved lattice Dirac operator, which allows us to
reach small quark masses, is used. We put emphasis on analyzing the quark mass
dependence of $f_V^\perp/f_V$ and find only a rather weak dependence. Our
results at the $\rho$ and $\phi$ masses agree well with QCD sum rule
calculations and those from previous lattice studies.


title: Nucleon axial charge from quenched lattice QCD with domain wall fermions

abstract:
  We present a quenched lattice calculation of the nucleon isovector vector and
axial-vector charges gV and gA. The chiral symmetry of domain wall fermions
makes the calculation of the nucleon axial charge particularly easy since the
Ward-Takahashi identity requires the vector and axial-vector currents to have
the same renormalization, up to lattice spacing errors of order O(a^2). The
DBW2 gauge action provides enhancement of the good chiral symmetry properties
of domain wall fermions at larger lattice spacing than the conventional Wilson
gauge action. Taking advantage of these methods and performing a high
statistics simulation, we find a significant finite volume effect between the
nucleon axial charges calculated on lattices with (1.2 fm)^3 and (2.4 fm)^3
volumes (with lattice spacing, a, of about 0.15 fm). On the large volume we
find gA = 1.212 +/- 0.027(statistical error) +/- 0.024(normalization error).
The quoted systematic error is the dominant (known) one, corresponding to
current renormalization. We discuss other possible remaining sources of error.
This theoretical first principles calculation, which does not yet include
isospin breaking effects, yields a value of gA only a little bit below the
experimental one, 1.2670 +/- 0.0030.


title: The Lattice $\Lambda$ Parameter in Domain Wall QCD

abstract:
  We evaluate the ratio of the scale parameter $\Lambda$ in domain wall QCD to
the one in the continuum theory at one loop level incorporating the effect of
massless quarks. We show that the Pauli-Villars regulator is required to
subtract the unphysical massive fermion modes which emerge in the fermion loop
contributions to the gluon self energy. Detailed results are presented as a
function of the domain wall height $M$.


title: Vector-like Fermion Doubling and Pair-creation on a lattice

abstract:
  Based on the Pauli principle and Heisenberg uncertainty relationship, we show
that the phenomenon of vectorlike fermion-doubling in quantum field theories on
a lattice is related to the phenomenon of pair-creation of massless fermions,
due to quantum-field fluctuations upon the zero-energy level of the ground
state of regularized quantum field theories on the lattice.


title:
Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice
  four-torus

abstract:
  It is known that exactly self-dual gauge-field configurations with
topological charge |Q|=1 cannot exist on the untwisted continuum 4-torus. We
explore the manifestation of this remarkable fact on the lattice 4-torus for
SU(3) using advanced techniques for controlling lattice discretization errors,
extending earlier work of De Forcrand et. al. for SU(2). We identify three
distinct signals for the instability of |Q|=1 configurations, and show that
these manifest themselves early in the cooling process, long before the
would-be instanton has shrunk to a size comparable to the lattice
discretization threshold. These signals do not appear for our |Q|=2
configurations. This indicates that these signals reflect the truly global
nature of the instability, rather than local discretization effects.
Monte-Carlo generated SU(3) gauge field configurations are cooled to the
self-dual limit using an O(a^4)-improved gauge action chosen to have small but
positive O(a^6) errors. This choice prevents lattice discretization errors from
destroying instantons provided their size exceeds the dislocation threshold of
the cooling algorithm. Lattice discretization errors are evaluated by comparing
the O(a^4)-improved gauge-field action with an O(a^4)-improved action
constructed from the square of an O(a^4)-improved lattice field-strength
tensor, thus having different O(a^6) discretization errors. The number of
action-density peaks, the instanton size and the topological charge of
configurations is monitored. We observe a fluctuation in the total topological
charge of |Q|=1 configurations, and demonstrate that the onset of this unusual
behavior corresponds with the disappearance of multiple-peaks in the action
density. At the same time discretization errors are minimal.


