title:
Correlated Instanton Orientations in the SU(2) Yang-Mills Vacuum and
  Pair Formation in the Deconfined Phase

abstract:
  Using the renormalization group motivated smoothing technique we study the
semiclassical structure of the pure Yang-Mills vacuum. We carefully check that
identified clusters of topological charge behave like instantons around their
centers. Looking at distance distributions of clusters we find
instanton-antiinstanton pair formation in the deconfined phase. We use suitably
normalized gauge invariant field strength correlators to obtain first
quantitative information on the relative color orientation of instantons. We
give further evidence for a modified instanton profile in the confined phase
and present a simple alternative model for it.


title: Monopoles and Vortices in the SU(2) Positive Plaquette Model

abstract:
  We study the heavy quark potential in the SU(2) positive plaquette model
using monopoles in the maximum abelian gauge, and vortices. Monopoles give a
quantitative description of the string tension. Vortices approximately
reproduce the entire heavy quark potential.


title: The quenched generating functional for hadronic weak interactions

abstract:
  The ultraviolet behaviour of the generating functional for hadronic weak
interactions with $|\Delta S| =1, 2$ is investigated to one loop for a generic
number of flavours and in the quenched approximation. New quenched chiral
logarithms generated by the weak interactions can be accounted for via a
redefinition of the weak mass term in the $\Delta S=\pm 1$ weak effective
Lagrangian at leading order. Finally, we illustrate how chiral logarithms are
modified by the quenched approximation in $K\to\pi\pi$ matrix elements with
$\Delta I=1/2$ and 3/2.


title: Hadronic Weak Interactions of Light Quarks

abstract:
  In this review, three subjects are discussed: a phenomenological application
of lattice predictions to $K^0$--$\bar K^0$ mixing in Super Symmetry; a
discussion of the non-perturbative renormalization methods for four-fermion
operators and a new approach to extract weak matrix elements in effective
theories denoted as OPE without OPE (operator product expansion without
operator product expansion)


title: The Schwinger Model with Perfect Staggered Fermions

abstract:
  We construct a new perfect action for free staggered fermions, which is more
local than the one obtained from the standard block average scheme. This pays
off in superior properties after a short ranged truncation. This action is
``gauged by hand'' and tested in Schwinger model simulations by means of a new
variant of hybrid MC. Using ``fat links'' for the gauge field, we obtain a tiny
``pion'' mass down to \beta \approx 1.5, and the ``eta'' mass follows very
closely the prediction of asymptotic scaling.


title: $f_B$ and $f_{B_s}$ using NRQCD

abstract:
  This talk summarizes the quenched calculation of $f_B$ and $f_{B_s}$
presented in hep-lat/9801038. The heavy quark is simulated using an $O(1/M^2)$
improved NRQCD action, and the tadpole improved clover action is used for the
light quarks. The axial current includes the $O(1/M)$ corrections in one-loop
perturbation theory and the $O(1/M^2)$ ones at tree-level. We discuss the
various systematic effects and consistency checks made in the calculation.


title: Wilson versus Clover fermions: A case for improvement

abstract:
  We present evidence for improvement with tadpole improved clover fermions
based on an analysis of the chiral behavior of $B_K$ and the quark condensate.
Also presented are a comparison of the mass splittings in the baryon octet and
decuplet, a calculation of $c_A$ using standard 2-point correlation functions,
and the problem of zero modes of the Dirac operator.


title: Domain wall fermions in vector gauge theories

abstract:
  I review domain wall fermions in vector gauge theories. Following a brief
introduction, the status of lattice calculations using domain wall fermions is
presented. I focus on results from QCD, including the light quark masses and
spectrum, weak matrix elements, the $n_f=2$ finite temperature phase
transition, and topology and zero modes and conclude with topics for future
study.


title: Non-perturbative Renormalization Constants using Ward Identities

abstract:
  We extend the application of vector and axial Ward identities to calculate
$b_A$, $b_P$ and $b_T$, coefficients that give the mass dependence of the
renormalization constants of the corresponding bilinear operators in the
quenched theory. The extension relies on using operators with non-degenerate
quark masses. It allows a complete determination of the $O(a)$ improvement
coefficients for bilinears in the quenched approximation using Ward Identities
alone. Only the scale dependent normalization constants $Z_P^0$ (or $Z_S^0$)
and $Z_T$ are undetermined. We present results of a pilot numerical study using
hadronic correlators.


title: Topological Susceptibility and Zero Mode Size in Lattice QCD

abstract:
  We use the overlap formalism to define a topological index on the lattice. We
study the spectral flow of the hermitian Wilson-Dirac operator and identify
zero crossings with topological objects. We determine the topological
susceptibility and zero mode size distribution, and we comment on the stability
of our results.


title:
Perturbative Renormalization Factors of Quark Bilinear Operators for
  Domain-wall QCD

abstract:
  We calculate one-loop renormalization factors of bilinear operators made of
physical quark fields for domain-wall QCD. We find that finite parts of such
renormalization factors have reasonable values at 1-loop except an overlap
factor between the physical quark field and the zero mode in the theory. We
point out that the 1-loop estimate of overall renormalization factors becomes
unreliable at the coupling where numerical simulations are currently performed,
due to the presence of this overlap factor. We show that this problem
disappears if the mean-field improved perturbation theory is employed for
renormalization factors.


title: Quark mass dependence of hadron masses from lattice QCD

abstract:
  We discuss lattice methods to obtain the derivatives of a lattice meson mass
with respect to the bare sea and valence quark masses. Applications are made to
quenched and dynamical fermion configurations. We find evidence for significant
differences between quenched and dynamical fermion configurations. We discuss
how to relate dependence on the bare lattice parameters to more
phenomenologically useful quantities.


title:
Numerical Study of the Gluon Propagator in Lattice Landau Gauge: the
  Three-Dimensional Case

abstract:
  We study the infrared behavior of the gluon propagator in lattice Landau
gauge, for pure SU(2) lattice gauge theory in a three-dimensional lattice.
Simulations are done for nine different values of the coupling $\beta$, from
$\beta = 0$ (strong coupling) to $\beta = 6.0$ (in the weak-coupling region).
In the limit of large lattice volumes, we observe in all cases a gluon
propagator decreasing as the momentum goes to zero.


title: Topical Results on Lattice Chiral Fermions in the CFA

abstract:
  We report new results on the lattice regularization of the chiral Schwinger
model and the chiral U(1) model in four dimensions in the CFA.


title: A note on the exact lattice chiral symmetry in the overlap formalism

abstract:
  Using the grassman-number-integral representation of the vacuum overlap
formula, it is shown that the symmetry of the auxiliary quantum fermion system
in the overlap formalism induces exact chiral symmetry of the action of the
type given by Luscher under the chiral transformation $\delta \psi_n =
\gamma_5(1-a D)\psi_n$ and $ \delta \bar \psi_n = \bar \psi_n \gamma_5$. With
this relation, we consider the connection between the covariant form of the
anomaly discussed in the context of the overlap formula and the axial anomaly
associated to the exact chiral symmetry in the action formalism. The covariant
gauge current in the overlap formalism is translated to the action formalism
and its explicit expression is obtained.


title:
Correction to four-loop RG functions in the two-dimensional lattice O(n)
  $\sigma$-model

abstract:
  We report the result of our evaluation of the Feynman diagrams appearing in
the determination of the four-loop renormalization group functions in the
two-dimensional lattice O($n$) $\sigma$-model by Caracciolo and Pelissetto. In
the list of the integrals used for the determination of those functions, we
find that three entries were not correctly evaluated. We give the values for
them corrected by us including those for all other integrals which we computed
with higher precision. These results are then applied to revise the
determination of the second analytic correction to correlation length $\xi$ and
spin susceptibility $\chi$ by Caracciolo et al. as well as our determination of
the mass gap by means of a finite volume technique where we explicitly made use
of the four-loop $\beta$-function. In both cases we find sizeable changes in
predictions. In the meantime there appeared a paper by Alles et al. where they
revised one finite integral in the list of our corrected integrals. After
having taken the new revised value into consideration, we found that there are
no noticeable changes in the perturbative predictions of the present paper
including the final conclusions.


