title:
Decay constants of B and D mesons from improved relativistic lattice QCD
  with two flavours of sea quarks

abstract:
  We present a calculation of the B and D meson decay constants in lattice QCD
with two (Nf=2) flavours of light dynamical quarks, using an O(a)-improved
Wilson action for both light and heavy quarks and a renormalization-group
improved gauge action. Simulations are made at three values of lattice spacing
a=0.22, 0.16, 0.11 fm and four values of sea quark mass in the range m_PS/m_V
\~= 0.8-0.6. Our estimate for the continuum values of the decay constants are
fBd = 208(10)(11) MeV, fBs = 250(10)(13)(^{+8}_{-0}) MeV, fDd = 225(14)(14)
MeV, fDs = 267(13)(17)(^{+10}_{-0}) MeV for Nf=2 where the statistical and
systematic errors are separately listed, and the third error for fBs and fDs
show uncertainty of determination of strange quark mass. We also carry out a
set of quenched simulations using the same action to make a direct examination
of sea quark effects. Taking the ratio of results for Nf=2 and Nf=0, we obtain
fb^{Nf=2}/fb^{Nf=0} = 1.11(6), fbs^{Nf=2}/fbs^{Nf=0} = 1.14(5),
fd^{Nf=2}/\fd^{Nf=0} = 1.03(6), fds^{Nf=2}/\fds^{Nf=0} = 1.07(5). They show a
10-15% increase in the Nf=2 results over those of Nf=0 for the B meson decay
constants, while evidence for such a trend is statistically less clear for the
D meson decay constants.


title: Z2 monopoles in D=2+1 SU(2) lattice gauge theory

abstract:
  We calculate the Euclidean action of a pair of Z2 monopoles (instantons), as
a function of their spatial separation, in D=2+1 SU(2) lattice gauge theory. We
do so both above and below the deconfining transition at T=Tc. At high T, and
at large separation, we find that the monopole `interaction' grows linearly
with distance: the flux between the monopoles forms a flux tube (exactly like a
finite portion of a Z2 domain wall) so that the monopoles are linearly
confined. At short distances the interaction is well described by a Coulomb
interaction with, at most, a very small screening mass, possibly equal to the
Debye electric screening mass. At low T the interaction can be described by a
simple screened Coulomb (i.e. Yukawa) interaction with a screening mass that
can be interpreted as the mass of a `constituent gluon'. None of this is
unexpected, but it helps to resolve some apparent controversies in the recent
literature.


title: A precise determination of T_c in QCD from scaling

abstract:
  Existing lattice data on the QCD phase transition are analyzed in
renormalized perturbation theory. In quenched QCD it is found that T_c scales
for lattices with only 3 time slices, and that T_c/Lambda_msbar=1.15 \pm 0.05.
A preliminary estimate in QCD with two flavours of dynamical quarks shows that
this ratio depends on the quark mass. For realistic quark masses we estimate
T_c/Lambda_msbar=0.49 \pm 0.02. We also investigate the equation of state in
quenched QCD at 1-loop order in renormalised perturbation theory.


title:
Effects of non-perturbatively improved dynamical fermions in UKQCD
  simulations

abstract:
  We present results for QCD with 2 degenerate flavours of quark using a
non-perturbatively improved action on a lattice volume of $16^3\times32$ where
the bare gauge coupling and bare dynamical quark mass have been chosen to
maintain a fixed physical lattice spacing and volume (1.71 fm). By comparing
measurements from these matched ensembles, including quenched ones, we find
evidence of dynamical quark effects on the short distance static potential, the
scalar glueball mass and the topological susceptibility. There is little
evidence of effects on the light hadron spectrum over the range of quark masses
studied ($m_{\pi}/m_{\rho}\geq 0.60$).


title: Spinons and holons on the lattice

abstract:
  We point out that the dynamical fermion mass generation in the 3D compact
U(1) lattice gauge theory with charged fermion and scalar fields (chi-U-phi_3
model) may be of relevance for the spinon-holon theory with local gauge
symmetry in the condensed matter physics. However, many properties of the model
are uncertain, so we make some conjectures to motivate their future
investigation. Most probably, for strong gauge coupling the model is by
universality equivalent to the familiar 3D four-fermion coupling models with
N_f=2. Available numerical results indicate that at the intermediate and weak
gauge coupling two universality classes with new interesting physics may arise.
One of them is associated with a tricritical point which probably exists in the
phase diagram of the model. The other one is determined by the dynamical
fermion mass generation in the compact QED_3, which is insufficiently
understood but of much interest by itself.


title: Study of compact abelian lattice gauge theories

abstract:
  This is a review, intended for lattice nonspecialists, of the studies of the
compact abelian gauge theories on the lattice performed by the Aachen lattice
field theory group. We discuss in particular the pure compact QED and a U(1)
lattice gauge theory with charged scalar and fermion fields in four and three
dimensions. Our data indicate that these lattice theories might define some
continuum field theories, or at least effective field theories with remarkable
nonperturbative properties like confinement and dynamical mass generation.


title: Unquenched Charmonium with NRQCD - Lattice 2000

abstract:
  We present results from a series of NRQCD simulations of the charmonium
system, both in the quenched approximation and with n_f = 2 dynamical quarks.
The spectra show evidence for quenching effects of ~10% in the S- and
P-hyperfine splittings. We compare this with other systematic effects.
Improving the NRQCD evolution equation altered the S-hyperfine by as much as 20
MeV, and we estimate radiative corrections may be as large as 40%.


title: Leptonic and semi-leptonic B decays

abstract:
  We present results for the semi-leptonic and leptonic decays of B mesons.
These non-perturbative matrix elements are important for constraining the CKM
matrix. Results are presented for the pseudoscalar and vector decay constants,
as well as flavour breaking ratios and heavy quark symmetry relations. We
consider the chiral and momentum dependence of the semi-leptonic form factors
of the decay B-> pi l nu and the soft pion relation (SPR) on the lattice. These
calculations were performed in the quenched approximation at two values of the
coupling with non-perturbatively order a improved action and currents.


title: Confining Configurations in QCD and Relation to Rigid Strings

abstract:
  The gauge field configurations of QCD gauge fields in the infrared regime are
obtained by magnetic symmetry condition. The effective dual action exhibits
dual Meissner effect with quarks included. A string representation of this
action corresponds to rigid string.


title: Dirac and Gor'kov spectra in two color QCD with chemical potential

abstract:
  We analyze the eigenvalue spectrum of the staggered Dirac matrix in two-color
QCD at nonzero baryon density when the eigenvalues become complex. The
quasi-zero modes and their role for chiral symmetry breaking and the
deconfinement transition are examined. The bulk of the spectrum and its
relation to quantum chaos is considered. A comparison with predictions from
random matrix theory is presented. An analogous analysis is performed for the
spectrum of the Gor'kov representation of the fermionic action.


title: Mixing of scalar glueballs and flavour-singlet scalar mesons

abstract:
  We discuss in detail the extraction of hadronic mixing strengths from lattice
studies. We apply this to the mixing of a scalar glueball and a scalar meson in
the quenched approximation. We also measure correlations appropriate for
flavour-singlet scalar mesons using dynamical quark configurations from UKQCD.
This enables us to compare the results from the quenched study of the mixing
with the direct determination of the mixed spectrum. Improved methods of
evaluating the disconnected quark diagrams are also presented.


title: Weak matrix elements and K-meson physics

abstract:
  An overview is presented about old and recent methods to compute the $K\to
\pi \pi$ decay amplitude.


title: Ergodicity and the Classical Lambda Phi^4 Lattice Field Theory

abstract:
  In this talk we present some studies in the approach to equilibrium of the
classical lambda phi^4 theory on the lattice, giving particular emphasis to its
pedagogical usefulness in the context of classical statistical field theory
(such as both the analytical and numerical evaluation of correlation
functions), as well as in the context of statistical mechanics (such as the
equivalence of ensembles in the thermodynamic limit). Since the quartic term
could be regarded as a smooth perturbation to the (integrable) gaussian theory,
we also discuss the connection of our results with the KAM theorem, showing
that the ergodic and non-ergodic regimes are not sharply separated.


title: A smoother approach to scaling by suppressing monopoles and vortices

abstract:
  Suppressing monopoles and vortices by introducing large chemical potentials
for them in the Wilson action for the SU(2) lattice gauge theory, we study the
nature of the deconfinement phase transition on N_sigma^3 X N_tau lattices for
N_tau =4, 5, 6 and 8 and N_sigma = 8-16. Using finite size scaling theory, we
obtain \omega = 1.93 +/- 0.03 for N_tau = 4, in excellent agreement with
universality. The critical couplings for N_tau= 4, 5, 6 and 8 lattices exhibit
large shifts towards the strong coupling region when compared with the usual
Wilson action, and suggest a lot smoother approach to scaling.


title:
Screening in Hot SU(2) Gauge Theory and Propagators in 3d Adjoint Higgs
  model

abstract:
  We investigate the large distance behavior of the electric and magnetic
propagators of hot SU(2) gauge theory in different gauges using lattice
simulations of the full 4d theory and the effective, dimensionally reduced 3d
theory. A comparison of the 3d and 4d data for the propagators suggests that
dimensional reduction works surprisingly well down to temperatures T=2 T_c. A
detailed study of the volume dependence of magnetic propagators is performed.
The electric propagators show exponential decay at large distances in all
gauges considered and a possible gauge dependence of the electric screening
mass turns out to be statistically insignificant.


title:
Structure and representation theory of double group of four-dimensional
  cubic group

abstract:
  We generalize the concept of cubic group into any dimension and derive their
conjugate classifications and representation theorys. Double group and spinor
representation are defined. A detailed calculation is carried out on the
structures of four-dimensional cubic group $O_4$ and its double group, as well
as all inequivalent single-valued representations and spinor representations of
$O_4$ . All representations are derived adopting Clifford theory of
decomposition of induced representations.


title:
Sinle-valued and spinor representations of orientation-preserved
  four-dimensional cubic group

abstract:
  We calculate the single-valued and spinor representations of $SO_4$, the
orientation-preserved subgroup of $O_4$, on the base of our previous work on
four-dimensional cubic group $O_4$.


title: Percolation and Critical Behaviour in SU(2) Gauge Theory

abstract:
  The paramagnetic-ferromagnetic transition in the Ising model can be described
as percolation of suitably defined clusters. We have tried to extend such
picture to the confinement-deconfinement transition of SU(2) pure gauge theory,
which is in the same universality class of the Ising model. The cluster
definition is derived by approximating SU(2) by means of Ising-like effective
theories. The geometrical transition of such clusters turns out to describe
successfully the thermal counterpart for two different lattice regularizations
of (3+1)-d SU(2).