title: Observing string breaking with Wilson loops

abstract:
  An uncontroversial observation of adjoint string breaking is proposed, while
measuring the static potential from Wilson loops only. The overlap of the
Wilson loop with the broken-string state is small, but non-vanishing, so that
the broken-string groundstate can be seen if the Wilson loop is long enough. We
demonstrate this in the context of the (2+1)d SU(2) adjoint static potential,
using an improved version of the Luscher-Weisz exponential variance reduction.
To complete the picture we perform the more usual multichannel analysis with
two basis states, the unbroken-string state and the broken-string state (two
so-called gluelumps).
  As by-products, we obtain the temperature-dependent static potential measured
from Polyakov loop correlations, and the fundamental SU(2) static potential
with improved accuracy. Comparing the latter with the adjoint potential, we see
clear deviations from Casimir scaling.


title: Lattice Gauge Fixing and the Violation of Spectral Positivity

abstract:
  Spectral positivity is known to be violated by some forms of lattice gauge
fixing. The most notable example is lattice Landau gauge, where the effective
gluon mass is observed to rise rather than fall with increasing distance. We
trace this violation to the use of quenched auxiliary fields in the lattice
gauge fixing process, and show that violation of spectral positivity is a
general feature of quenching. We illustrate this with a simple quenched
mass-mixing model in continuum field theory, and with a quenched form of the
Ising model. For lattice gauge fixing associated with Abelian projection and
lattice Landau gauge, we show that spectral positivity is violated by processes
similar to those found in quenched QCD. For covariant gauges parametrized by a
gauge-fixing parameter $\alpha $, the SU(2) gluon propagator is well described
by a simple quenched mass-mixing formula. The gluon mass parameter appears to
be independent of $\alpha$ for sufficiently large $\alpha$.


title: Lattice results with three quark flavours

abstract:
  There have been exciting advances recently in finite temperature calculations
with three quark flavours and with non-zero chemical potential. The role of
improved actions is explained and recent results from the Bielefeld group and
MILC collaboration with improved Kogut-Susskind quarks are presented. Three new
approaches to finite chemical potential are discussed.


title: Chirally improving Wilson fermions - I. O(a) improvement

abstract:
  We show that it is possible to improve the chiral behaviour and the approach
to the continuum limit of correlation functions in lattice QCD with Wilson
fermions by taking arithmetic averages of correlators computed in theories
regularized with Wilson terms of opposite sign. Improved hadronic masses and
matrix elements can be obtained by similarly averaging the corresponding
physical quantities separately computed within the two regularizations. To deal
with the problems related to the spectrum of the Wilson--Dirac operator, which
are particularly worrisome when Wilson and mass terms are such as to give
contributions of opposite sign to the real part of the eigenvalues, we propose
to use twisted-mass lattice QCD for the actual computation of the quantities
taking part to the averages. The choice $\pm \pi/2$ for the twisting angle is
particularly interesting, as O($a$) improved estimates of physical quantities
can be obtained even without averaging data from lattice formulations with
opposite Wilson terms. In all cases little or no extra computing power is
necessary, compared to simulations with standard Wilson fermions or
twisted-mass lattice QCD.


title:
Determination of the Improvement Coefficient c_SW up to One-Loop Order
  with the Conventional Perturbation Theory

abstract:
  We calculate the $O(a)$ improvement coefficient c_SW in the
Sheikholeslami-Wohlert quark action for various improved gauge actions with
six-link loops. We employ the conventional perturbation theory introducing the
fictitious gluon mass to regularize the infrared divergence. Our results for
some improved gauge actions are in agreement with those previously obtained
with the Schr{\"o}dinger functional method.