title: Exact chiral symmetry, topological charge and related topics

abstract:
  It has been shown recently that Dirac operators satisfying the
Ginsparg-Wilson relation provide a solution of the chirality problem in QCD at
finite lattice spacing. We discuss different ways to construct these operators
and their properties. The possibility to define lattice chiral gauge theories
is briefly discussed as well.


title: Pseudo-Character Expansions for U(N)-Invariant Spin Models on CP^{N-1}

abstract:
  We define a set of orthogonal functions on the complex projective space
CP^{N-1}, and compute their Clebsch-Gordan coefficients as well as a large
class of 6-j symbols. We also provide all the needed formulae for the
generation of high-temperature expansions for U(N)-invariant spin models
defined on CP^{N-1}.


title: Effects of Nonperturbative Improvement in Quenched Hadron Spectroscopy

abstract:
  We discuss a comparative analysis of unimproved and nonperturbatively
improved quenched hadron spectroscopy, on a set of 104 gauge configurations, at
beta=6.2. We also present here our results for meson decay constants, including
the constants f_D and f_Ds in the charm-quark region.


title:
Large-q expansion of the energy cumulants for the two-dimensional
  q-state Potts model

abstract:
  We have calculated the large-q expansion for the energy cumulants at the
phase transition point in the two-dimensional q-state Potts model to the 23rd
order in $1/\sqrt{q}$ using the finite lattice method. The obtained series
allow us to give very precise estimates of the cumulants for $q>4$ on the first
order transition point. The result confirm us the correctness of the conjecture
by Bhattacharya et al. on the asymptotic behavior of the cumulants for $q \to
4_+$.


title:
Anisotropic Improved Gauge Actions; --Perturbative and Numerical Studies
  --

abstract:
  The $\Lambda$ parameter on the anisotropic lattice, the spatial and
temperature coupling constant $g_{\sigma}$, $g_{\tau}$ and their derivative
with respaect to the the anisotropy parameter $\xi$ are studied perturbatively
for the class of improved actions, which cover tree level Symanzik's, Iwasaki's
and QCDTARO's improved actions. The $\eta(=g_{\tau}/g_{\sigma})$ becomes less
than 1 for Iwasaki's and QCDTARO's action, which is confirmed nonperturbatively
by numerical simulations. Derivatives of the coupling constants with respect to
the anisotropy parameter, $\partial g_{\tau}/\partial \xi$ and $\partial
g_{\sigma}/\partial \xi$, change sign for those improved actions.


title: Transport Coefficients of Quark Gluon Plasma From Lattice Gauge Theory

abstract:
  Numerical results for the transport coefficients of quark gluon plasma are
obtained by lattice simulations on on $16^3 \times 8$ lattice with the quench
approximation where we apply the gauge action proposed by Iwasaki. The bulk
viscosity is consistent with zero, and the shear viscosity is slightly smaller
than the typical hadron masses. They are not far from the simple extrapolation
on the figure of perturbative calculation in high temperature limit down to $T
\sim T_{c}$. The gluon propagator in the confined and deconfined phases are
also discussed.


title: Parallel Tempering in Lattice QCD with O(a)-Improved Wilson Fermions

abstract:
  We present details of our investigation of the Parallel Tempering algorithm.
We consider the application of action matching technology to the selection of
parameters. We then present a simple model of the autocorrelations for a
particular parallel tempered system. Finally we present numerical results from
applying the algorithm to lattice QCD with O(a)-improved dynamical fermions
with twin ensemble systems


title: Local topological and chiral properties of QCD

abstract:
  To elucidate the role played by instantons in chiral symmetry breaking, we
explore their properties in full QCD, around the critical temperature. We study
in particular spatial correlations between low-lying Dirac eigenmodes and
instantons. Our measurements are compared with the predictions of
instanton-based models.


title:
High-Accuracy Calculations of the Critical Exponents of Dyson's
  Hierarchical Model

abstract:
  We calculate the critical exponent gamma of Dyson's hierarchical model by
direct fits of the zero momentum two-point function, calculated with an Ising
and a Landau-Ginzburg measure, and by linearization about the Koch-Wittwer
fixed point. We find gamma= 1.299140730159 plus or minus 10^(-12). We extract
three types of subleading corrections (in other words, a parametrization of the
way the two-point function depends on the cutoff) from the fits and check the
value of the first subleading exponent from the linearized procedure. We
suggest that all the non-universal quantities entering the subleading
corrections can be calculated systematically from the non-linear contributions
about the fixed point and that this procedure would provide an alternative way
to introduce the bare parameters in a field theory model.


title: Light hadron spectrum with Kogut-Susskind quarks

abstract:
  We made an extensive study of the light hadron spectrum using the Wilson
gauge action and Kogut-Susskind quarks. Using both dynamical quarks and the
quenched approximation, we determine hadron masses for five and four gauge
couplings respectively, with at least five quark masses at each coupling. In
the continuum limit, we find a significant difference between two flavors of
dynamical quarks and the quenched approximation for a range of quark masses.


title: Baryonic thermal fluctuations in finite temperature QCD

abstract:
  We show how, contrary to physical intuition, thermal fluctuations of physical
states having a non-vanishing baryonic number can be fully neglected in the
thermodynamics of QCD at any physical temperature. We also discuss on the
consistency between our results and the CPT theorem. The last part of this
article is devoted to comment some interesting physical features which follow
from this result.


title: To what distances do we know the confining potential?

abstract:
  We argue that asymptotically linear static potential is built in into the
common procedure of extracting it from lattice Wilson loop measurements. To
illustrate the point, we extract the potential by the standard lattice method
in a model vacuum made of instantons. A beautiful infinitely rising linear
potential is obtained in the case where the true potential is actually
flattening. We argue that the flux tube formation might be also an artifact of
the lattice procedure and not necessarily a measured physical effect.
  We conclude that at present the rising potential is known for sure up to no
more than about 0.7 fm. It may explain why no screening has been clearly
observed so far for adjoint sources and for fundamental sources but with
dynamical fermions.
  Finally, we speculate on how confinement could be achieved even if the static
potential in the pure glue theory is not infinitely rising.


title: Gauge Fixing and the Gibbs Phenomenon

abstract:
  We address the question of why global gauge fixing, specifically to the
lattice Landau gauge, becomes an extremely lengthy process for large lattices.
We construct an artificial "gauge-fixing" problem which has the essential
features encountered in actuality. In the limit in which the size of the system
to be gauge fixed becomes infinite, the problem becomes equivalent to finding a
series expansion in functions which are related to the Jacobi polynomials. The
series converges slowly, as expected. It also converges non-uniformly, which is
an observed characteristic of gauge fixing. In the limiting example, the
non-uniformity arises through the Gibbs phenomenon.


title: Lattice Study of $U_{A}(1)$ Anomaly: The Role of QCD-Monopoles

abstract:
  We investigate the role of QCD-monopoles for the $U_{A}(1)$ anomaly in the
maximally abelian gauge within the SU(2) lattice gauge theory. The existence of
the strong correlation between instantons and QCD-monopoles in the abelian
gauge was already shown by both analytic and numerical works including the
Monte Carlo simulation. Their interrelation brings us a conjecture that the
presence of QCD-monopoles plays a considerable role on the $U_{A}(1)$ anomaly.
We find an evidence for our conjecture on a determination of the fermionic zero
modes of the Dirac operator in both the ``monopole removed'' gauge
configuration and the ``photon removed'' gauge configuration.


title: Estimated Errors in |Vcd|/|Vcs| from Semileptonic D Decays

abstract:
  We estimate statistical and systematic errors in the extraction of the CKM
ratio |Vcd|/|Vcs| from exclusive D-meson semileptonic decays using lattice QCD
and anticipated new experimental results.


title: B -> pi l nu at three lattice spacings

abstract:
  The increasing accuracy of experimental results for the exclusive,
semileptonic decay B -> pi l nu requires a similarly accurate calculation of
the hadronic matrix elements, to determine |Vub|. We present preliminary
results for the form factors of the B to light meson decay mode. Using results
from three lattices in the range 5.7 <= beta <= 6.1 we study the dependence on
the lattice spacing.


title: Renormalization of Currents for Massive Fermions

abstract:
  The renormalization of vector and axial-vector currents for massive fermions
(in the ``Fermilab formalism'') is discussed. We give results for
non-degenerate masses, which are needed for semi-leptonic form factors.