title: QCD Thermodynamics with 2 and 3 Quark Flavors

abstract:
  We discuss the flavor dependence of the pressure and critical temperature
calculated in QCD with 2, 2+1 and 3 flavors using improved gauge and staggered
fermion actions on lattices with temporal extent Nt=4. For T > 2 Tc we find
that bulk thermodynamics of QCD with 2 light and a heavier strange quark is
well described by 3-flavor QCD while the transition temperature is closer to
that of 2-flavor QCD. Furthermore, we present evidence that the chiral critical
point of 3-flavor QCD, i.e. the second order endpoint of the line of first
order chiral phase transitions, belongs to the universality class of the 3d
Ising model.


title:
Two-colour QCD at finite fundamental quark-number density and related
  theories

abstract:
  We are simulating SU(2) Yang-Mills theory with four flavours of dynamical
quarks in the fundamental representation of SU(2) `colour' at finite chemical
potential, mu for quark number, as a model for QCD at finite baryon number
density. In particular we observe that for mu large enough this theory
undergoes a phase transition to a state with a diquark condensate which breaks
quark-number symmetry. In this phase we examine the spectrum of light scalar
and pseudoscalar bosons and see evidence for the Goldstone boson associated
with this spontaneous symmetry breaking. This theory is closely related to QCD
at finite chemical potential for isospin, a theory which we are now studying
for SU(3) colour.


title:
Can One Study Heavy Meson Semileptonic Decays on Coarse Anisotropic
  Lattices ?

abstract:
  Exploratory studies of heavy meson semileptonic decays on coarse lattices
using Symanzik improved glue, NRQCD heavy and D234 light quarks are discussed.
Comparisons are made between calculations on anisotropic and isotropic
lattices. We find evidence that having an anisotropy helps in extracting better
signals at higher momenta.


title:
$K \to \pi \pi$ Decays with Domain Wall Fermions: Towards Physical
  Results

abstract:
  We are using domain wall fermions to study $K \to \pi \pi$ matrix elements by
measuring $K \to \pi$ and $K \to 0$ matrix elements on the lattice and
employing chiral perturbation theory to relate these to the desired physical
result. The residual chiral symmetry breaking of domain wall fermions with a
finite extent in the fifth dimension impacts these measurements. Using the
Ward-Takahashi identities, we investigate residual chiral symmetry breaking
effects for divergent quantities and study pathologies of the quenched
approximation for small quark mass. We then discuss the $\Delta S = 1$ operator
$O_2$, where chiral symmetry is vital for the subtraction of unphysical
effects.


title: The standard model and parity conservation

abstract:
  On the basis of previous work on chiral gauged fermions on a lattice, we
discuss the lattice-regularization of the standard model by introducing two
Weyl fields interacting with quarks and leptons. These interactions form
massive bound states to gauge-invariantly decouple doublers at high energies
and these bound states dissolve into their constituents at low energies. No any
hard spontaneous symmetry breakings occur at the lattice scale \pi/a. As a
consequence, the gauge symmetries of the standard model are realized by both
massive vectorlike spectra at high energies and massless chiral spectra at low
energies. Such a scenario is consistent with the gauge-anomaly cancelation,
flavor-singlet anomaly and Witten's anomaly. These studies predict that the
parity symmetry must be restored at high energies.


title: Obstructions to dimensional reduction in hot QCD

abstract:
  I describe results on screening masses in hot gauge theories. Wilsonian
effective long distance theories called dimensionally reduced (DR) theories
describe very well the longest screening length in pure gauge theories. In the
presence of fermions, meson-like screening lengths dominate the long-distance
physics for 3T_c/2 < T < 3 T_c, and thus obstruct perturbative DR.
Extrapolation of our results indicates that a form of this obstruction may
remain till temperatures of 10 T_c or higher, and therefore affect the entire
range of temperature expected to be reached even at the Large Hadron Collider.


title: The Perfect Laplace Operator for Non-Trivial Boundaries

abstract:
  The application of Renormalization Group (RG) methods to find perfect
discretizations of partial differential equations is a promising but little
investigated approach. We calculate the classically perfect fixed-point Laplace
operator for boundaries of non-trivial shape analytically and numerically and
present a parametrization that can be used for solving the Poisson equation.


title: Magnetic condensation and confinement in lattice gauge theory

abstract:
  We investigate Abelian monopoles and Abelian vortices condensation in finite
temperature SU(2) and SU(3) pure lattice gauge theories.


title: Exact Chiral Symmetry for Domain Wall Fermions with Finite L_s

abstract:
  We show how the standard domain wall action can be simply modified to allow
arbitrarily exact chiral symmetry at finite fifth dimensional extent $L_s$. We
note that the method can be used for both quenched and dynamical calculations.
We test the method using smooth and thermalized gauge field configurations. We
also make comparisons of the performance (cost) of the domain wall operator for
spectroscopy compared to other methods such as the overlap-Dirac operator and
find both methods are comparable in cost.


title: Critical Behavior of a Chiral Condensate with a Meron Cluster Algorithm

abstract:
  A new meron cluster algorithm is constructed to study the finite temperature
critical behavior of the chiral condensate in a $(3+1)$ dimensional model of
interacting staggered fermions. Using finite size scaling analysis the infinite
volume condensate is shown to be consistent with the behavior of the form
$(T_c-T)^{0.314(7)}$ for temperatures less than the critical temperature and
$m^{1/4.87(10)}$ at the critical temperature confirming that the critical
behavior belongs to the 3-d Ising universality class within one to two sigma
deviation. The new method, along with improvements in the implementation of the
algorithm, allows the determination of the critical temperature $T_c$ more
accurately than was possible in a previous study.


title: Study of the Leutwyler-Smilga regimes: Lessons for full QCD simulations

abstract:
  Some key points out of my recent study of the characteristic features of the
small ($x \ll 1$), intermediate ($x \simeq 1$) and large ($x \gg 1$)
Leutwyler-Smilga regimes for QCD-type theories in a finite volume ($x = V
\Sigma m$) are presented, and a few immediate consequences for full QCD
simulations are discussed.


title: Structure Functions on the lattice

abstract:
  We report on a lattice computation of the second moment of the pion matrix
element of the twist-2 non-singlet operator corresponding to the average
momentum of parton densities. We apply a fully non-perturbatively evaluated
running renormalization constant as well as a careful extrapolation of our
results to the continuum limit. Thus the only limitation of our final result is
the quenched approximation.


title: Introduction to stochastic error correction methods

abstract:
  We propose a method for eliminating the truncation error associated with any
subspace diagonalization calculation. The new method, called stochastic error
correction, uses Monte Carlo sampling to compute the contribution of the
remaining basis vectors not included in the initial diagonalization. The method
is part of a new approach to computational quantum physics which combines both
diagonalization and Monte Carlo techniques.


title: Flavor and Quark Mass Dependence of QCD Thermodynamics

abstract:
  We calculate the transition temperature in 2 and 3-flavor QCD using improved
gauge and staggered fermion actions on lattices with temporal extent Nt=4. We
find Tc=173(8)MeV and 154(8)MeV for nf=2 and 3, respectively. In the case of
3-flavor QCD we present evidence that the chiral critical point, i.e. the
second order endpoint of the line of first order chiral phase transitions,
belongs to the universality class of the 3d Ising model.


title:
Critical exponents and equation of state of three-dimensional spin
  models

abstract:
  Three-dimensional spin models of the Ising and XY universality classes are
studied by a combination of high-temperature expansions and Monte Carlo
simulations. Critical exponents are determined to very high precision. Scaling
amplitude ratios are computed via the critical equation of state. Our results
are compared with other theoretical computations and with experiments, with
special emphasis on the lambda transition of 4He.


title: Vortices in SU(2) lattice gauge theory

abstract:
  We investigate some properties of thick vortices and thick monopoles in the
SU(2) lattice gauge theory by inserting operators that create these
excitations. We measure the derivative of the free energy of the vortex with
respect to the coupling and we find that it falls exponentially with the cross
sectional area of the vortex. We also study the monopole-monopole potential
energy of thick and thin monopoles. Our results suggest that vortices and
monopoles of increasing thickness will play an important role in the large
$\beta$ limit.


title: Four-quark operators in hadrons

abstract:
  We present calculations of matrix elements of 4-quark operators in the pion
and in the nucleon extracted from quenched Monte Carlo simulations at beta =
6.0 using Wilson fermions. These operators are relevant for higher-twist
effects. We are particularly careful to avoid mixing with lower-dimensional
operators by choosing appropriate flavour structures.


title: Vortices versus monopoles in color confinement

abstract:
  We construct the creation operator of a vortex for SU(2) pure gauge theory
using the methods developed for monopoles. We interpret its vacuum expectation
value as a disorder parameter for the deconfinement phase transition and find
that it behaves in the vacuum in a similar way to monopoles. Results are
extrapolated to the thermodynamical limit using finite-size scaling.


title: A nonperturbative determination of cA

abstract:
  We describe a non-perturbative determination of $c_A$ using correlators
containing the axial-vector and pseudoscalar currents at zero and non-zero
momentum. We apply the method of Bhattacharya et al to extract $c_A$ from the
requirement that the ratio of appropriate correlators for the PCAC relation
becomes independent of time in the excited state region. We find that the
result depends strongly on the order of the derivatives used in the PCAC
relation. We also find that, using the lowest order derivatives, we cannot get
a consistent value of $c_A$ between zero and non-zero momentum cases. The $c_A$
values that we obtain as we improve the derivatives are consistent and decrease
in magnitude heading towards the perturbative result.


title: Deconfinement Through Chiral Transition In 2 Flavour QCD

abstract:
  We propose that in QCD with dynamical quarks, colour deconfinement occurs
when an external field induced by the chiral condensate strongly aligns the
Polyakov loop. This effect sets in at the chiral symmetry restoration
temperature $T_{\chi}$ and thus makes deconfinement and chiral symmetry
restoration coincide. The predicted singular behavior of Polyakov loop
susceptibilities at $T_{\chi}$ is shown to be supported by finite temperature
lattice calculations.


title: Lattice gauge theory: A retrospective

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:
Quenched and first unquenched lattice HQET determination of the Bs-Meson
  width difference

abstract:
  We present recent results for the prediction of the Bs lifetime difference
from lattice Heavy Quark Effective Theory simulations. In order to get a
next-to-leading order result we have calculated the matching between QCD and
HQET and the two-loop anomalous dimensions in the HQET for all the \Delta B=2
operators, in particular for the operators which enter the width difference. We
present results from quenched and, for the first time, from unquenched
simulations. We obtain for the Bs lifetime difference,
(\Delta\Gamma_Bs/\Gamma_Bs)^{(que.)}=(5.1+/- 1.9+/- 1.7)10^(-2) and
(\Delta\Gamma_Bs/\Gamma_Bs)^{(unq.)}=(4.3+/- 2.0+/- 1.9)10^(-2) from the
quenched and unquenched simulations respectively


title: Dirac eigenvalues and eigenvectors at finite temperature

abstract:
  We investigate the eigenvalues and eigenvectors of the staggered Dirac
operator in the vicinity of the chiral phase transition of quenched SU(3)
lattice gauge theory. We consider both the global features of the spectrum and
the local correlations. In the chirally symmetric phase, the local correlations
in the bulk of the spectrum are still described by random matrix theory, and we
investigate the dependence of the bulk Thouless energy on the simulation
parameters. At and above the critical point, the properties of the low-lying
Dirac eigenvalues depend on the $Z_3$-phase of the Polyakov loop. In the real
phase, they are no longer described by chiral random matrix theory. We also
investigate the localization properties of the Dirac eigenvectors in the
different $Z_3$-phases.