title:
Perturbative matching of staggered four-fermion operators with
  hypercubic fat links

abstract:
  We calculate the one-loop matching coefficients between continuum and lattice
four-fermion operators for lattice operators constructed using staggered
fermions and improved by the use of fattened links. In particular, we consider
hypercubic fat links and SU(3) projected Fat-7 links, and their mean-field
improved versions. We calculate only current-current diagrams, so that our
results apply for operators whose flavor structure does not allow
``eye-diagrams''. We present general formulae, based on two independent
approaches, and give numerical results for the cases in which the operators
have the taste (staggered flavor) of the pseudo-Goldstone pion. We find that
the one-loop corrections are reduced down to the 10-20% level, resolving the
problem of large perturbative corrections for staggered fermion calculations of
matrix elements.


title: Monte Carlo errors with less errors

abstract:
  We explain in detail how to estimate mean values and assess statistical
errors for arbitrary functions of elementary observables in Monte Carlo
simulations. The method is to estimate and sum the relevant autocorrelation
functions, which is argued to produce more certain error estimates than binning
techniques and hence to help toward a better exploitation of expensive
simulations. An effective integrated autocorrelation time is computed which is
suitable to benchmark efficiencies of simulation algorithms with regard to
specific observables of interest. A Matlab code is offered for download that
implements the method. It can also combine independent runs (replica) allowing
to judge their consistency.


title: The apeNEXT project (Status report)

abstract:
  We present the current status of the apeNEXT project. Aim of this project is
the development of the next generation of APE machines which will provide
multi-teraflop computing power. Like previous machines, apeNEXT is based on a
custom designed processor, which is specifically optimized for simulating QCD.
We discuss the machine design, report on benchmarks, and give an overview on
the status of the software development.


title: Glueball Regge Trajectories in (2+1) Dimensional Gauge Theories

abstract:
  We compute glueball masses for even spins ranging from 0 to 6, in the D=2+1
SU(2) lattice gauge theory. We do so over a wide range of lattice spacings, and
this allows a well-controlled extrapolation to the continuum limit. When the
resulting spectrum is presented in the form of a Chew-Frautschi plot we find
that we can draw a straight Regge trajectory going through the lightest
glueballs of spin 0, 2, 4 and 6. The slope of this trajectory is small and
turns out to lie between the predictions of the adjoint-string and flux-tube
glueball models. The intercept we find, \alpha_0 ~ -1, is much lower than is
needed for this leading trajectory to play a `Pomeron-like' role of the kind it
is often believed to play in D=3+1. We elaborate the Regge theory of high
energy scattering in 2 space dimensions, and we conclude, from the observed low
intercept, that high-energy glueball scattering is not dominated by the leading
Regge pole exchange, but rather by a more complex singularity structure in the
region 0 <= Re{\lambda} <= 1/2 of the complex angular momentum \lambda plane.
We show that these conclusions do not change if we go to larger groups,
SU(N>2), and indeed to SU(\infty), and we contrast all this with our very
preliminary calculations in the D=3+1 SU(3) gauge theory.


title: Nonlinear Realization of Chiral Symmetry on the Lattice

abstract:
  We formulate lattice theories in which chiral symmetry is realized
nonlinearly on the fermion fields. In this framework the fermion mass term does
not break chiral symmetry. This property allows us to use the Wilson term to
remove the doubler fermions while maintaining exact chiral symmetry on the
lattice. Our lattice formulation enables us to address non-perturbative
questions in effective field theories of baryons interacting with pions and in
models involving constituent quarks interacting with pions and gluons. We show
that a system containing a non-zero density of static baryons interacting with
pions can be studied on the lattice without encountering complex action
problems. In our formulation one can also decide non-perturbatively if the
chiral quark model of Georgi and Manohar provides an appropriate low-energy
description of QCD. If so, one could understand why the non-relativistic quark
model works.