title: Recent Results from the CP-PACS Collaboration

abstract:
  We present an overview of recent results from the CP-PACS computer on the
quenched light hadron spectrum and an on-going two-flavour full QCD study. We
find that our quenched hadron mass results are compatible with the mass
formulae predicted by quenched chiral perturbation theory, which we adopt in
our final analysis. Quenched hadron masses in the continuum limit show
unambiguous and systematic deviations from experiment. For our two-flavour full
QCD simulation we present preliminary results on the light hadron spectrum,
quark masses and the static potential. The question of dynamical sea quark
effects in these quantities is discussed.


title: On the Analog Strong CP Problem in the $CP^{N-1}$ Models

abstract:
  Addressed is the question of whether a natural mechanism exists to resolve
the strong CP problem. The analogous issue for the two-dimensional $CP^{N-1}$
models is analyzed using computer simulations.


title: Spectrum of the Hermitian Wilson Dirac operator

abstract:
  Recent results on the spectral properties of the Hermitian Wilson-Dirac
operator are presented.


title:
Improving QCD with fermions: the 2 dimensional case of QCD with Sea
  Quarks

abstract:
  We study QCD in 2 dimensions using the improved lattice fermionic Hamiltonian
proposed by Luo, Chen, Xu and Jiang. The vector mass and the chiral condensate
are computed for various $SU(N_C)$ gauge groups. We do observe considerable
improvement in comparison with the Wilson quark case.


title:
Perturbative matching of lattice and continuum heavy-light currents with
  NRQCD heavy quarks

abstract:
  The temporal and spatial components of the heavy-light vector current and the
spatial components of the axial current are expressed in terms of
lattice-regulated operators suitable for simulations of B and D mesons. The
currents are constructed by matching the appropriate scattering amplitudes in
continuum QCD and a lattice model to one-loop order in perturbation theory. In
the lattice theory, the heavy quarks are treated using the nonrelativistic
(NRQCD) formulation and the light quarks are described by the tadpole-improved
clover action. The light quarks are treated as massless. Our currents include
relativistic and discretization corrections through O(alpha_s/M, a alpha_s),
where M is the heavy-quark mass, a is the lattice spacing, and alpha_s is the
QCD coupling. As in our previous construction of the temporal component of the
heavy-light axial current, mixing between several lattice operators is
encountered at one-loop order, and O(a alpha_s) dimension-four improvement
terms are identified.


title:
Large-$q$ expansion of the two-dimensional $q$-state Potts model by the
  finite lattice method

abstract:
  We have calculated the large-$q$ expansion for the energy and magnetization
cumulants at the first order phase transition point in the two-dimensional
$q$-state Potts model to the 21st or 23rd order in $1/\sqrt{q}$ using the
finite lattice method. The obtained series allow us to give highly convergent
estimates of the cumulants for $q>4$. The results confirm us the correctness of
the conjecture by Bhattacharya {\em et al.} on the asymptotic behavior of the
energy cumulants for $q \to 4_+$ and a similar new conjecture on the
magnetization cumulants.


title:
Simulating Four-Dimensional Simplicial Gravity using Degenerate
  Triangulations

abstract:
  We extend a model of four-dimensional simplicial quantum gravity to include
degenerate triangulations in addition to combinatorial triangulations
traditionally used. Relaxing the constraint that every 4-simplex is uniquely
defined by a set of five distinct vertexes, we allow triangulations containing
multiply connected simplexes and distinct simplexes defined by the same set of
vertexes. We demonstrate numerically that including degenerated triangulations
substantially reduces the finite-size effects in the model. In particular, we
provide a strong numerical evidence for an exponential bound on the entropic
growth of the ensemble of degenerate triangulations, and show that a
discontinuous crumpling transition is already observed on triangulations of
volume N_4 ~= 4000.


title: Super-heavy Quarkonia and the Gluon Condensate

abstract:
  The early idea that a non-perturbative gluon condensate affects the spectrum
of heavy quarks is revisited in the light of modern simulation techniques. We
evaluate the low lying spectrum of bound states of two heavy quarks for large
hypothetical quark mass, m_Q > m_b, using non-relativistic QCD and compare with
other models to test the consistency.


title:
Discretization Errors and Rotational Symmetry: The Laplacian Operator on
  Non-Hypercubical Lattices

abstract:
  Discretizations of the Laplacian operator on non-hypercubical lattices are
discussed in a systematic approach. It is shown that order $a^2$ errors always
exist for discretizations involving only nearest neighbors. Among all lattices
with the same density of lattice sites, the hypercubical lattices always have
errors smaller than other lattices with the same number of spacetime
dimensions. On the other hand, the four dimensional checkerboard lattice (also
known as the Celmaster lattice) is the only lattice which is isotropic at order
$a^2$. Explicit forms of the discretized Laplacian operators on root lattices
are presented, and different ways of eliminating order $a^2$ errors are
discussed.


title: GW fermion propagators and chiral condensate

abstract:
  By exploiting the chiral symmetry, we derive analytic formulas for the
massless and the massive Ginsparg-Wilson fermion propagators. Using these
formulas, we derive an expression for the chiral condensate which is the order
parameter for spontaneous chiral symmetry breaking in QCD. These formulas
provide the proper way to compute the fermion propagators and may save a
significant amount of computing time especially for large lattices in four
dimensions.


title: Instantons, the QCD Vacuum, and Hadronic Physics

abstract:
  A large body of evidence from lattice calculations indicates that instantons
play a major role in the physics of light hadrons. This evidence is summarized,
and recent results concerning the instanton content of the SU(3) vacuum,
instanton contributions to the static potential, and a new class of instanton
solutions at finite temperature are reviewed.


title: Recent results on light hadron and quark masses

abstract:
  Recent results for the spectrum of light hadrons provide clear evidence for
the failure of quenched QCD and encouraging signs that simulations with
dynamical sea quarks rectify some of the discrepancies, although string
breaking has not yet been observed. The use of perturbation theory to match
lattice quark masses to continuum schemes remains questionable, but
non-perturbative methods are poised to remove this uncertainty. The inclusion
of dynamical sea quarks substantially reduces estimates of the light quark
masses. New results for the lightest glueball and the lightest exotic hybrid
state provide useful input to phenomenology, but still have limited or no
treatment of mixing. The $O(a)$-improved Wilson quark action is
well-established in quenched QCD for $\beta\geq 5.7$, with most parameters
obtainable non-perturbatively, in which range scaling violations are small.
Progress has also been made with high-order improvement schemes for both Wilson
and staggered quarks.


title: Field transformation and Monte Carlo simulations

abstract:
  A new method to compute observables at many values of the parameters \lambda
for a model with lattice action {\cal{S}}(\phi, \lambda) is described. After
fixing a reference set \lambda^r of parameters, a single simulation is carried
out by using a ``reference action'' {\cal{S}} (\phi^r, \lambda^r) to generate
configurations of the field \phi^r. Then a suitable analytic transformation is
performed from the configurations of \phi^r to the ones corresponding to the
action {\cal{S}} (\phi, \lambda). Such a transformation allows to obtain the
observables for values of the parameters \lambda close to \lambda^r. I present
studies on the reliability of the algorithm in the case of the \phi^4 model in
2 dimensions.


title: B -> D l nu form factors and the determination of |Vcb|

abstract:
  The zero recoil limit of the B -> D l nu form factors is calculated on the
lattice, which provides a model-independent determination of |Vcb|. Considering
a ratio of form factors, in which the bulk of statistical and systematic errors
cancel, we obtain a precise result both for h_+(1) and for h_-(1).


title: Effects of Chemical Potential on Hadron Masses at Finite Temperature

abstract:
  We study the effects of the chemical potential on the $\rho$ meson mass at
finite temperature. Our preliminary results show that some effects are seen in
the vicinity of the phase transition point. Although the signal is still too
noisy to obtain conclusive physical results within limited statistics, the mass
susceptibility is consistent with zero.


title: Pseudoscalar Vertex, Goldstone Boson and Quark Masses on the Lattice

abstract:
  We analyse the Structure Function collaboration data on the quark
pseudoscalar vertex and extract the Goldstone boson pole contribution, in 1/p2.
The strength of the pole is found to be quite large at presently accessible
scales. We draw the important consequences of this finding for the various
definitions of quark masses, and point out potential problems with the operator
product expansion.


title:
QCD, Supersymmetric QCD, Lattice QCD and String Theory: Synthesis on the
  Horizon?