title: Geometry of 4d Simplicial Quantum Gravity with a U(1) Gauge Field

abstract:
  The geometry of 4D simplicial quantum gravity with a U(1) gauge field is
studied numerically. The phase diagram shows a continuous transition when
gravity is coupled with a U(1) gauge field. At the critical point measurements
of the curvature distribution of S^4 space shows an inflated geometry with
homogeneous and symmetric nature. Also, by choosing a 4-simplex and fixing the
scalar curvature geometry of the space is measured.


title:
Numerical Analysis of the Double Scaling Limit in the bosonic part of
  the IIB Matrix Model

abstract:
  The bosonic IIB matrix model, which contains the bosonic part of the IIB
matrix model conjectured to be a non-perturbative definition of the type IIB
superstring theory, is studied using a numerical method. The large N scaling
behavior of the model is shown performing a Monte Carlo simulation. The
expectation value of the Wilson loop operator is measured and the string
tension is estimated. From the numerical results, the prescription of the
double scaling limit is obtained.


title: Nontrivial fixed point in nonabelian models

abstract:
  We investigate the percolation properties of equatorial strips in the
two-dimensional O(3) nonlinear $\sigma$ model. We find convincing evidence that
such strips do not percolate at low temperatures, provided they are
sufficiently narrow. Rigorous arguments show that this implies the vanishing of
the mass gap at low temperature and the absence of asymptotic freedom in the
massive continuum limit. We also give an intuitive explanation of the
transition to a massless phase and, based on it, an estimate of the transition
temperature.


title: SUSY Ward identities in N=1 SYM theory on the lattice

abstract:
  The SUSY Ward identities (WIs) for the N=1 SU(2) SUSY Yang Mills theory
discretized on the lattice with Wilson fermions (gluinos) are considered. The
study is performed in the framework of a Monte Carlo simulation of the model
with light dynamical gluinos. The renormalization and mixing constants of the
lattice SUSY current $Z_S$ and $Z_T$ and the additively renormalized gluino
mass $m_S$ are unknown parameters of the SUSY WIs. Using suitable on-shell
combinations of the WIs, the ratios $Z_T/Z_S$ and $m_S/Z_S$ are determined
non-perturbatively at one value of the coupling constant $g_0$ and two values
of the hopping parameter $\kappa$.


title: Damping and the Hartree Ensemble Approximation

abstract:
  We study a Hartree ensemble approximation for real-time dynamics in the toy
model of 1+1 dimensional scalar field theory. Damping behavior seen in
numerical simulations is compared with analytical predictions based on
perturbation theory in the original (non-Hartree-approximated) model.


title: Spinodal Decomposition in Finite Temperature SU(2) and SU(3)

abstract:
  After a rapid increase in temperature across the deconfinement temperature
T_d to temperatures T >> T_d, pure gauge theories exhibit unstable long
wavelength fluctuations in the approach to equilibrium. This phenomenon is
analogous to spinodal decomposition observed in condensed matter physics, and
also seen in models of disordered chiral condensate formation. At high
temperature, the unstable modes occur only in the range 0 < k < k_c, where k_c
is on the order of the Debye screening mass m_D. Equilibration always occurs
via spinodal decomposition for SU(2). For SU(3) at T near T_d, nucleation
replaces spinodal decomposition as the dominant equilibration mechanism. Monte
Carlo simulations of SU(2) and SU(3) lattice gauge theories exhibit the
predicted phenomena. For SU(2), the observed value of k_c is in reasonable
agreement with a value predicted from previous lattice measurements of m_D.


title:
Perturbative renormalization of the $\Delta B=2$ four-quark operators in
  lattice NRQCD

abstract:
  We present a perturbative calculation of the renormalization constants for
the $\Delta B=2$ four-quark operators, which is needed to evaluate the bag
parameters $B_B$ and $B_S$ in lattice QCD. The one-loop coefficients are
calculated for the $O(1/M)$ NRQCD heavy quark action and the $O(a)$-improved
Wilson action for light quark. Using these coefficients, which remove
$O(\alpha_s/aM)$ error, we reanalyze our previous calculation of the bag
parameters.


title: Perfect Gauge Actions on Anisotropic Lattices

abstract:
  On anisotropic lattices, where generally the lattice is rather coarse in
spatial directions, a parametrized classically perfect action could help
reducing lattice artifacts considerably. We investigate the possibility of
constructing such actions for SU(3) gauge theory. We present two different
methods to do so, either repeating the procedure used to create our newly
parametrized isotropic FP action, or performing one single step starting with
the isotropic result. The anisotropic action is parametrized using an ansatz
including anisotropically APE-like smeared (``fat'') links. The parametrized
classically perfect action with anisotropy $\xi=a_s/a_t=2$ is constructed and
the renormalized anisotropy is measured using the torelon dispersion relation.
It turns out that the renormalization is small.


title: Center vortices in MCG - finite-size and gauge-copy effects

abstract:
  In SU(2) lattice gauge theory in maximal center gauge, we investigate the
dependence of center-projected Creutz ratios and the vortex density on lattice
size and the number of gauge copies. The dependence on the number of copies is
rather strong on small lattices, but almost disappears on lattices sufficiently
large compared to the expected average vortex thickness. The center-projected
string tension, evaluated on sufficiently large lattices, is in good agreement
with the full asymptotic string tension, and the vortex density scales
according to the second-order asymptotic-freedom formula.


title: Determining gA using non-perturbatively O(a) improved Wilson fermions

abstract:
  A completely non-perturbative estimate is given for gA using both quenched
and unquenched O(a) improved Wilson fermions. Particular attention is paid to
the determination of the axial renormalisation constant, ZA, using the Ward
identity for the propagator. For the quenched case, we have results at three
lattice spacings allowing a continuum extrapolation.


title: Disconnected Electromagnetic Form Factors

abstract:
  Preliminary results of a calculation of disconnected nucleon electromagnetic
factors factors on the lattice are presented. The implementation of the
numerical subtraction scheme is outlined. A comparison of results for electric
and magnetic disconnected form factors on two lattice sizes with those of the
Kentucky group is presented. Unlike previous results, the results found in this
calculation are consistent with zero in these sectors.


title:
Progress using generalized lattice Dirac operators to parametrize the
  Fixed-Point QCD action

abstract:
  We report on an ongoing project to parametrize the Fixed-Point Dirac operator
for massless quarks, using a very general construction which has arbitrarily
many fermion offsets and gauge paths, the complete Clifford algebra and
satisfies all required symmetries. Optimizing a specific construction with
hypercubic fermion offsets, we present some preliminary results.


title: Finite Temperature Simulations from Quantum Field Dynamics?

abstract:
  We describe a Hartree ensemble method to approximately solve the Heisenberg
equations for the \phi^4 model in 1+1 dimensions. We compute the energies and
number densities of the quantum particles described by the \phi field and find
that the particles initially thermalize with a Bose-Einstein distribution for
the particle density. Gradually, however, the distribution changes towards
classical equipartition. Using suitable initial conditions quantum
thermalization is achieved much faster than the onset of this undesirable
equipartition. We also show how the numerical efficiency of our method can be
significantly improved.


title:
Light quark masses for dynamical, non-perturbatively O(a) improved
  Wilson fermions

abstract:
  We present results for the light quark masses in lattice QCD with two
degenerate flavours of dynamical fermions. We used configurations generated by
the UKQCD and QCDSF collaborations at six different combinations of beta and
kappa_sea.


title: Fermionic Loops in Numerical Stochastic Perturbation Theory

abstract:
  We discuss the inclusion of fermionic loops contributions in Numerical
Stochastic Perturbation Theory for Lattice Gauge Theories. We show how the
algorithm implementation is in principle straightforward and report on the
status of the project.


title: Quark Loop Effects with an Improved Staggered Action

abstract:
  We have been studying effects of dynamical quarks on various hadronic
observables, using our recently formulated improvement for staggered fermions.
To illustrate improvement, we show that the light hadron spectrum in the
quenched approximation gives remarkably good scaling. We highlight three new
results: (1) We find no apparent quark loop effects in the Edinburgh plot with
2+1 flavors of dynamical quarks at a = 0.14 fm. (2) We show that dynamical
quarks modify the shape of the heavy quark potential. (3) We present results
hinting at meson decay effects in light hadron spectroscopy.


title: Zero Temperature String Breaking with Staggered Quarks

abstract:
  The separation of a heavy quark and antiquark pair leads to the formation of
a tube of flux, or "string", which should break in the presence of light
quark-antiquark pairs. This expected zero-temperature phenomenon has proven
elusive in simulations of lattice QCD. In an extension of work reported last
year we present clear evidence for string breaking in QCD with two flavors of
dynamical staggered sea quarks and apply our results to a simple three-state
mixing model for string breaking. We find that mixing is weak and falls to zero
at level crossing.


title:
Reformulating Yang-Mills theory in terms of local gauge invariant
  variables

abstract:
  An explicit canonical transformation is constructed to relate the physical
subspace of Yang-Mills theory to the phase space of the ADM variables of
general relativity. This maps 3+1 dimensional Yang-Mills theory to local
evolution of metrics on 3 manifolds.


title: Topology in full QCD with 2 colours at finite temperature and density

abstract:
  We present preliminary results about topology and several other quantities at
non-zero baryon density and finite temperature in full QCD with N_c=2.


title: Relativistic Quarkonia from Anisotropic Lattices

abstract:
  We report on new results for the spectrum of quarkonia using a fully
relativistic approach on anisotropic lattices with quark masses in the range
from strange to bottom. A fine temporal discretisation also enables us to
resolve excitations high above the ground state. In particular we studied the
mass dependence and scaling of hybrid states.


title: Ginsparg-Wilson relation with R=(a \gamma_5 D)^{2k}

abstract:
  The Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$
with $R = (a \gamma_5 D)^{2k}$ is discussed. An explicit realization of D is
constructed. It is shown that this sequence of topologically-proper lattice
Dirac operators tend to a nonlocal operator in the limit $k \to \infty$. This
suggests that the locality of a lattice Dirac operator is irrelevant to its
index.


title: Static three quark potential in the quenched lattice QCD

abstract:
  We study the static three quark potential using lattice QCD simulation. At
zero temperature, the three quark potential is extracted from the baryonic
Wilson loop and fitted to the phenomenological form, the sum of the Coulomb
term, linearly rising term and the constant. We compare two types of the linear
term, ``$Y$'' and ``$\Delta$'' type, and find that the string tension almost
coincide with $\sigma_{Q\bar{Q}}$ in the former case. We also investigate the
three quark potential at finite temperature using the Polyakov loop
correlation. In the deconfined phase, the screened potential is observed
similarly to the case of $Q\bar{Q}$ system.