title: Chiral perturbation theory at O(a^2) for lattice QCD

abstract:
  We construct the chiral effective Lagrangian for two lattice theories: one
with Wilson fermions and the other with Wilson sea fermions and Ginsparg-Wilson
valence fermions. For each of these theories we construct the Symanzik action
through order $a^2$. The chiral Lagrangian is then derived, including terms of
order $a^2$, which have not been calculated before. We find that there are only
few new terms at this order. Corrections to existing coefficients in the
continuum chiral Lagrangian are proportional to $a^2$, and appear in the
Lagrangian at order $a^2 p^2$ or higher. Similarly, O(4) symmetry breaking
terms enter the Symanzik action at order $a^2$, but contribute to the chiral
Lagrangian at order $a^2 p^4$ or higher. We calculate the light meson masses in
chiral perturbation theory for both lattice theories. At next-to-leading order,
we find that there are no order $a^2$ corrections to the valence-valence meson
mass in the mixed theory due to the enhanced chiral symmetry of the valence
sector.


title: Spectral Properties of the Overlap Dirac Operator in QCD

abstract:
  We discuss the eigenvalue distribution of the overlap Dirac operator in
quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and
\beta = 6. We distinguish the topological sectors and study the distributions
of the leading non-zero eigenvalues, which are stereographically mapped onto
the imaginary axis. Thus they can be compared to the predictions of random
matrix theory applied to the \epsilon-expansion of chiral perturbation theory.
We find a satisfactory agreement, if the physical volume exceeds about (1.2
fm)^{4}. For the unfolded level spacing distribution we find an accurate
agreement with the random matrix conjecture on all volumes that we considered.


title: The QCDOC supercomputer: hardware, software, and performance

abstract:
  An overview is given of the QCDOC architecture, a massively parallel and
highly scalable computer optimized for lattice QCD using system-on-a-chip
technology. The heart of a single node is the PowerPC-based QCDOC ASIC,
developed in collaboration with IBM Research, with a peak speed of 1 GFlop/s.
The nodes communicate via high-speed serial links in a 6-dimensional mesh with
nearest-neighbor connections. We find that highly optimized four-dimensional
QCD code obtains over 50% efficiency in cycle accurate simulations of QCDOC,
even for problems of fixed computational difficulty run on tens of thousands of
nodes. We also provide an overview of the QCDOC operating system, which manages
and runs QCDOC applications on partitions of variable dimensionality. Finally,
the SciDAC activity for QCDOC and the message-passing interface QMP specified
as a part of the SciDAC effort are discussed for QCDOC. We explain how to make
optimal use of QMP routines on QCDOC in conjunction with existing C and C++
lattice QCD codes, including the publicly available MILC codes.


title: The Early Days of Lattice Gauge Theory

abstract:
  I discuss some of the historical circumstances that drove us to use the
lattice as a non-perturbative regulator. This approach has had immense success,
convincingly demonstrating quark confinement and obtaining crucial properties
of the strong interactions from first principles. I wrap up with some
challenges for the future.


title: A note on Neuberger's double pass algorithm

abstract:
  We analyze Neuberger's double pass algorithm for the matrix-vector
multiplication R(H).Y (where R(H) is (n-1,n)-th degree rational polynomial of
positive definite operator H), and show that the number of floating point
operations is independent of the degree n, provided that the number of sites is
much larger than the number of iterations in the conjugate gradient. This
implies that the matrix-vector product $ (H)^{-1/2} Y \simeq R^{(n-1,n)}(H)
\cdot Y $ can be approximated to very high precision with sufficiently large n,
without noticeably extra costs. Further, we show that there exists a threshold
$ n_T $ such that the double pass is faster than the single pass for $ n > n_T
$, where $ n_T \simeq 12 - 25 $ for most platforms.


title: Pseudoscalar Decay Constants in Staggered Chiral Perturbation Theory

abstract:
  In a continuation of an ongoing program, we use staggered chiral perturbation
theory to calculate the one-loop chiral logarithms and analytic terms in the
pseudoscalar meson leptonic decay constants, $f_{\pi^+_5}$ and $f_{K^+_5}$. We
consider the partially quenched, ``full QCD'' (with three dynamical flavors),
and quenched cases.