abstract:
  Supersymmetric gauge theories in four dimensions have taught us many
important physics lessons. These can both inform and be informed by future work
on the lattice. I focus on three issues: the properties of supersymmetric
Yang-Mills theory and its relation to the non-supersymmetric case; the
properties of gauge theories with matter and their relation to real QCD; and,
briefly, the recent discovery that gauge theories and string theories are more
deeply connected than ever previously realized. Specific questions for lattice
gauge theorists to consider are raised in the context of the first two topics.


title: Microscopic Spectral Density of the Dirac Operator in Quenched QCD

abstract:
  Measurements of the lowest-lying eigenvalues of the staggered fermion Dirac
operator are made on ensembles of equilibrium gauge field configurations in
quenched SU(3) lattice gauge theory. The results are compared with exact
analytical predictions in the microscopic finite-volume scaling regime.


title:
Investigating and Optimizing the Chiral Properties of Lattice Fermion
  Actions

abstract:
  We study exceptional modes of both the Wilson and the clover action in order
to understand why quenched clover spectroscopy suffers so severely from
exceptional configurations. We show that, in contrast to the case of the Wilson
action, a large clover coefficient can make the exceptional modes extremely
localized and thus very sensitive to short distance fluctuations. We describe a
way to optimize the chiral behavior of Wilson-type lattice fermion actions by
studying their low energy real eigenmodes. We find a candidate action, the
clover action with fat links with a tuned clover term. We present a calculation
of spectroscopy and matrix elements at Wilson gauge coupling beta=5.7. When
compared to simulations with the standard (nonperturbatively improved) clover
action at small lattice spacing, the action shows good scaling behavior, with
an apparent great reduction in the number of exceptional configurations.


title:
Evidence for discrete chiral symmetry breaking in N=1 supersymmetric
  Yang-Mills theory

abstract:
  In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with
dynamical gauginos we find evidence for two degenerate ground states at the
supersymmetry point corresponding to zero gaugino mass. This is consistent with
the expected pattern of spontaneous discrete chiral symmetry breaking $Z_4 \to
Z_2$ caused by gaugino condensation.


title: Non-perturbative quark mass renormalization in quenched lattice QCD

abstract:
  The renormalization factor relating the bare to the renormalization group
invariant quark masses is accurately calculated in quenched lattice QCD using a
recursive finite-size technique. The result is presented in the form of a
product of a universal factor times another factor, which depends on the
details of the lattice theory but is easy to compute, since it does not involve
any large scale differences. As a byproduct the Lambda-parameter of the theory
is obtained with a total error of 8%.


title: On the Neuberger overlap operator

abstract:
  We compute Neuberger's overlap operator by the Lanczos algorithm applied to
the Wilson-Dirac operator. Locality of the operator for quenched QCD data and
its eigenvalue spectrum in an instanton background are studied.


title: Status of Heavy Quark Physics on the Lattice

abstract:
  The status of lattice calculations of some phenomenology of heavy quarks is
presented. Emphasis is on progress made in calculating those quantities
relevant to estimating parameters of the quark mixing matrix, namely leptonic
decay constants, the bag parameter of neutral $B$ mixing, and semileptonic form
factors. New results from studies of quarkonia are highlighted.


title: On Nambu Monopole Dynamics in the SU(2) Lattice Higgs Model

abstract:
  It is shown that the SU(2) Higgs model on a lattice is equivalent to the
Georgi--Glashow model in the limit of a small coupling constant between the
Higgs and gauge fields. It can therefore be concluded that the transition
between the confinement and symmetric phases in the 3+1 dimensional SU(2) Higgs
model at finite temperature is accompanied by condensation of Nambu monopoles.


title: Instanton Content of the SU(3) Vacuum

abstract:
  We study the topological content of the SU(3) vacuum using a method based on
RG mapping developed for SU(2) gauge theory earlier. RG mapping, in which a
series of APE-smearing steps is done while tracking the observables, reduces
the short range fluctuations in the gauge fields while preserving the long
structure. This allows us to study the instanton size distribution and
topological susceptibility for SU(3) gauge theory. We arrive at a value for the
topological susceptibility ${\chi}^{1/4}$, of 203(5) MeV. The size distribution
peaks at $\rho = 0.3fm$, and is in good agreement with the prediction of the
instanton liquid models.


title:
Abelian Monopoles and Action Density in SU(2) Gluodynamics on the
  Lattice

abstract:
  We show that the extended Abelian magnetic monopoles in the Maximal Abelian
projection of lattice SU(2) gluodynamics are locally correlated with the
magnetic and the electric parts of the SU(2) action density. These correlations
are observed in the confined and in the deconfined phases.


title:
Lattice study of the Kink soliton and the zero-mode problem for phi4 in
  two dimensions

abstract:
  We study the $\lambda\phi^4_{1+1}$ kink solion and the zero-mode contribution
to the Kink soliton mass in regions beyond the semiclassical regime. The
calculations are done in the non-trivial scaling region and where appropriate
the results are compared with the continuum, semiclassical values. We show, as
a function of parameter space, where the zero-mode contributions become
significant.


title:
Non-perturbatively Improved Heavy-Light Mesons: Masses and Decay
  Constants

abstract:
  We present a study of the heavy-light spectrum and of the D- and B-meson
decay constants. The results wer e obtained in the quenched approximation, by
using the non-perturbatively improved Clover lattice action at beta=6.2, with a
sample of 100 configurations, on a 24^3 x 64 lattice. After a careful analysis
of th e systematic errors present in the extraction of the physical results, by
assuming quite conservative discretization errors, we find f_Ds=231 +/-
12^{+6}_{-1} MeV, f_D = 211 +/- 14^{+0}_{-12} MeV, f_Ds/f_D=1.10(2), f_Bs = 204
+/- 16^{+28}_{-0} MeV, f_B = 179 +/- 18^{+26}_{-9} MeV,
f_Bs/f_B=1.14(3)^{+0}_{-1}. Our results, which have smaller discretization
errors than many previous estimates at fixed value of the lattice spacing $a$,
support a large value of f_B in the quenched approximation.


title: The Phase Diagram of Three-Dimensional SU(3) + Adjoint Higgs Theory

abstract:
  We study the phase diagram of the three-dimensional SU(3)+adjoint Higgs
theory with lattice Monte Carlo simulations. A critical line consisting of a
first order line, a tricritical point and a second order line, divides the
phase diagram into two parts distinguished by <Tr A0^3>=0 and /=0. The location
and the type of the critical line are determined by measuring the condensates
<Tr A0^2> and <Tr A0^3>, and the masses of scalar and vector excitations.
Although in principle there can be different types of broken phases,
corresponding perturbatively to unbroken SU(2)xU(1) or U(1)xU(1) symmetries, we
find that dynamically only the broken phase with SU(2)xU(1)-like properties is
realized. The relation of the phase diagram to 4d finite temperature QCD is
discussed.


title: Continuum Limit of Scalar Masses and Mixing Energies

abstract:
  We evaluate the continuum limit of the valence approximation to the mass of
scalar quarkonium and to the scalar quarkonium-glueball mixing energy for a
range of different quark masses. Our results answer several questions raised by
the proposed identification of $f_0(1710)$ as composed primarily of the
lightest scalar glueball.


title: Progress in Lattice Gauge Theory

abstract:
  I summarize recent progress in lattice gauge theory, with particular emphasis
on results from numerical simulations. A major success has been the
determination of the light hadron spectrum in the quenched approximation with
sufficient accuracy to expose statistically significant disagreements with the
experimental spectrum. The differences are, however, fairly small, $\sim
5-10%$. The data are also accurate enough to show evidence for artifacts of
quenching predicted by chiral perturbation theory. I give an update on results
for light quark masses, the kaon B-parameter, and the decay constants and
B-parameters of heavy-light mesons. Most of these are known in the quenched
approximation to $\sim 10%$ accuracy or better, and preliminary estimates of
quenching errors are of comparable size. One exception is the light quark
masses, for which the quenching errors appear to be larger. I discuss the
computational requirements for simulations of QCD with all approximations
controlled, and argue that they will likely begin once computers sustain about
10 Teraflops. This is 30-40 times faster than present state-of-the-art
machines. This estimate assumes that improvements in the discretization of
lattice fermions are sufficient to allow continuum extrapolations to be made
with a minimum lattice spacing of $\approx 0.1 $fm. I review results obtained
with improved discretizations and conclude that they satisfy this requirement
in most cases. Examples of successful improvement include the calculation of
the glueball spectrum and excited heavy-quark potentials in pure Yang-Mills
theory. Finally, I discuss recent developments which may allow simulations of
QCD with full chiral symmetry even at finite lattice spacing.