title: The interaction between center monopoles in SU(2) Yang-Mills

abstract:
  We study the potential between a static center monopole and antimonopole in
4d SU(2) Yang-Mills theory. Using a new numerical method, we show that the 't
Hooft loop is a dual order parameter with respect to the Wilson loop, for the
deconfinement phase transition. We observe a 3d Ising-like critical behaviour
for the dual string tension related to the spatial 't Hooft loop as a function
of the temperature.


title:
Monte Carlo Study of Two-Color QCD with Finite Chemical Potential -
  Status report of Wilson fermion simulation

abstract:
  Using Wilson fermions, we study SU(2) lattice QCD with the chemical potential
at $\beta=1.6$. The ratio of fermion determinants is evaluated at each
Metropolis link update step. We calculate the baryon number density, the
Polyakov loops and the pseudoscalar and vector masses on $4^4$ and $4^3\times
8$ lattices. Preliminary data show the pseudoscalar meson becomes massive
around $\mu=0.4$, which indicates the chiral symmetry restoration. The
calculation is broken down when approaching to the transition region. We
analyze the behavior of the fermion determinant and eigen value distributions
of the determinant, which shows a peculiar ``Shell-and-Bean'' pattern near the
transition.


title: Chiral symmetry in lattice QCD

abstract:
  A chiral invariant effective action for lattice QCD is proposed. Its
connection to the multifermion model is established. A possibility of using
this action for computer simulations is discussed.


title:
QCD topology using scale controlled cooling: Densities and cooling
  invariant observables

abstract:
  We aim at reducing the uncertainties inherent in the analysis of the
topological structure by using scale controlled smoothing and observables
independent on the "microscopic" description of the instanton ensemble.


title: Vortex structure of the vacuum and confinement

abstract:
  We discuss the recently published numerical computations of the vortex free
energy. They dramatically demonstrate that the excitation probability for a
sufficiently thick vortex approaches unity at large beta, i.e. that thick
vortices `condense' in the vacuum. This is known to imply confinement. An
analytical approach for exploring this phenomenon is also outlined.


title: Center Vortices at Strong Couplings

abstract:
  A long-range effective action is derived for strong-coupling lattice SU(2)
gauge theory in D=3 dimensions. It is shown that center vortices emerge as
stable saddlepoints of this action.


title:
Full QCD Light Hadron Spectrum and Quark Masses: Final Results from
  CP-PACS

abstract:
  We present the final results of the CP-PACS calculation of the light hadron
spectrum and quark masses with two flavors of dynamical quarks. Simulations are
made with a renormalization-group improved gauge action and a mean-field
improved clover quark action for sea quark masses corresponding to $m_{\rm
PS}/m_{\rm V} \approx 0.8$--0.6 and the lattice spacing $a=0.22$--0.11 fm. For
the meson spectrum in the continuum limit a clearly improved agreement with
experiment is observed compared to the quenched case, demonstrating the
importance of sea quark effects. For light quark masses we obtain
$m_{ud}^{\bar{MS}}(2GeV)=3.44^{+0.14}_{-0.22}$ MeV and
$m_s^{\bar{MS}}(2GeV)=88^{+4}_{-6}$ MeV ($K$-input) and
$m_s^{\bar{MS}}(2GeV)=90^{+5}_{-11}$ MeV ($\phi$-input), which are reduced by
about 25% compared to the values in quenched QCD.


title: Kaon B parameter from quenched domain-wall QCD

abstract:
  We report on a calculation of $B_K$ with domain wall fermion action in
quenched QCD. Simulations are made with a renormalization group improved gauge
action at $\beta=2.6$ and 2.9 corresponding to $a^{-1}\approx 2$GeV and 3GeV.
Effects due to finite fifth dimensional size $N_5$ and finite spatial size
$N_\sigma$ are examined in detail. Matching to the continuum operator is made
perturbatively at one loop order. We obtain $B_K(\mu = 2 {GeV})= 0.5746(61)$,
where the error is statistical only, as an estimate of the continuum value in
the $\msbar$ scheme with naive dimensional regularization. This value is
smaller but consistent with $B_K(\mu = 2 {GeV})= 0.628(42)$ obtained by the
JLQCD Collaboration using the Kogut-Susskind quark action. Results for strange
quark mass are also reported.


title: Results on the Gluon Propagator in Lattice Covariant Gauges

abstract:
  We illustrate preliminary results on the gluon propagator computed in generic
covariant lattice gauges in the quenched approximation with the Wilson action.
We have applied a recently proposed procedure to fix a generic covariant gauge
on the lattice. We make a comparison among results obtained at two different
values of the gauge parameter and in the standard Landau's gauge.


title: Maxwell Theory from Matrix Model

abstract:
  We present a scenario for deriving Maxwell theory from IIB matrix model. Four
dimensional spacetime and theories on it relate different dimensional ones by
applying appropriate limits of the backgrounds of matrix model. It is
understood by looking at open strings bits as bi-local fields on the spacetime,
which are decoupled from the bulk in the limits. The origin of
electric-magnetic duality is also discussed in matrix model.


title: Precision study of large-N Yang-Mills theory in 2+1 dimensions

abstract:
  The boundstate problem in 2+1-dimensional large-N Yang-Mills theory is
accurately solved using the light-front Hamiltonian of transverse lattice gauge
theory. We conduct a thorough investigation of the space of couplings on coarse
lattices, finding a single renormalised trajectory on which Poincar\'e
symmetries are enhanced in boundstate solutions. Augmented by existing data
from finite-N Euclidean lattice simulations, we obtain accurate estimates of
the low-lying glueball spectrum at N=infinty


title: Numerical studies of confinement in the lattice Landau gauge

abstract:
  Critical conjectures on confinement in the Landau gauge is numerically tested
in focus to Gribov copy effects. One of the subjects is of the Kugo-Ojima
confinement criterion and the other is of various viewpoints in the
Gribov-Zwanziger theory. We use the smearing gauge as a reference gauge free of
Gribov copy, and performed three types of simulations, log U, U-linear and log
U in the smearing gauge. It is found that Gribov copy effect on the Kugo-Ojima
parameter is small. log U and U-linear simulations yield only global scale
factor difference in gluon propagator and in ghost propagator, and about 10%
difference in Kugo-Ojima parameter. The horizon function defined by Zwanziger
is evaluated in three types of gauge field and compared. All data show the
negative horizon function as expected.


title: Some universal properties of the string breaking

abstract:
  In gauge systems coupled to matter, the static potential flattens out at a
scale where the confining string breaks by formation of a dynamical pair of
particles. Surprisingly, such a breaking is invisible in Wilson loops even when
the inter-charge separation is much larger than the flattening scale. Observing
string breaking also requires using different operators. A known string
mechanism provides us with a simple explanation, leading to the area law for
large Wilson loops, as observed in most gauge models coupled to whatever kind
of matter. It is also pointed out that in a simple 3D Z_2 gauge-Higgs model,
once reformulated in terms of Fortuin Kasteleyn clusters, this peculiar
behaviour of the Wilson operator can be ascribed to non-trivial linking of a
percolating cluster to the Wilson loop. Some numerical tests on this model are
also presented.


title: Numerical Study of dense adjoint 2-color matter

abstract:
  We study the global symmetries of SU(2) gauge theory with N flavors of
staggered fermions in the presence of a chemical potential. We motivate the
special interest of the case N=1 (staggered) with fermions in the adjoint
representation of the gauge group. We present results from numerical
simulations with both hybrid Monte Carlo and the Two-Step Multi-Bosonic
algorithm.


title:
Light hadron spectroscopy with two flavors of O(a) improved dynamical
  quarks

abstract:
  We report on our study of light hadron spectrum and quark masses in QCD with
two flavors of dynamical quarks. Simulations are made with the plaquette gauge
action and the non-perturbatively $O(a)$ improved Wilson quark action. We
simulate 5 sea qaurk masses corresponding to $m_{PS}/m_{V} \simeq 0.8$--0.6 at
$\beta=5.2$ on $12^3 \times 48$, $16^3 \times 48$ and $20^3 \times 48$
lattices. A comparison with previous calculations in quenched QCD indicates sea
quark effects in meson and quark masses.


title:
Topologically non-trivial configurations in 3-dimensional Yang-Mills
  theory

abstract:
  Recently Anishetty, Majumdar and Sharatchandra have proposed a way of
characterizing topologically non-trivial configurations for 2+1-dimensional
Yang-Mills theory in a local and manifestly gauge invariant manner. Here we
develop criteria to locate such objects in lattice gauge theory and find them
in numerical simulations.


title: Gauge independence of Abelian and monopole dominance

abstract:
  We formulate a stochastic gauge fixing method to study the gauge dependence
of Abelian projection. In this method, one can change the gauge from the
maximally Abelian one to no gauge fixing continuously. We have found that the
linear part of the heavy quark potential from Abelian contribution depends
little on the gauge parameter. Similar results have been obtained for the
monopole contribution part.We also investigate the gauge dependence of the
length of monopole loop, which is known to be important for the confinement,
and monopole density. These results suggest that the picture that monopole
plays an important role for the confinement of QCD dose not depend on choice of
the gauge.


title: B^0-\bar{B}^0 mixing with quenched lattice NRQCD

abstract:
  We present our recent results for the B-parameters, which parameterize the
\Delta B=2 transition amplitudes. Calculations are made in quenched QCD at
\beta=5.7, 5.9, and 6.1, using NRQCD for heavy quark and the $O(a)$-improved
action for light quark. The operators are perturbatively renormalized including
corrections of O(\alpha_s/am_Q). We examine scaling behavior of the
B-parameters in detail, and discuss the systematic uncertainties using scatter
of results with different analysis procedures adopted. As a result, we find
B_{B_d}(m_b)=0.84(2)(8), B_{B_s}/B_{B_d}=1.017(10)(^{+4}_{-0}) and
B_{S_s}(m_b)=0.87(1)(9)(^{+1}_{-0}) in the quenched approximation.


title: Charmonium in finite temperature lattice QCD

abstract:
  We study hadron properties near the deconfining transition in the finite
temperature lattice QCD. This paper focus on the heavy quarkonium states, such
as $J/\psi$ meson. We compare the meson correlators above and below $T_c$ and
discuss the possibility of the $c\bar{c}$ bound state by observing the wave
function.


title: Non-perturbative scaling tests of twisted mass QCD

abstract:
  We present a scaling study of lattice QCD with O(a) improved Wilson fermions
and a chirally twisted mass term. In order to get precise results with a
moderate computational effort, we have considered a system of physical size of
0.75^3 * 1.5 fm^4 with Schroedinger functional boundary conditions in the
quenched approximation. Looking at meson observables in the pseudoscalar and
vector channels, we find that O(a) improvement is effective and residual cutoff
effects are fairly small.