title:
Chiral perturbation theory with Wilson-type fermions including $a^2$
  effects: $N_f=2$ degenerate case

abstract:
  We have derived the quark mass dependence of $m_{\pi}^2$, $m_{\rm AWI}$ and
$f_{\pi}$, using the chiral perturbation theory which includes the $a^2$ effect
associated with the explicit chiral symmetry breaking of the Wilson-type
fermions, in the case of the $N_f=2$ degenerate quarks. Distinct features of
the results are (1) the additive renormalization for the mass parameter $m_q$
in the Lagrangian, (2) $O(a)$ corrections to the chiral log ($m_q\log m_q$)
term, (3) the existence of more singular term, $\log m_q$, generated by $a^2$
contributions, and (4) the existence of both $m_q\log m_q$ and $\log m_q$ terms
in the quark mass from the axial Ward-Takahashi identity, $m_{\rm AWI}$. By
fitting the mass dependence of $m_\pi^2$ and $m_{\rm AWI}$, obtained by the
CP-PACS collaboration for $N_f=2$ full QCD simulations, we have found that the
data are consistently described by the derived formulae. Resumming the most
singular terms $\log m_q$, we have also derived the modified formulae, which
show a better control over the next-to-leading order correction.


title: Analytic estimates for penguin operators in quenched QCD

abstract:
  Strong penguin operators are singlets under the right-handed flavor symmetry
group SU(3)_R. However, they do not remain singlets when the operator is
embedded in (partially) quenched QCD, but instead they become linear
combinations of two operators with different transformation properties under
the (partially) quenched symmetry group. This is an artifact of the quenched
approximation. Each of these two operators is represented by a different set of
low-energy constants in the chiral effective theory. In this paper, we give
analytic estimates for the leading low-energy constants, in quenched and
partially quenched QCD. We conclude that the effects of quenching on Q_6 are
large.


title: Three-dimensional Gonihedric Potts model

abstract:
  We study, by the Mean Field and Monte Carlo methods, a generalized q-state
Potts gonihedric model. The phase transition of the model becomes stronger with
increasing $q.$ The value $k_c(q),$ at which the phase transition becomes
second order, turns out to be an increasing function of $q.$


title: 10 D Euclidean dynamical triangulations

abstract:
  We investigate numerically 10 - dimensional Euclidean quantum gravity (with
discretized Einstein - Hilbert action) in the framework of the dynamical
triangulation approach. For the considered values of the gravitational coupling
we observed two phases, the behavior of which is found to be similar to that of
the crumpled and elongated phases of 3, 4 and 5 dimensional models.
Surprisingly, (for the observed lattice sizes) the natural state of the 10 D
system (when the Einstein - Hilbert action is turned off) is found to resemble
branched polymer while in the low dimensional systems the natural state belongs
to the crumpled phase.


title: Lattice QCD at Finite Density -- An introductory review

abstract:
  This is a pedagogical review of the lattice study of finite density QCD,
which is intended to provide the minimum necessary contents, so that the paper
may be used as the first reading for a newcomer to the field and also for those
working in nonlattice communities. After a brief introduction to argue why
finite density QCD can be a new attractive subject, we describe fundamental
formulae which are necessary for the following sections. Then we survey lattice
QCD simulations in small chemical potential regions, where several prominent
works have been reported recently. Next, two-color QCD calculations are
discussed, where we have a chance to glance at many new features of finite
density QCD, and indeed recent simulations indicated quark pair condensation
and the in-medium effect. Tables of SU(3) and SU(2) lattice simulations at
finite baryon density are given. In the next section, we make a survey of
several related works which may be a starting point of the new development in
the future, although some works do not attract much attention now. Materials
are described in a pedagogical manner. Starting from a simple 2-d model, we
briefly discuss a lattice analysis of NJL model. We describe a non-perturbative
analytical approach, i.e., strong coupling approximation method and some
results. Canonical ensemble approach instead of usual grand canonical ensample
may be another route to reach high density. We examine the density of state
method and show this old idea includes recently proposed factorization method.
An alternative method, complex Langevin equation and an interesting model,
finite isospin model, are also discussed. In Appendix, we give several
technical points which are useful in practical calculations.