title:
One loop renormalization for the axial Ward-Takahashi identity in
  Domain-wall QCD

abstract:
  We calculate one-loop correction to the axial Ward-Takahashi identity given
by Furman and Shamir in domain-wall QCD. It is shown perturbatively that the
renormalized axial Ward-Takahashi identity is satisfied without fine tuning and
the ``conserved'' axial current receives no renormalization, giving $Z_A=1$.
This fact will simplify the calculation of the pion decay constant in numerical
simulations since the decay constant defined by this current needs no lattice
renormalization factor.


title:
Hybrid Monte Carlo algorithm for lattice QCD with two flavors of
  dynamical Ginsparg-Wilson quarks

abstract:
  We study aspects concerning numerical simulations of Lattice QCD with two
flavors of dynamical Ginsparg-Wilson quarks with degenerate masses. A Hybrid
Monte Carlo algorithm is described and the formula for the fermionic force is
derived for two specific implementations. The implementation with optimal
rational approximation method is favored both in CPU time and memory
consumption.


title: Lattice Approach to the $\Delta I=1/2$ Rule

abstract:
  We discuss a number of old and new methods for computing $K\to\pi\pi$
amplitudes on the lattice. They all involve a non-perturbative determination of
matching coefficients. We show how problems related to operator mixing can be
greatly reduced by using point-split hadronic currents.


title: Hadrons with a heavy colour-adjoint particle

abstract:
  We discuss the spectrum of hadrons with a heavy colour-adjoint particle -
motivated by the gluino of supersymmetry. Using the lattice approach, we
explore in detail the gluonic bound states - the `glueballino' or `gluelump'.
We also make a first determination of the spectrum of the `adjoint mesons' -
which have a light quark and antiquark bound to the heavy adjoint particle. A
comparison of the spectra of these two systems is also made.


title: QCD with zero, two and four flavors of light quarks - results from QCDSP

abstract:
  We present the results from full QCD simulations with four flavors of light
stag gered dynamical quarks on {\it {\it QCDSP}} supercomputer. Previous
results are reproduced and the simulation reported here yields new results
consistent with o ur previous runs. The hadron spectrum obtained with Wilson
valence fermions reported here will allow us to determine if our earlier
conclusions are independent of lattice form alism.


title: String-breaking in quenched QCD

abstract:
  We present results on a new operator for the investigation of string-breaking
effects in quenched SU(2)-colour QCD. The ground state of a spatially-separated
static-light meson-antimeson pair is a combination of a state with two distinct
mesons, expected to dominate for large separations, and a state where the light
quarks have annihilated, which contributes at short distances. The cross-over
between these two regimes provides the string-breaking scale.


title: The domain wall fermion chiral condensate in quenched QCD

abstract:
  We examine the chiral limit of domain wall fermions in quenched QCD. One
expects that in a quenched simulation, exact fermion zero modes will give a
divergent, 1/m behavior in the chiral condensate for sufficiently small valence
quark masses. Unlike other fermion formulations, domain wall fermions clearly
demonstrate this behavior.


title:
Loop representation for 2-D Wilson lattice fermions in a scalar
  background field

abstract:
  We show that the fermion determinant for 2-D Wilson lattice fermions coupled
to an external scalar field is equivalent to self avoiding loops interacting
with the external field. In an application of the resulting formula we
integrate the scalar field with a Gaussian action to generate the N-component
Gross-Neveu model. The loop representation for this model is discussed.


title: Interaction potential in compact three-dimensional QED with mixed action

abstract:
  We use a variational wave function to calculate the energy of the interaction
between external charges in the compact Abelian gauge theory in 2+1 dimensions
with mixed action. Our variational wave functions preserve the compact gauge
invariance of the theory both in the vacuum and in the charged sectors. We find
that a good estimate of the interaction energy is obtained only when we allow
more variational parameters in the charged sector than in the vacuum sector.
These extra parameters are the profile of an induced electric field. We find
that the theory has a two-phase structure: When the charge-2 coupling is large
and negative there is no mass gap in the theory and no confinement, while
otherwise a mass gap is generated dynamically and the theory confines charges.
The pure Wilson theory is in the confining phase.


title: Lattice String Breaking and Heavy Meson Decays

abstract:
  We show how string breaking on the lattice, treated as a mixing effect, can
be related to decay rates for heavy quark systems. We use this to make a
preliminary calculation of the energy split at maximum mixing for static quarks
in QCD from the decay rate for $\Upsilon(4S)\to B{\bar B}$. We extend the
calculation to achieve rough estimates for the contributions of channels
involving $B, B^*, B_s and B_s^*$ mesons to the width of the $\Upsilon(5S)$.


title: Gauge-invariant nonlocal quark condensates in QCD

abstract:
  We study, by numerical simulations on a lattice, the behaviour of the
gauge-invariant nonlocal quark condensates in the QCD vacuum both in the
quenched approximation and with four flavours of dynamical staggered fermions.
The correlation length of the condensate is determined to be roughly twice as
big as in the case of the gluon field strength correlators.


title:
Small eigenvalues of the SU(3) Dirac operator on the lattice and in
  Random Matrix Theory

abstract:
  We have calculated complete spectra of the staggered Dirac operator on the
lattice in quenched SU(3) gauge theory for \beta = 5.4 and various lattice
sizes. The microscopic spectral density, the distribution of the smallest
eigenvalue, and the two-point spectral correlation function are analyzed. We
find the expected agreement of the lattice data with universal predictions of
the chiral unitary ensemble of random matrix theory up to a certain energy
scale, the Thouless energy. The deviations from the universal predictions are
determined using the disconnected scalar susceptibility. We find that the
Thouless energy scales with the lattice size as expected from theoretical
arguments making use of the Gell-Mann--Oakes--Renner relation.


title:
Minimizing storage in implementations of the overlap lattice-Dirac
  operator

abstract:
  The overlap lattice-Dirac operator contains the sign function $\epsilon (H)$.
Recent practical implementations replace $\epsilon (H)$ by a ratio of
polynomials, $H P_n (H^2)/Q_n (H^2)$, and require storage of $2n+2$ large
vectors. Here I show that one can use only 4 large vectors at the cost of
executing the core conjugate algorithm twice. The slow-down might be less than
by a factor of 2, depending on the architecture of the computer one uses.


title:
Finite Temperature LGT in a Finite Box with BPS Monopole Boundary
  Conditions

abstract:
  Finite temperature SU(2) lattice gauge theory is investigated in a 3D cubic
box with fixed boundary conditions (b.c.) provided by a discretized, static BPS
monopole solution with varying core scale ${\mu}$. For discrete ${\mu}$-values
we find stable classical solutions either of electro-magnetic ('dyon') or of
purely magnetic type inside the box. Near the deconfinement transition we study
the influence of the b.c. on the quantized fields inside the box. In contrast
to the purely magnetic background field case, for the dyon case we observe
confinement for temperatures above the usual critical one.


title: Exotica and the Confining Flux

abstract:
  Recent developments in Quantum Chromodynamics (QCD) are reviewed on three
major topics where nonperturbative gluon excitations of the QCD vacuum and the
physical properties of the confining flux play a central role: (1) New lattice
results on the spectrum and wave functions of heavy quark-antiquark molecules,
known as heavy hybrids, will be discussed. (2) Recent advances on the glueball
spectrum in lattice QCD will be presented with some theoretical observations.
(3) Progress in our understanding of the nonperturbative internal structure of
the confining flux and its excitation spectrum will be reported.


title: Passing through the `chiral limit' in quenched QCD with Wilson fermions

abstract:
  We investigate the limit of vanishing quark mass in quenched lattice QCD with
unimproved Wilson fermions at $\beta=6.0$. Exploiting the correlations of
propagators at different time slices we extract pion masses extremely close to
the `chiral limit', despite the presence of `exceptional configurations'. With
this at hand, the existence of quenched chiral logarithms can be demonstrated,
provided, finite size effects are small. With reference to the phase diagram
proposed by Aoki also the range $\kappa > \kappa_c$ is investigated. The width
of a potential parity-flavor violating phase can, if at all, hardly be
resolved.