title:
Spectra of massive QCD Dirac Operators from Random Matrix Theory: all
  three chiral symmetry breaking patterns

abstract:
  The microscopic spectral eigenvalue correlations of QCD Dirac operators in
the presence of dynamical fermions are calculated within the framework of
Random Matrix Theory (RMT). Our approach treats the low--energy correlation
functions of all three chiral symmetry breaking patterns (labeled by the Dyson
index $\beta=1,2$ and 4) on the same footing, offering a unifying description
of massive QCD Dirac spectra. RMT universality is explicitly proven for all
three symmetry classes and the results are compared to the available lattice
data for $\beta=4$.


title: Laplacian gauge and instantons

abstract:
  We exhibit the connection between local gauge singularities in the Laplacian
gauge and topological charge, which opens the possibility of studying instanton
excitations without cooling. We describe our version of Laplacian gauge-fixing
for SU(N).


title: Residual Chiral Symmetry Breaking in Domain-Wall Fermions

abstract:
  We study the effective quark mass induced by the finite separation of the
domain walls in the domain-wall formulation of chiral fermion as the function
of the size of the fifth dimension ($L_s$), the gauge coupling ($\beta$) and
the physical volume ($V$). We measure the mass by calculating the small
eigenvalues of the hermitian domain-wall Dirac operator ($H_{\rm
DWF}(m_0=1.8))$ in the topologically-nontrivial quenched SU(3) gauge
configurations. We find that the induced quark mass is nearly independent of
the physical volume, decays exponentially as a function of $L_s$, and has a
strong dependence on the size of quantum fluctuations controlled by $\beta$.
The effect of the choice of the lattice gluon action is also studied.


title: The role of diagonalization within a diagonalization/Monte Carlo scheme

abstract:
  We discuss a method called quasi-sparse eigenvector diagonalization which
finds the most important basis vectors of the low energy eigenstates of a
quantum Hamiltonian. It can operate using any basis, either orthogonal or
non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian,
finite-dimensional, or infinite-dimensional. The method is part of a new
computational approach which combines both diagonalization and Monte Carlo
techniques.


title: The role of Monte Carlo within a diagonalization/Monte Carlo scheme

abstract:
  We review the method of stochastic error correction which eliminates the
truncation error associated with any subspace diagonalization. Monte Carlo
sampling is used to compute the contribution of the remaining basis vectors not
included in the initial diagonalization. The method is part of a new approach
to computational quantum physics which combines both diagonalization and Monte
Carlo techniques.


title: Superconductivity with the Meron-Cluster Algorithm

abstract:
  The meron-cluster algorithm was previously used to extensively study the
physics associated with the spontaneous breaking of a discrete symmetry. We
recently discovered that a larger class of models with spontaneous breaking of
continuous symmetries can also be simulated using the meron-cluster algorithm.
Here we study one of these new models which belongs to the attractive Hubbard
model family. In particular we study the spontaneous breaking of the U(1)
fermion number symmetry in two dimensions and find clear evidence for a
Kosterlitz-Thouless transition to a superconducting phase.


title:
Chiral Symmetry Breaking for Domain Wall Fermions in Quenched Lattice
  QCD

abstract:
  The domain wall fermion formulation exhibits full chiral symmetry for finite
lattice spacing except for the effects of mixing between the domain walls.
Close to the continuum limit these symmetry breaking effects should be
described by a single residual mass. We determine this mass from the
conservation law obeyed by the conserved axial current in quenched simulations
with beta=5.7 and 6.0 and domain wall separations varying between 12 and 48 on
8^3x32 and 16^3x32 lattices. Using the resulting values for the residual mass
we perform two complete and independent calculations of the pion decay
constant. Good agreement is found between these two methods and with
experiment.


title:
Pad\'e-Z$_2$ stochastic estimator of determinants applied to quark loop
  expansion of lattice QCD

abstract:
  We use the Pad\'e-Z$_2$ stochastic estimator for calculating Tr log M to
compute quark loop corrections to quenched QCD. We examine the main source of
error in this technique and look at a way of controlling it.


title:
Domain Wall Fermion Study of Scaling in Non-perturbative Renormalization
  of Quark Composite Operators

abstract:
  We compute non-perturbatively the renormalization coefficients of scalar and
pseudoscalar operators, local vector and axial currents, conserved vector and
axial currents, and $O^{\Delta S=2}_{LL}$ over a wide range of energy scales
using a scaling technique that connects the results of simulations at different
values of coupling $\beta$. We use the domain wall fermion formulation in the
quenched approximation at a series of three values of $\beta = 6.0, 6.45, 7.05$
corresponding to lattice spacing scaling by factors of two.


title: Simulation of n_f =3 QCD by Hybrid Monte Carlo

abstract:
  Simulations of odd flavors QCD can be performed in the framework of the
hybrid Monte Carlo algorithm where the inverse of the fermion matrix is
approximated by a polynomial. In this exploratory study we perform three
flavors QCD simulations. We make a comparison of the hybrid Monte Carlo
algorithm and the R-algorithm which also simulates odd flavors systems but has
step-size errors. We find that results from our hybrid Monte Carlo algorithm
are in agreement with those from the R-algorithm obtained at very small
step-size.


title: QCDOC: A 10-teraflops scale computer for lattice QCD

abstract:
  The architecture of a new class of computers, optimized for lattice QCD
calculations, is described. An individual node is based on a single integrated
circuit containing a PowerPC 32-bit integer processor with a 1 Gflops 64-bit
IEEE floating point unit, 4 Mbyte of memory, 8 Gbit/sec nearest-neighbor
communications and additional control and diagnostic circuitry. The machine's
name, QCDOC, derives from ``QCD On a Chip''.


title: Quenched charmonium spectrum on anisotropic lattices

abstract:
  We present the results of quenched charmonium spectrum for S- and P-states,
obtained by a relativistic heavy quark method on anisotropic lattices.
Simulations are carried out using the standard plaquette gauge action and a
meanfield-improved clover quark action at $a_t^{-1} = 3$--6 GeV with the
renormalized anisotropy fixed to $\xi \equiv a_s/a_t =3$. We study the scaling
of our fine and hyperfine mass splittings, and compare with previous results.


title: Lattice QCD at finite temperature

abstract:
  Recent developments in finite-temperature QCD with dynamical quarks are
reviewed focusing on the topics of critical temperature, the equation of state,
and critical behaviors around the chiral phase transition.


title: Calculation of $K\to \pi$ matrix elements in quenched domain-wall QCD

abstract:
  We explore the possibility for an evaluation of non-leptonic $\Delta S=1$ $K$
decay amplitudes through the calculation of $K\to\pi$ matrix elements using
domain-wall QCD. The relation between the physical $K\to\pi\pi$ matrix elements
and $K\to\pi$ matrix elements deduced from chiral perturbation theory is
recapitulated. Quenched numerical simulations are performed on an $16^3\times
32\times 16$ lattice at a lattice spacing $a^{-1}\approx 2$GeV for both the
standard plaquette gauge action and a renormalization-group improved gauge
action, and reasonable signals for $K\to\pi$ matrix elements are obtained.
Preliminary results are reported on the $K\to\pi\pi$ matrix elements, and
results from two actions are compared.


title: Differential decay rate for $B \to \pi l \nu$ semileptonic decays

abstract:
  We present our study on $B \to \pi l \nu$ semileptonic decay form factors
with NRQCD action for heavy quark from a quenched lattice QCD simulation at
$\beta$=5.9 on a $16^3\times 48$ lattice. We obtain form factors defined in the
context of heavy quark effective theory by Burdman et al. and find that their
$1/m_B$ correction is small. The limit of physical heavy and light quark masses
can be performed without introducing any model function, and we obtain a
prediction for the differential decay rate $d\Gamma/dq^2$. We also discuss the
soft pion limit of the form factors.


title: What happens to Lattice Fermion near Continuum Limit?

abstract:
  A Ginsparg-Wilson Relation (GWR) is obtained in the presence of chiral
symmetry breaking terms. It leads to the PCAC relation as well as an anomaly
relation on the lattice. For general fermions, the deviation from the exact GWR
is getting small when the block-spin transformations are performed iteratively.
Based on a simple geometrical interpretation of the Dirac operator satisfying
the GWR, we find some physical properties shared by the lattice fermions near
the continuum limit. In two-dimensions, we explicitly construct the GW Dirac
operator by using a conformal mapping.


title: Moments of Structure Functions in Full QCD

abstract:
  Moments of the quark density distribution, moments of the quark helicity
distribution, and the tensor charge are calculated in full QCD. Calculations of
matrix elements of operators from the operator product expansion have been
performed on $16^3 \times 32$ lattices for Wilson fermions at $\beta = 5.6$
using configurations from the SESAM collaboration and at $\beta = 5.5$ using
configurations from SCRI. One-loop perturbative renormalization corrections are
included. Selected results are compared with corresponding quenched
calculations and with calculations using cooled configurations.


title: Domain wall fermion calculation of nucleon g_A/g_V

abstract:
  We present a preliminary domain-wall fermion lattice-QCD calculation of
isovector vector and axial charges, g_V and g_A, of the nucleon. Since the
lattice renormalizations, Z_V and Z_A, of the currents are identical with DWF,
the lattice ratio (g_A/g_V)^{lattice} directly yields the continuum value.
Indeed Z_V determined from the matrix element of the vector current agrees
closely with Z_A from a non-perturbative renormalization study of quark
bilinears. We also obtain spin related quantities Delta-q/g_V and delta-q/g_V.


title: Constructing Improved Overlap Fermions in QCD

abstract:
  We describe an explicit construction of approximate Ginsparg-Wilson fermions
for QCD. We use ingredients of perfect action origin, and further elements. The
spectrum of the lattice Dirac operator reveals the quality of the
approximation. We focus on beta =6 for optimisation. Such fermions are intended
to be inserted into the overlap formula. Hence we also test the speed of
convergence under polynomial evaluation of the overlap formula.


title: Chemical potential response of meson masses at finite temperature

abstract:
  We study the response of meson masses to the chemical potential
($\partial{m}/\partial{\mu}$) at high temperature and at zero chemical
potential on $N_f=2$ lattice with staggered fermions. Preliminary results for
the meson composed of different quarks show that
$\partial{m}/\partial{\mu}|_{\mu=0}$ is negative in the confinement phase and
positive in the deconfinement phase.


title:
Exact results and approximation schemes for the Schwinger model with the
  overlap Dirac operator

abstract:
  We propose new techniques to implement numerically the overlap-Dirac operator
which exploit the physical properties of the underlying theory to avoid nested
algorithms. We test these procedures in the two-dimensional Schwinger model and
the results are very promising. We also present a detailed computation of the
spectrum and chiral properties of the Schwinger Model in the overlap lattice
formulation.


title: Strange Magnetic Moment of The Nucleon from Lattice QCD

abstract:
  We calculate the strange magnetic moment of the nucleon on a quenched $16^3
\times 24$ lattice at $\beta = 6.0$, and with Wilson fermions at $\kappa$ =
0.148, 0.152, and 0.154. The strange quark contribution from the disconnected
insertion is estimated stochastically by employing the $Z_2$ noise method.
Using an unbiased subtraction along with the help of charge conjugation and
hermiticity, we reduce the error by a factor of 2 with negligible overhead. Our
result is $G_{M}^{s} = -0.28\pm0.10 \mu_{N}$.