title: Contents of Lattice 98 Proceedings

abstract:
  We give here a compilation of papers presented at Lattice 98 (XVI Intl.
Symposium on Lattice Field Theory, Boulder, Colorado, USA, 13-18 July 1998).
The contents are in html form with clickable links to the papers that exist on
the hep-lat archives. We hope that this will make it easier to access the
presentations at the conference. Comments on, and corrections to, this
compilation should be sent to degrand@aurinko.colorado.edu. Version 3: some
more additions to the list.


title:
Coupling Constant and Quark Loop Expansion for Corrections to the
  Valence Approximation

abstract:
  For full QCD vacuum expectation values we construct an expansion in quark
loop count and in powers of a coupling constant. The leading term in this
expansion is the valence (quenched) approximation vacuum expectation value.
Higher terms give corrections to the valence approximation. A test of the
expansion is presented for moderately heavy quarks on a small lattice. We
consider briefly an application of the expansion to quarkonium-glueball mixing.


title: Quantum Spins and Quantum Links: The D-Theory Approach to Field Theory

abstract:
  A new non-perturbative approach to quantum field theory is proposed. Instead
of performing a path integral over configurations of classical fields, D-theory
works with discrete quantized variables. Classical spin fields are replaced by
quantum spins, and classical gauge fields are replaced by quantum links. The
classical fields of a d-dimensional quantum field theory reappear as low-energy
effective degrees of freedom of the discrete variables, provided the
(d+1)-dimensional D-theory is massless. When the extent of the extra Euclidean
dimension becomes small in units of the correlation length, an ordinary
d-dimensional quantum field theory emerges by dimensional reduction. The
D-theory formulation of some spin models and gauge theories is constructed
explicitly. In particular, QCD emerges as a quantum link model.


title: Quenched QCD with domain wall fermions

abstract:
  We report on simulations of quenched QCD using domain wall fermions, where we
focus on basic questions about the formalism and its ability to produce
expected low energy hadronic physics for light quarks. The work reported here
is on quenched $8^3 \times 32$ lattices at $\beta = 5.7$ and 5.85, using values
for the length of the fifth dimension between 10 and 48. We report results for
parameter choices which lead to the desired number of flavors, a study of
undamped modes in the extra dimension and hadron masses.


title: Asymptotic Scaling and Infrared Behavior of the Gluon Propagator

abstract:
  The Landau gauge gluon propagator for the pure gauge theory is evaluated on a
32^3x64 lattice with a physical volume of (3.35^3x6.7)fm^4. Comparison with two
smaller lattices at different lattice spacings allows an assessment of finite
volume and finite lattice spacing errors. Cuts on the data are imposed to
minimize these errors. Scaling of the gluon propagator is verified between
beta=6.0 and beta=6.2. The tensor structure is evaluated and found to be in
good agreement with the Landau gauge form, except at very small momentum
values, where some small finite volume errors persist. A number of functional
forms for the momentum dependence of the propagator are investigated. The form
D(q^2)=D_ir+D_uv, where D_ir(q^2) ~ (q^2+M^2)^-\eta and D_uv is an infrared
regulated one-loop asymptotic form, is found to provide an adequate description
of the data over the entire momentum region studied - thereby bridging the gap
between the infrared confinement region and the ultraviolet asymptotic region.
The best estimate for the exponent \eta is 3.2(+0.1/-0.2)(+0.2/-0.3), where the
first set of errors represents the uncertainty associated with varying the
fitting range, while the second set of errors reflects the variation arising
from different choices of infrared regulator in D_uv. Fixing the form of D_uv,
we find that the mass parameter M is (1020+/-100)MeV.


title: The Deconfinement Phase Transition in One-Flavour QCD

abstract:
  We present a study of the deconfinement phase transition of one-flavour QCD,
using the multiboson algorithm. The mass of the Wilson fermions relevant for
this study is moderately large and the non-hermitian multiboson method is a
superior simulation algorithm. Finite size scaling is studied on lattices of
size $8^3\times 4$, $12^3\times 4$ and $16^3\times 4$. The behaviours of the
peak of the Polyakov loop susceptibility, the deconfinement ratio and the
distribution of the norm of the Polyakov loop are all characteristic of a
first-order phase transition for heavy quarks. As the quark mass decreases, the
first-order transition gets weaker and turns into a crossover. To investigate
finite size scaling on larger spatial lattices we use an effective action in
the same universality class as QCD. This effective action is constructed by
replacing the fermionic determinant with the Polyakov loop identified as the
most relevant Z(3) symmetry breaking term. Higher-order effects are
incorporated in an effective Z(3)-breaking field, $h$, which couples to the
Polyakov loop. Finite size scaling determines the value of $h$ where the first
order transition ends. Our analysis at the end - point, $h_{ep}$, indicates
that the effective model and thus QCD is consistent with the universality class
of the three dimensional Ising model.
  Matching the field strength at the end point, $h_{ep}$, to the $\kappa$
values used in the dynamical quark simulations we estimate the end point,
$\kappa_{ep}$, of the first-order phase transition. We find $\kappa_{ep}\sim
0.08 $ which corresponds to a quark mass of about 1.4 GeV .


title: Topological Aspect of Abelian Projected SU(2) Lattice Gauge Theory

abstract:
  We show that the hypothesis of abelian dominance allows QCD-monopoles to
preserve the topological feature of the QCD vacuum within SU(2) lattice gauge
theory. An analytical study is made to find the relationship between the
topological charge and QCD-monopoles in the lattice formulation. The
topological charge is explicitly represented in terms of the monopole current
and the abelian component of gauge fields in the abelian dominated system. We
numerically examine the relation and demonstrate the abelian dominance in the
topological structure by using Monte Carlo simulation.


title:
A study of chiral symmetry in quenched QCD using the Overlap-Dirac
  operator

abstract:
  We compute fermionic observables relevant to the study of chiral symmetry in
quenched QCD using the Overlap-Dirac operator for a wide range of the fermion
mass. We use analytical results to disentangle the contribution from exact zero
modes and simplify our numerical computations. Details concerning the numerical
implementation of the Overlap-Dirac operator are presented.


title:
Background Configurations, Confinement and Deconfinement on a Lattice
  with BPS Monopole Boundary Conditions

abstract:
  Finite temperature SU(2) lattice gauge theory is investigated in a 3D cubic
box with fixed boundary conditions provided by a discretized, static BPS
monopole solution with varying core scale $\mu$. Using heating and cooling
techniques we establish that for discrete $\mu$-values stable classical
solutions either of self-dual or of pure magnetic type exist inside the box.
Having switched on quantum fluctuations we compute the Polyakov line and other
local operators. For different $\mu$ and at varying temperatures near the
deconfinement transition we study the influence of the boundary condition on
the vacuum inside the box. In contrast to the pure magnetic background field
case, for the self-dual one we observe confinement even for temperatures quite
far above the critical one.


title: Abelian chiral gauge theories on the lattice with exact gauge invariance

abstract:
  It is shown that U(1) chiral gauge theories with anomaly-free multiplets of
Weyl fermions can be put on the lattice without breaking the gauge invariance
or violating any other fundamental principle. The Ginsparg-Wilson relation
plays a key role in this construction, which is non-perturbative and includes
all topological sectors of the theory in finite volume. In particular, the
cancellation of the gauge anomaly and the absence of global topological
obstructions can be established on the basis of this relation and the lattice
symmetries alone.


title: Rigorous arguments against current wisdoms in finite density QCD

abstract:
  QCD at finite chemical potential is analytically investigated in the region
of large bare fermion masses. We show that, contrary to the general wisdom, the
phase of the fermion determinant is irrelevant at zero temperature. However if
the system is put at finite temperature, the contribution of the phase is
finite. We also discuss on the quenched approximation and suggest that the
origin of the failure of this approximation in finite density QCD could relay
on the fundamental role that Pauli exclusion principle plays in this case.


title: Improved lattice QCD with quarks: the 2 dimensional case

abstract:
  QCD in two dimensions is investigated using the improved fermionic lattice
Hamiltonian proposed by Luo, Chen, Xu, and Jiang. We show that the improved
theory leads to a significant reduction of the finite lattice spacing errors.
The quark condensate and the mass of lightest quark and anti-quark bound state
in the strong coupling phase (different from t'Hooft phase) are computed. We
find agreement between our results and the analytical ones in the continuum.