title:
Low Dirac Eigenmodes and the Topological and Chiral Structure of the QCD
  Vacuum

abstract:
  Several lattice calculations which probe the chiral and topological structure
of QCD are discussed. The results focus attention on the low-lying eigenmodes
of the Dirac operator in typical gauge field configurations.


title: Recent results using the overlap Dirac operator

abstract:
  I derive the overlap Dirac operator starting from the overlap formalism,
discuss the numerical hurdles in dealing with this operator and present ways to
overcome them.


title:
U(1) Chiral gauge theory on lattice with gauge-fixed domain wall
  fermions

abstract:
  We investigate a U(1) lattice chiral gauge theory with domain wall fermions
and gauge fixing. In the reduced model limit, our perturbative and numerical
investigations at Yukawa coupling y=1 show that there are no extra mirror
chiral modes. The longitudinal gauge degrees of freedom have no effect on the
free domain wall fermion spectrum consisting of opposite chiral modes at the
domain wall and the anti-domain wall which have an exponentially damped
overlap. Our numerical investigation at small Yukawa couplings also leads to
similar conclusions as above.


title: Static correlation lengths in QCD at high temperature and finite density

abstract:
  A brief review is given of the sign problem in finite density lattice QCD and
various attempts to overcome it. To date there is still no solution to this
problem which would work for realistic QCD. The main focus then is on the
deconfined phase, where QCD can be described by a dimensionally reduced
effective action. After summarizing derivation and validity of the effective
theory, it is demonstrated that it can be simulated efficiently in the presence
of a chemical potential for quarks $\mu/T\lsim 4$. Direct comparison of
simulations with imaginary and real $\mu$ suggests that equilibrium plasma
properties could be analytically continued from 4d QCD simulations at imaginary
$\mu$.


title: Monopoles, Vortices and Confinement is SU(3) Lattice Gauge Theory

abstract:
  We present results for the heavy quark potential computed in SU(3) from
magnetic monopoles and from center vortices. The monopoles are identified after
fixing SU(3) lattice configurations to the maximal abelian gauge. The center
vortices are identified after using an indirect center gauge fixing scheme
which we describe for SU(3). Z(3) center vortices are extracted and used to
compute the potential. The values of the string tensions from monopoles and
vortices are compared to the full SU(3) string tension.


title:
Two-loop Perturbative Quark Mass Renormalization from Large Beta Monte
  Carlo

abstract:
  We present the calculation of heavy Wilson quark mass renormalization
constants from large beta Monte Carlo simulations. Simulations were performed
at various beta larger than 9, each on several spatial lattice sizes to allow
for an infinite volume extrapolation. We use twisted boundary conditions to
suppress tunneling and work in Coulomb gauge with appropriate adjustments for
the temporal links. The one-loop coefficient obtained from this method is in
agreement with the analytical result and a preliminary result for the second
order coefficient is reported.


title: QCD at a Finite Density of Static Quarks

abstract:
  Recently, cluster methods have been used to solve a variety of sign problems
including those that arise in the presence of fermions. In all cases an
analytic partial re-summation over a class of configurations in the path
integral was necessary. Here the new ideas are illustrated using the example of
QCD at a finite density of static quarks. In this limit the sign problem
simplifies since the fermionic part decouples. Furthermore, the problem can be
solved completely when the gauge dynamics is replaced by a Potts model. On the
other hand in QCD with light quarks the solution will require a partial
re-summation over both fermionic and gauge degrees of freedom. The new approach
points to unexplored directions in the search for a solution to this more
challenging sign problem.


title:
Testing perturbative results with non-perturbative methods for the
  Hierarchical model

abstract:
  We present non-perturbative methods to calculate accurately the renormalized
quantities for Dyson's Hierarchical Model. We apply this method and calculate
the critical exponent gamma with 12 and 4 significant digits in the high and
low temperature phases, respectively. We report accurate values for universal
ratios of amplitudes and preliminary results concerning the comparison with
perturbative results.


title: Zero-momentum modes and chiral limit in compact lattice QED

abstract:
  The influence of zero-momentum gauge modes on physical observables is
investigated for compact lattice QED with dynamical and quenched Wilson
fermions. Within the Coulomb phase, zero-momentum modes are shown to hide the
critical behaviour of gauge invariant fermion observables near the chiral
limit. Methods for eliminating zero-momentum modes are discussed.


title: N* Spectrum using an O(a)-Improved Fermion Action

abstract:
  The construction of operators and calculational methods for the determination
of the N* spectrum are discussed. The masses of the parity partners of the
nucleon and delta are computed from the O(a)-improved data of the UKQCD
Collaboration, and a clear splitting observed between the mass of the nucleon
and its parity partner.


title: QCD vacuum structure

abstract:
  Several issues related to the structure of the QCD vacuum are reviewed. We
concentrate mostly on results concerning instantons and center vortices.


title: Lattice Chiral Gauge Theories

abstract:
  I review the substantial progress which has been made recently with the
non-perturbative construction of chiral gauge theories on the lattice. In
particular, I discuss three different approaches: a gauge invariant method
using fermions which satisfy the Ginsparg-Wilson relation, and two gauge
non-invariant methods, one using different cutoffs for the fermions and the
gauge fields, and one using gauge fixing. Open problems within all three
approaches are addressed.


title: Recent Progress of Lattice QCD in China

abstract:
  Lattice QCD is the most reliable non-perturbative method in quantum field
theory. In the last few years, some problems crucial to high energy experiments
have been solved. We review some recent work done by the Chinese lattice
community.


title:
f_B for Various Actions : Approaching the Continuum Limit with Dynamical
  Fermions

abstract:
  We present results for pseudoscalar decay constants of heavy-light mesons
using both quenched and N_f = 2 dynamical fermion configurations. A variety of
fermion actions is investigated : Wilson, nonperturbative clover, and fat-link
clover. For heavy quarks the Fermilab formalism is applied. In the quenched
approximation, results with the nonperturbatively improved clover action of the
Alpha collaboration allow us to study the systematic error of the continuum
extrapolation from the Wilson action. In addition, we use quenched
configurations to explore the effects of fattening. The lessons from the
quenched analyses are then applied to data with dynamical fermions, where both
Wilson and fat-link clover actions have been used. This allows us to attempt a
continuum extrapolation of the dynamical results.


title:
On the 1-loop lattice perturbation theory of the supersymmetric Ward
  identities

abstract:
  The one loop corrections to the supersymmetric Ward identities (WIs) in the
discretized N=1 SU(2) supersymmetric Yang-Mills theory can be investigated by
means of lattice perturbation theory. The supersymmetry (SUSY) is explicitly
broken by the lattice discretization as well as by the introduction of Wilson
fermions. However, the renormalization of the supercurrent can be carried out
in a scheme that restores the nominal continuum WIs. We present our work in
progress which is concerned with the 1-loop renormalization of the local
supercurrent, i.e. with the perturbative computation of the corresponding
renormalization constants and mixing coefficients.


title: Towards the lattice study of M-theory

abstract:
  We propose the Wilson discretization of the supersymmetric Yang-Mills Quantum
Mechanics as a lattice version of the matrix model of M-theory. An SU(2) model
is studied numerically in the quenched approximation for D=4. A clear signal
for the existence of two different phases is found and the continuum
pseudocritical temperature is determined. We have also extracted the continuum
limit of the total size of the system in both phases and for different
temperatures.


title:
Eigenvalues of the hermitian Wilson-Dirac operator and chiral properties
  of the domain-wall fermion

abstract:
  Chiral properties of QCD formulated with the domain-wall fermion (DWQCD) are
studied using the anomalous quark mass m_{5q} and the spectrum of the
4-dimensional Wilson-Dirac operator. Numerical simulations are made with the
standard plaquette gauge action and a renormalization-group improved gauge
action. Results are reported on the density of zero eigenvalue obtained with
the accumulation method, and a comparison is made with the results for m_{5q}.


title: Matrix model formulation of four dimensional gravity

abstract:
  The attempt of extending to higher dimensions the matrix model formulation of
two-dimensional quantum gravity leads to the consideration of higher rank
tensor models. We discuss how these models relate to four dimensional quantum
gravity and the precise conditions allowing to associate a four-dimensional
simplicial manifold to Feynman diagrams of a rank-four tensor model.


title:
The Gribov Ambiguity for Maximal Abelian and Center Gauges in SU(2)
  Lattice Gauge Theory

abstract:
  We present results for the fundamental string tension in SU(2) lattice gauge
theory after projection to maximal abelian and direct maximal center gauges. We
generate 20 Gribov copies/configuration. Abelian and center projected string
tensions slowly decrease as higher values of the gauge functionals are reached.


title: Regulated chiral gauge theory

abstract:
  After a brief introduction to the overlap two examples relating to
topological properties of chiral fermion systems in interaction with gauge
fields are presented: It is shown how the overlap preserves the continuum
structure of exact fermionic zero modes in gauge backgrounds that are
instanton-like and why chiral anomalies are inevitable.


title: Non-perturbative Renormalisation with Domain Wall Fermions

abstract:
  We present results from a study of the renormalisation of both quark bilinear
and four-quark operators for the domain wall fermion action, using the
non-perturbative renormalisation technique of the Rome-Southampton group. These
results are from a quenched simulation, on a 16^3 x 32 lattice, with beta=6.0
and L_s=16.


title: Benchmarking MILC code with OpenMP and MPI

abstract:
  A trend in high performance computers that is becoming increasingly popular
is the use of symmetric multiprocessing (SMP) rather than the older paradigm of
MPP. MPI codes that ran and scaled well on MPP machines can often be run on an
SMP machine using the vendor's version of MPI. However, this approach may not
make optimal use of the (expensive) SMP hardware. More significantly, there are
machines like Blue Horizon, an IBM SP with 8-way SMP nodes at the San Diego
Supercomputer Center that can only support 4 MPI processes per node (with the
current switch). On such a machine it is imperative to be able to use OpenMP
parallelism on the node, and MPI between nodes. We describe the challenges of
converting MILC MPI code to using a second level of OpenMP parallelism, and
benchmarks on IBM and Sun computers.


title:
Current Status of the Numerical Simulations of d=3 SU(2) Lattice Gauge
  Theory in the Dual Formulation

abstract:
  We have continued our systematic investigations of the numerical simulations
of lattice gauge theories in the dual formulation. These include: i) a more
practical implementation of the quasi-local updating technique, ii) a thorough
investigation of the sign problem, iii) issues related to the ergodicity of the
various update algorithms, iv) a novel way of measuring conventional
observables like plaquette in the dual formalism and v) investigations of
thermalisation. While the dual formulation holds out a lot of promises in
principle, there are still some ways to go before it can be made into an
attractive alternative lattice formulation.