title:
Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in the
  Maximally Abelian Gauge in Lattice QCD

abstract:
  We study effective mass generation of off-diagonal gluons and infrared
abelian dominance in the maximally abelian (MA) gauge. Using the SU(2) lattice
QCD, we investigate the propagator and the effective mass of the gluon field in
the MA gauge with the U(1)$_3$ Landau gauge fixing. The Monte Carlo simulation
is performed on the $12^3 \times 24$ lattice with $2.2 \le \beta \le 2.4$, and
also on the $16^4$ and $20^4$ lattices with $2.3 \le \beta \le 2.4$. In the MA
gauge, the diagonal gluon component $A_\mu^3$ shows long-range propagation, and
infrared abelian dominance is found for the gluon propagator. In the MA gauge,
the off-diagonal gluon component $A_\mu^\pm$ behaves as a massive vector boson
with the effective mass $M_{\rm off} \simeq 1.2$ GeV in the region of $r \gsim
0.2$ fm, and its propagation is limited within short range. We conjecture that
infrared abelian dominance can be interpreted as infrared inactivity of the
off-diagonal gluon due to its large mass generation induced by the MA gauge
fixing.


title: MDP_QCD: Object Oriented Programming for Lattice Gauge Theory

abstract:
  This is a manual (built by examples) to explain the use of MDP_QCD. It
consists of an ensemble of classes and functions (written in GNU C++) to help
in writing programs for lattice QCD in a particularly Object Oriented fashion.
Some tricks are implemented to optimize speed and reduce memory usage on PCs,
workstations and parallel computers with sheared memory. The basic classes are:
Matrix, gauge_field, fermi_field and stochastic light_propagators (the code
works for any SU(N) gauge group).


title:
Computation of the b-quark Mass with Perturbative Matching at the
  Next-to-Next-to-Leading Order

abstract:
  We compute the two-loop term in the perturbation series for the quark-mass in
the lattice Heavy Quark Effective Theory. This is an ingredient in the matching
factor required to obtain the $b$-quark mass from lattice simulations of the
HQET. Combining our calculations with numerical results from the APE
collaboration, we find, at two-loop order, $\bar m_b \equiv
m_b^{\bar{MS}}(m_b^{\bar{MS}}) =4.41\pm 0.05\pm 0.10 $GeV. It was expected that
the two-loop term would have a significant effect and this is indeed what we
find. Depending on the choice of "reasonable" coupling constant in the one-loop
estimates the result for $\bar m_b$ can change by several hundred MeV when the
two-loop terms are included.


title: Ginsparg-Wilson Relation and Lattice Supersymmetry

abstract:
  The Ginsparg-Wilson(G-W) relation is extended for supersymmetric free
theories on a lattice.
  Exact lattice supersymmetry(SUSY) can be defined without any ambiguities in
difference operators. The lattice action constructed by a block-spin
transformation is invariant under the symmetry. $U(1)_R$ 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. It is argued that the relation may be generalized
for interacting cases.


title:
Axial anomaly and topological charge in lattice gauge theory with
  Overlap Dirac operator

abstract:
  An explicit, detailed evaluation of the classical continuum limit of the
axial anomaly/index density of the overlap Dirac operator is carried out in the
infinite volume setting, and in a certain finite volume setting where the
continuum limit involves an infinite volume limit. Our approach is based on a
novel power series expansion of the overlap Dirac operator. The correct
continuum expression is reproduced when the parameter $m_0$ is in the physical
region $0<m_0<2$. This is established for a broad range of continuum gauge
fields. An analogous result for the fermionic topological charge, given by the
index of the overlap Dirac operator, is then established for a class of
topologically non-trivial fields in the aforementioned finite volume setting.
Problematic issues concerning the index in the infinite volume setting are also
discussed.


title: The Phase Structure of the Weakly Coupled Lattice Schwinger Model

abstract:
  The weak coupling expansion is applied to the single flavour Schwinger model
with Wilson fermions on a symmetric toroidal lattice of finite extent. We
develop a new analytic method which permits the expression of the partition
function as a product of pure gauge expectation values whose zeroes are the
Lee-Yang zeroes of the model. Application of standard finite-size scaling
techniques to these zeroes recovers previous numerical results for the small
and moderate lattice sizes to which those studies were restricted. Our
techniques, employable for arbitrarily large lattices, reveal the absence of
accumulation of these zeroes on the real hopping parameter axis at constant
weak gauge coupling. The consequence of this previously unobserved behaviour is
the absence of a zero fermion mass phase transition in the Schwinger model with
single flavour Wilson fermions at constant weak gauge coupling.


title: On the Universality Class of Monopole Percolation in Scalar QED

abstract:
  We study the critical properties of the monopole-percolation transition in
U(1) lattice gauge theory coupled to scalars at infinite ($\beta=0$) gauge
coupling. We find strong scaling corrections in the critical exponents that
must be considered by means of an infinite-volume extrapolation. After the
extrapolation, our results are as precise as the obtained for the four
dimensional site-percolation and, contrary to previously stated, fully
compatible with them.


title: Cooling, Physical Scales and Topology

abstract:
  We develop a cooling method controlled by a physical cooling radius that
defines a scale below which fluctuations are smoothed out while leaving physics
unchanged at all larger scales. We apply this method to study topological
properties of lattice gauge theories, in particular the behaviour of
instantons, dislocations and instanton--anti-instanton pairs. Monte Carlo
results for the SU(2) topology are presented. We find that the method provides
a means to prevent instanton--anti-instanton annihilation under cooling. While
the instanton sizes are largely independent from the smoothing scale, the
density and pair separations are determined by the particular choice made for
this quantity. We discuss the questions this raises for the "physicality" of
these concepts.


title:
$O(a\alpha_s)$ matching coefficients for the $\Delta B$=2 operators in
  the lattice static theory

abstract:
  We present the perturbative matching coefficient to $O(a\alpha_s)$ which
relates the $\Delta B$=2 operator in the continuum to that of the lattice
static theory, which is important in the accurate extraction of the continuum
value of the $B_B$ from lattice simulations. The coefficients are obtained by
the one-loop calculations in both of the continuum and lattice theory. We find
that two new dimension seven operators appear at the $O(a\alpha_s)$ with the
O(1) coefficients. We also discuss the possible cancellation of $O(a\alpha_s)$
correction in the ratio $B_B=<\bar{B}|\Op_L|B>/ ((8/3)(f_{B}M_{B})^2)$
qualitatively.


title: Mesonic decay constants in lattice NRQCD

abstract:
  Lattice NRQCD with leading finite lattice spacing errors removed is used to
calculate decay constants of mesons made up of heavy quarks. Quenched
simulations are done with a tadpole improved gauge action containing plaquette
and six-link rectangular terms. The tadpole factor is estimated using the
Landau link. For each of the three values of the coupling constant considered,
quarkonia are calculated for five masses spanning the range from charmonium
through bottomonium, and one set of quark masses is tuned to the B(c).
"Perturbative" and nonperturbative meson masses are compared. One-loop
perturbative matching of lattice NRQCD with continuum QCD for the heavy-heavy
vector and axial vector currents is performed. The data are consistent with the
vector meson decay constants of quarkonia being proportional to the square root
of their mass and the B(c) decay constant being equal to 420(13) MeV.


title: On the spectral density from instantons in quenched QCD

abstract:
  We investigate the contribution of instantons to the eigenvalue spectrum of
the Dirac operator in quenched QCD. The instanton configurations that we use
have been derived, elsewhere, from cooled SU(3) lattice gauge fields and, for
comparison, we also analyse a random `gas' of instantons. Using a set of
simplifying approximations, we find a non-zero chiral condensate. However we
also find that the spectral density diverges for small eigenvalues, so that the
chiral condensate, at zero quark mass, diverges in quenched QCD. The degree of
divergence decreases with the instanton density, so that it is negligible for
the smallest number of cooling sweeps but becomes substantial for larger number
of cools. We show that the spectral density scales, that finite volume
corrections are small and we see evidence for the screening of topological
charges. However we also find that the spectral density and chiral condensate
vary rapidly with the number of cooling sweeps -- unlike, for example, the
topological susceptibility. Whether the problem lies with the cooling or with
the identification of the topological charges is an open question. This problem
needs to be resolved before one can determine how important is the divergence
we have found for quenched QCD.