title: High Temperature Limit of the $ N= 2 $ IIA Matrix Model

abstract:
  The high temperature limit of a system of two D-0 branes is investigated. The
partition function can be expressed as a power series in $\beta$ (inverse
temperature). The leading term in the high temperature expression of the
partition function and effective potential is calculated {\em exactly}.
Physical quantities like the mean square separation can also be exactly
determined in the high temperature limit. We comment on SU(3) IIB matrix model
and the difficulties to study it.


title: Maximum Entropy Analysis of the Spectral Functions in Lattice QCD

abstract:
  First principle calculation of the QCD spectral functions (SPFs) based on the
lattice QCD simulations is reviewed. Special emphasis is placed on the Bayesian
inference theory and the Maximum Entropy Method (MEM), which is a useful tool
to extract SPFs from the imaginary-time correlation functions numerically
obtained by the Monte Carlo method. Three important aspects of MEM are (i) it
does not require a priori assumptions or parametrizations of SPFs, (ii) for
given data, a unique solution is obtained if it exists, and (iii) the
statistical significance of the solution can be quantitatively analyzed.
  The ability of MEM is explicitly demonstrated by using mock data as well as
lattice QCD data. When applied to lattice data, MEM correctly reproduces the
low-energy resonances and shows the existence of high-energy continuum in
hadronic correlation functions. This opens up various possibilities for
studying hadronic properties in QCD beyond the conventional way of analyzing
the lattice data. Future problems to be studied by MEM in lattice QCD are also
summarized.


title: Fixed Point SU(3) Gauge Actions: Scaling Properties and Glueballs

abstract:
  We present a new parametrization of a SU(3) fixed point (FP) gauge action
using smeared ("fat") gauge links. We report on the scaling behaviour of the FP
action on coarse lattices by means of the static quark-antiquark potential, the
hadronic scale $r_0$, the string tension $\sigma$ and the critical temperature
$T_c$ of the deconfining phase transition. In addition, we investigate the low
lying glueball masses where we observe no scaling violations within the
statistical errors.


title: $K\to\pi\pi$ Decays with Domain Wall Fermions: Lattice Matrix Elements

abstract:
  We present a lattice calculation of the $K\to\pi$ and $K\to 0$ matrix
elements of the $\Delta S=1$ effective weak Hamiltonian which can be used to
determine $\epsilon^\prime/\epsilon$ and the $\Delta I=1/2$ rule for $K$ decays
in the Standard Model. The matrix elements for $K\to\pi\pi$ decays are related
to $K\to\pi$ and $K\to 0$ using lowest order chiral perturbation theory. We
also present results for the kaon $B$ parameter, $B_K$. Our quenched domain
wall fermion simulation was done at $\beta=6.0$ ($a^{-1}\approx 2$ GeV),
lattice size $16^3\times 32\times 16$, and domain wall height $M_5=1.8$.


title:
Pathologies of the large-N limit for RP^{N-1}, CP^{N-1}, QP^{N-1} and
  mixed isovector/isotensor sigma-models

abstract:
  We compute the phase diagram in the N\to\infty limit for lattice RP^{N-1},
CP^{N-1} and QP^{N-1} sigma-models with the quartic action, and more generally
for mixed isovector/isotensor models. We show that the N=\infty limit exhibits
phase transitions that are forbidden for any finite N. We clarify the origin of
these pathologies by examining the exact solution of the one-dimensional model:
we find that there are complex zeros of the partition function that tend to the
real axis as N\to\infty. We conjecture the correct phase diagram for finite N
as a function of the spatial dimension d. Along the way, we prove some new
correlation inequalities for a class of N-component sigma-models, and we obtain
some new results concerning the complex zeros of confluent hypergeometric
functions.


title: Baryon Masses in the 1/N Expansion

abstract:
  The masses of baryons and heavy quark baryons are studied analytically in an
expansion in 1/N, SU(3) flavor symmetry breaking and heavy-quark symmetry
breaking. The measured baryon masses are in striking agreement with the 1/N
hierarchy.


title:
Hadron masses from dynamical, non-perturbatively O(a) improved Wilson
  fermions

abstract:
  We present results on light hadron masses from simulations of full QCD and
report on experiences in running such simulations on a Hitachi SR8000-F1
supercomputer.


title: A Visualization of the SU(2) Vacuum on the Lattice

abstract:
  Configurations of pure SU(2) gauge field theory on the lattice are
transformed to Landau gauge. After Fourier transformation, large momentum
amplitudes are suppressed (filtered) by a variable amount, and the
configurations are transformed back to x-space. Spectacular peaks in electric
and magnetic field strengths are found, which share many properties with either
almost pointlike instantons in regular gauge or with extended anti-instantons
in singular gauge. The environment around those peaks are visualized with
respect to the action, to the topological charge density, to the gauge fields
and to electric and magnetic field strengths. The density of the peaks is of
order 1 / fm**4, and it scales according to the string tension under a
variation of the coupling constant. The evolution of the peaks under the amount
of Fourier filtering is visualy compared to the evolution under cooling, and
the gauge dependence of the peaks is discussed. Advantages and shortcomings of
this method are discussed, with emphasis on possible strong distortions of the
action and topological charge density, which become gauge dependent. Finally, I
compare the character of the SU(2)-configurations to those of noncompact
abelian theory.


title:
Quasi-local Update Algorithms for Numerical Simulations of d=3 SU(2) LGT
  in the Dual Formulation

abstract:
  In the dual formulation of d=3 SU(2) LGT, the link variables are group
representations and valid configurations are those satisfying a number of
triangle inequalities. In \cite{lat99} algorithms for local updates that
automatically respect these constraints were described. It was also pointed out
there that these local updates were not ergodic. In this presentation, we
describe two different quasi-local updating algorithms which, in conjunction
with the local updates, appear to be ergodic.


title: Monopoles, vortices and confinement in SU(3) gauge theory

abstract:
  We compute, in SU(3) pure gauge theory, the vacuum expectation value (vev) of
the operator which creates a $Z_3$ vortex wrapping the lattice through periodic
boundary conditions (dual Polyakov line). The technique used is the same
already tested in the SU(2) case. The dual Polyakov line proves to be a good
disorder parameter for confinement, and has a similar behaviour to the monopole
condensate. The new features which characterise the construction of the
disorder operator in SU(3) are emphasised.


title: Scale Setting for $\alpha_s$ Beyond Leading Order

abstract:
  We present a general procedure for applying the scale-setting prescription of
Brodsky, Lepage and Mackenzie to higher orders in the strong coupling constant
$\alphas$. In particular, we show how to apply this prescription when the
leading coefficient or coefficients in a series in $\alphas$ are anomalously
small. We give a general method for computing an optimum scale numerically,
within dimensional regularization, and in cases when the coefficients of a
series are known. We find significant corrections to the scales for $R_{e^+
e^-}$, $\Gamma(B \to X_u e \bar{\nu})$, $\Gamma(t \to b W)$, and the ratios of
the quark pole to $\MSbar$ and lattice bare masses.


title: Supersymmetry on Lattice Using Ginsparg-Wilson Relation

abstract:
  The Ginsparg-Wilson(G-W) relation for chiral symmetry is extended for a
supersymmetrical(SUSY) case on a lattice.
  It is possible to define exact lattice supersymmetry which are devided into
two different cases according to using difference operators.
  $U(1)_R$ symmetry on the lattice is also realized as one of exact symmetries.
For an application, the extended G-W relation is given for a two-dimensional
model with chiral multiplets.


title:
SU(2) lattice gauge theory at non-zero temperature with fixed holonomy
  boundary condition

abstract:
  We study SU(2) lattice gauge theory at $T>0$ in a finite box with fixed
holonomy value at the spatial boundary. We search for (approximate) classical
solutions of the lattice field equations and find in particular the dissociated
calorons recently discussed by van Baal and collaborators.


title: On the Doubling Phenomenon in Lattice Chern-Simons Theories

abstract:
  We analyse the pure Chern-Simons theory on an Euclidean infinite lattice. We
point out that, as a consequence of its symmetries, the Chern-Simons theory
does not have an integrable kernel. Due to the linearity of the action in the
derivatives, the situation is very similar to the one arising in the lattice
formulation of fermionic theories. Doubling of bosonic degrees of freedom is
removed by adding a Maxwell term with a mechanism similar to the one proposed
by Wilson for fermionic models.


title: The unquenched Upsilon spectrum

abstract:
  We describe the bottomonium spectrum obtained on the UKQCD dynamical
ensembles and its comparison to quenched results. We include a determination of
alpha_s and m_b from the dynmaical results.


title:
Flop Transitions in Cuprate and Color Superconductors: From SO(5) to
  SO(10) Unification?

abstract:
  The phase diagrams of cuprate superconductors and of QCD at non-zero baryon
chemical potential are qualitatively similar. The Neel phase of the cuprates
corresponds to the chirally broken phase of QCD, and the high-temperature
superconducting phase corresponds to the color superconducting phase. In the
SO(5) theory for the cuprates the $SO(3)_s$ spin rotational symmetry and the
$U(1)_{em}$ gauge symmetry of electromagnetism are dynamically unified. This
suggests that the $SU(2)_L \otimes SU(2)_R \otimes U(1)_B$ chiral symmetry of
QCD and the $SU(3)_c$ color gauge symmetry may get unified to SO(10). Dynamical
enhancement of symmetry from $SO(2)_s \otimes \Z(2)$ to $SO(3)_s$ is known to
occur in anisotropic antiferromagnets. In these systems the staggered
magnetization flops from an easy 3-axis into the 12-plane at a critical value
of the external magnetic field. Similarly, the phase transitions in the SO(5)
and SO(10) models are flop transitions of a ``superspin''. Despite this fact, a
renormalization group flow analysis in $4-\epsilon$ dimensions indicates that a
point with full SO(5) or SO(10) symmetry exists neither in the cuprates nor in
QCD.


title: Computer Simulations of 3d Lorentzian Quantum Gravity

abstract:
  We investigate the phase diagram of non-perturbative three-dimensional
Lorentzian quantum gravity with the help of Monte Carlo simulations. The system
has a first-order phase transition at a critical value $k_0^c$ of the bare
inverse gravitational coupling constant $k_0$. For $k_0 > k_0^c$ the system
reduces to a product of uncorrelated Euclidean 2d gravity models and has no
intrinsic interest as a model of 3d gravity. For $k_0 < k_0^c$, extended
three-dimensional geometries dominate the functional integral despite the fact
that we perform a sum over geometries and no particular background is
distinguished at the outset. Furthermore, all systems with $k_0 < k_0^c$ have
the same continuum limit. A different choice of $k_0$ corresponds merely to a
redefinition of the overall length scale.


title: Asymptotically free theories based on discrete subgroups

abstract:
  We study the critical behavior of discrete spin models related to the 2d O(3)
non-linear sigma model. Precise numerical results suggest that models with
sufficiently large discrete subgroups are in the same universality class as the
original sigma model. We observe that at least up to correlation lengths
$\xi\approx 300$ the cut-off effects follow effectively an $\propto a$
behaviour both in the O(3) and in the dodecahedron model.


title: Cooling, Monopoles, and Vortices in SU(2) Lattice Gauge Theory

abstract:
  We study monopoles and vortices in SU(2) lattice gauge theory on a 24**4
lattice at beta=2.50. We find a value of fundamental string tension from
monopoles in the maximum Abelian gauge consistent with the full SU(2) value.
Using direct and indirect center gauges, we find fundamental string tension
values from P-vortices which are larger than the full SU(2) result. After a
single cooling sweep, the string tensions from monopoles and P-vortices are all
30% lower than the full SU(2) value, while the U(1) string tension in the
maximum Abelian gauge remains consistent with the full SU(2) result. Blocking
the lattice after cooling does not restore the low values of string tension
found with monopoles and vortices.


title: Finite size scaling analysis of compact QED

abstract:
  We describe results of a high-statistics finite size scaling analysis of 4d
compact U(1) lattice gauge theory with Wilson action at the phase transition
point. Using a multicanonical hybrid Monte Carlo algorithm we generate data
samples with more than 150 tunneling events between the metastable states of
the system, on lattice sizes up to 18^4. We performed a first analysis within
the Borgs-Kotecky finite size scaling scheme. As a result, we report evidence
for a first-order phase transition with a plaquette energy gap, G=0.02667(20),
at a transition coupling, beta_T=1.011128(11).


title:
An investigation into the Fermilab approach to heavy quarks on the
  lattice

abstract:
  We use a space-time asymmetric O(a) improved fermion action and fix the
asymmetry non-perturbatively to restore the relativistic dispersion relation.
We compute spectra and matrix elements of quarkonia and heavy-light mesons and
compare with results obtained using a symmetric action with the Fermilab
interpretation i.e. that the physics of heavy lattice quarks depends solely on
their kinetic mass. We provide additional evidence to support this.


title: N* Mass Spectrum from an Anisotropic Action

abstract:
  Results are reported for N* masses in the 1/2+ and 1/2- sectors on an
anisotropic lattice. The gauge action is the usual plaquette plus rectangle
type, the quark action is of the D234 type, both having tadpole-improved
tree-level coefficients. Clear splittings from the nucleon ground state are
observed with smeared operators and 500 configurations. The first excited
states in each channel are further isolated, using a correlation matrix and the
variational method. The basic pattern of these splittings is consistent with
experimental observations.


title:
On the short distance nonperturbative corrections in heavy quark
  expansion

abstract:
  We study the corrections due to renormalons to the heavy hadron decay
width.The renormalons contribution estimated in terms of finite gluon mass
based on the assumption that the gluon mass represents the short distance
nonperturbative effects in the standard OPE (and hence in the heavy quark
expansion). We found that the corrections are about 10% of the leading decay
rate. We point out the implications for the assumption of quark-hadron duality
in heavy quark expansion.


title: Short Range Linear Potential in 3D Lattice Compact QED

abstract:
  We study the static potential between electric charges in the finite
temperature three dimensional compact gauge theory on the lattice. We show that
in the deconfinement phase at small separations between the charges the
potential contains a linearly rising piece which goes over into the Coulomb
potential as the distance between the charges is increased. The linear
potential is due to the gas of magnetic dipoles which are realized as
monopole-antimonopole bound states.


title: Is the chiral U(1) theory trivial?

abstract:
  The chiral U(1) theory differs from the corresponding vector theory by an
imaginary contribution to the effective action which amounts to a phase factor
in the partition function. The vector theory, i.e. QED, is known to be trivial
in the continuum limit. It is argued that the presence of the phase factor will
not alter this result and the chiral theory is non-interacting as well.


title: Heavy Quark Physics on the Lattice

abstract:
  I review the current status of lattice calculations of the properties of
bound states containing one or more heavy quarks. Many of my remarks focus on
the heavy-light leptonic decay constants, such as $f_B$, for which the
systematic errors have by now been quite well studied. I also discuss
$B$-parameters, semileptonic form factors, and the heavy-light and heavy-heavy
spectra. Some of my ``world averages'' are: $f_B=200(30) MeV$, $f_B\sqrt{\hat
B_{B_d}}= 230(40) MeV$, $f_{B_s}/f_B=1.16(4)$ and $f_{B_s}\sqrt{\hat
B_{B_s}}/f_B\sqrt{\hat B_{B_d}}=1.16(5)$.


title:
Heavy --> Light semileptonic decays of pseudoscalar mesons from lattice
  QCD

abstract:
  We have computed the form factors for B --> pi and D --> K(pi) semileptonic
decays on the lattice by using full non-perturbative O(a) improvement, in the
quenched approximation. Our results are expressed in terms of few parameters
which describe the q^2-dependence and normalization of the form factors.


title: Domain wall fermions and applications

abstract:
  Domain wall fermions provide a complimentary alternative to traditional
lattice fermion approaches. By introducing an extra dimension, the amount of
chiral symmetry present in the lattice theory can be controlled in a linear
way. This results in improved chiral properties as well as robust topological
zero modes. A brief introduction on the subject and a discussion of chiral
properties and applications, such as zero and finite temperature QCD, N = 1
super Yang-Mills, and four-fermion theories, is presented.


title:
A consistency check for Renormalons in Lattice Gauge Theory: beta^(-10)
  contributions to the SU(3) plaquette

abstract:
  We compute the perturbative expansion of the Lattice SU(3) plaquette to
beta^(-10) order. The result is found to be consistent both with the expected
renormalon behaviour and with finite size effects on top of that.


title: Lattice supersymmetry with domain wall fermions

abstract:
  Supersymmetry, like Poincare symmetry, is softly broken at finite lattice
spacing provided the gaugino mass term is strongly suppressed. Domain wall
fermions provide the mechanism for suppressing this term by approximately
imposing chiral symmetry on the lattice. We present the first numerical
simulations of N=1 supersymmetric SU(2) Yang-Mills on the lattice in d=4
dimensions using domain wall fermions.


title: Thermodynamics of free domain wall and overlap fermions

abstract:
  Studies of non-interacting lattice fermions give an estimate of the size of
discretization errors and finite size effects for more interesting problems
like finite temperature QCD. We present a calculation of the thermodynamic
equation of state for free domain wall and overlap fermions.


title: Analysis of the DeltaI=1/2 Rule and e'/e with Overlap Fermions

abstract:
  We study the renormalization of the DeltaS=1 effective weak Hamiltonian with
overlap fermions. The mixing coefficients among dimension-six operators are
computed at one loop in perturbation theory. As a consequence of the chiral
symmetry at finite lattice spacing and of the GIM mechanism, which turns out to
be quadratic in the masses, the K-->pi pi and K -->pi matrix elements relevant
for the Delta I =1/2 rule can be computed without any power subtractions. The
analogous amplitudes for e'/e require one divergent subtraction only, which can
be performed non-perturbatively using K-->0 matrix elements.


title: Comparing Clusters and Supercomputers for Lattice QCD

abstract:
  Since the development of the Beowulf project to build a parallel computer
from commodity PC components, there have been many such clusters built. The
MILC QCD code has been run on a variety of clusters and supercomputers. Key
design features are identified, and the cost effectiveness of clusters and
supercomputers are compared.


title: Overlap Fermions on a $20^4$ Lattice

abstract:
  We report results on hadron masses, fitting of the quenched chiral log, and
quark masses from Neuberger's overlap fermion on a quenched $20^4$ lattice with
lattice spacing $a = 0.15$ fm. We used the improved gauge action which is shown
to lower the density of small eigenvalues for $H^2$ as compared to the Wilson
gauge action. This makes the calculation feasible on 64 nodes of CRAY-T3E. Also
presented is the pion mass on a small volume ($6^3 \times 12$ with a Wilson
gauge action at $\beta = 5.7$). We find that for configurations that the
topological charge $Q \ne 0$, the pion mass tends to a constant and for
configurations with trivial topology, it approaches zero possibly linearly with
the quark mass.


title: Recent Developments in Superstring Theory

abstract:
  The talk contains a brief introduction string theory, followed by a
discussion of some of the recent developments.


title: Unquenched QCD simulation results

abstract:
  The recent progress on unquenched QCD simulations is critically reviewed.
After some discussions on problems and subtleties in unquenched simulations,
hadron spectra obtained from both quenched and unquenched simulations are
compared among various gauge and quark actions. It is found that the Edinburgh
plot does not agree in the continuum limit between Wilson and KS quark actions
even in quenched QCD. Dynamical quark effects on hadron spectra, in particular,
on meson masses are then presented for Wilson-type quark actions. Finally
dynamical quark effects on other quantities such as the topological
susceptibility and the flavor-singlet meson mass are discussed.


title: Heavy Quark Phenomenology from Lattice QCD

abstract:
  Recent results relevant for the B-physics phenomenology, obtained from
lattice QCD simulations by the APE Collaboration, are reviewed. This includes
the B0-B0bar mixing amplitude, B-> pi semileptonic decay and the relative width
difference of B0_s mesons, $(\Delta \Gamma/\Gamma)_{B_s}$.


title: String Breaking in Four Dimensional Lattice QCD

abstract:
  Virtual quark pair screening leads to breaking of the string between
fundamental representation quarks in QCD. For unquenched four dimensional
lattice QCD, this (so far elusive) phenomenon is studied using the recently
developed truncated determinant algorithm (TDA). The dynamical configurations
were generated on an Athlon 650 MHz PC. Quark eigenmodes up to 420 MeV are
included exactly in these TDA studies performed at low quark mass on large
coarse (but O($a^2$) improved) lattices. A study of Wilson line correlators in
Coulomb gauge extracted from an ensemble of 1000 two-flavor dynamical
configurations reveals evidence for flattening of the string tension at
distances R $\geq$ approximately 1 fm.


title: Non-equilibrium field theory

abstract:
  I discuss various topics in relativistic non-equilibrium field theory related
to high energy physics and cosmology. I focus on non-perturbative problems and
how they can be treated on the lattice.


title: Kosterlitz-Thouless theory and lattice artifacts

abstract:
  The massive continuum limit of the 1+1 dimensional O(2) nonlinear
$\sigma$-model (XY model) is studied using its equivalence to the Sine-Gordon
model at its asymptotically free point. It is shown that leading lattice
artifacts are universal but they vanish only as inverse powers of the logarithm
of the correlation length. Such leading artifacts are calculated for the case
of the scattering phase shifts and the correlation function of the Noether
current using the bootstrap S-matrix and perturbation theory respectively.


title:
Probability Distribution Function of the Diquark Condensate in Two
  Colours QCD

abstract:
  We consider diquark condensation in finite density lattice SU(2). We first
present an extension of Vafa-Witten result, on spontaneous breaking of
vector-like global symmetries, that allows us to formulate a no-go theorem for
diquark condensation in a region of the chemical potential-mass parameter
space. We then describe a new technique to calculate diquark condensation at
any number of flavours directly at zero external source without using any
potentially dangerous extrapolation procedure. We apply it to the strong
coupling limit and find compelling evidences for a second order phase
transition, where a diquark condensate appears, as well as quantitative
agreement between lattice results and low-energy effective Lagrangian
calculations.