title: Quantum Chaos in Compact Lattice QED

abstract:
  Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$
compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We
investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as
a measure of the fluctuation properties of the eigenvalues in the strong
coupling and the Coulomb phase. In both phases we find agreement with the
Wigner surmise of the unitary ensemble of random-matrix theory indicating
quantum chaos. Combining this with previous results on QCD, we conjecture that
quite generally the non-linear couplings of quantum field theories lead to a
chaotic behavior of the eigenvalues of the Dirac operator.

categories: hep-lat chao-dyn cond-mat hep-ph hep-th nlin.CD


title:
Toward the Chiral Limit of QCD: Quenched and Dynamical Domain Wall
  Fermions

abstract:
  A serious difficulty in conventional lattice field theory calculations is the
coupling between the chiral and continuum limits. With both staggered and
Wilson fermions, the chiral limit cannot be realized without first taking the
limit of vanishing lattice spacing. In this talk, we report on extensive
studies of the domain wall formulation of lattice fermions, which avoids this
difficulty at the expense of requiring that fermion propagators be computed in
five dimensions. A variety of results will be described for quenched and
dynamical simulations at both zero and finite temperature. Conclusions about
the benefits of this new method and some new physical results will be
presented. These results were obtained on the QCDSP machines recently put into
operation at Columbia and the RIKEN Brookhaven Research Center.


title:
Effective Monopole Potential for SU(2) Lattice Gluodynamics in Spatial
  Maximal Abelian Gauge

abstract:
  We investigate the dual superconductor hypothesis in finite-temperature SU(2)
lattice gluodynamics in the Spatial Maximal Abelian gauge. This gauge is more
physical than the ordinary Maximal Abelian gauge due to absence of
non-localities in temporal direction. We show numerically that in the Spatial
Maximal Abelian gauge the probability distribution of the abelian monopole
field is consistent with the dual superconductor mechanism of confinement: the
abelian condensate vanishes in the deconfinement phase and is not zero in the
confinement phase.


title: Gauged O(n) spin models in one dimension

abstract:
  We consider a gauged O(n) spin model, n >= 2, in one dimension which contains
both the pure O(n) and RP(n-1) models and which interpolates between them. We
show that this model is equivalent to the non-interacting sum of the O(n) and
Ising models. We derive the mass spectrum that scales in the continuum limit,
and demonstrate that there are two universality classes, one of which contains
the O(n) and RP(n-1) models and the other which has a tuneable parameter but
which is degenerate in the sense that it arises from the direct sum of the O(n)
and Ising models.


title: Testing the efficiency of different improvement programs

abstract:
  We study the finite-size behaviour of a tree-level on-shell improved action
for the N-vector model. We present numerical results for N=3 and analytic
results in the large-N limit for the mass gap. We also report a perturbative
computation at one loop of the mass gap for states of spatial momentum p. We
present a detailed comparison of the behaviour of this action with that of
other formulations, including the perfect action, and a critical discussion of
the different approaches to the problem of action improvement.


title: Connected Correlators in Quantum Gravity

abstract:
  We discuss the concept of connected, reparameterization invariant matter
correlators in quantum gravity. We analyze the effect of discretization in two
solvable cases: branched polymers and two-dimensional simplicial gravity. In
both cases the naively defined connected correlators for a fixed volume display
an anomalous behavior, which could be interpreted as a long-range order. We
suggest that this is in fact only a highly non-trivial finite-size effect and
propose an improved definition of the connected correlator, which reduces the
effect. Using this definition we illustrate the appearance of a long-range spin
order in the Ising model on a two-dimensional random lattice in an external
magnetic field $H$, when $H \to 0$ and $\beta=\beta_C$.


title: The Schwinger Model with Perfect Staggered Fermions

abstract:
  We construct and test a quasi-perfect lattice action for staggered fermions.
The construction starts from free fermions, where we suggest a new blocking
scheme, which leads to excellent locality of the perfect action. An adequate
truncation preserves a high quality of the free action. An Abelian gauge field
is inserted in d=2 by effectively tuning the couplings to a few short-ranged
lattice paths, based on the behavior of topological zero modes. We simulate the
Schwinger model with this action, applying a new variant of Hybrid Monte Carlo,
which damps the computational overhead due to the non-standard couplings. We
obtain a tiny ``pion'' mass down to very small \beta, while the ``\eta'' mass
follows very closely the prediction of asymptotic scaling. The observation that
even short-ranged quasi-perfect actions can yield strong improvement is most
relevant in view of QCD.


title: Hybrid Quarkonia on Asymmetric Lattices

abstract:
  We report on a study of heavy hybrid states using the NRQCD approach on
coarse and asymmetric lattices, where we discard vacuum polarisation effects
and neglect all spin-correction terms. We find a clear hybrid signal on all our
lattices ($a_s= 0.15 ... 0.47$ fm). We have studied in detail the lattice
spacing artefacts, finite volume effects and mass dependence. Within the above
approximations we predict the hybrid excitation in Charmonium to be 1.323(13)
GeV above its ground state. The bottomonium hybrid was found to be 1.542(8) GeV
above its ground state.


title: Eigenvalue spectrum of massless Dirac operators on the lattice

abstract:
  We present a detailed study of the interplay between chiral symmetry and
spectral properties of the Dirac operator in lattice gauge theories. We
consider, in the framework of the Schwinger model, the fixed point action and a
fermion action recently proposed by Neuberger. Both actions show the remnant of
chiral symmetry on the lattice as formulated in the Ginsparg-Wilson relation.
We check this issue for practical implementations, also evaluating the fermion
condensate in a finite volume by a subtraction procedure. Moreover, we
investigate the distribution of the eigenvalues of a properly defined
anti-hermitian lattice Dirac operator, studying the statistical properties at
the low lying edge of the spectrum. The comparison with the predictions of
chiral Random Matrix Theory enables us to obtain an estimate of the infinite
volume fermion condensate.


title:
Matrix elements relevant for Delta I=1/2 rule and epsilon-prime from
  Lattice QCD with staggered fermions

abstract:
  We perform a study of matrix elements relevant for the Delta I=1/2 rule and
the direct CP-violation parameter epsilon-prime from first principles by
computer simulation in Lattice QCD. We use staggered (Kogut-Susskind) fermions,
and employ the chiral perturbation theory method for studying K to 2 Pi decays.
Having obtained a reasonable statistical accuracy, we observe an enhancement of
the Delta I=1/2 amplitude, consistent with experiment within our large
systematic errors. Finite volume and quenching effects have been studied and
were found small compared to noise. The estimates of epsilon-prime are hindered
by large uncertainties associated with operator matching. In this paper we
explain the simulation method, present the results and address the systematic
uncertainties.


title: May vortices produce a mass gap in 2D spin models at weak coupling

abstract:
  We consider the 2D SU(N) principal chiral model and discuss a vortex
condensation mechanism which could explain the existence of a non-zero mass gap
at arbitrarily small values of the coupling constant. The mechanism is an
analogue of the vortex condensation mechanism of confinement in 4D non-Abelian
gauge theories. We formulate a sufficient condition for the mass gap to be
non-vanishing in terms of the behaviour of the vortex free energy. The SU(2)
model is studied in detail. In one dimension we calculate the vortex free
energy exactly. An effective model for the center variables of the spin
configurations of the 2D SU(2) model is proposed and the Z(2) correlation
function is derived in this model. We define a Z(2) mass gap in both the full
and effective model and argue that they should coincide whenever the genuine
mass gap is non-zero. We show via Monte-Carlo simulations of the SU(2) model
that the Z(2) mass gap reproduces the full mass gap with perfect accuracy. We
also test this mechanism in the positive link model which is an analogue of the
positive plaquette model in gauge theories and find excellent agreement between
the full and the Z(2) mass gap.


title: String breaking by dynamical fermions in three-dimensional lattice QCD

abstract:
  The first observation is made of hadronic string breaking due to dynamical
fermions in zero temperature lattice QCD. The simulations are done for SU(2)
color in three dimensions, with two flavors of staggered fermions. The results
have clear implications for the large scale simulations that are being done to
search (so far, without success) for string breaking in four-dimensional QCD.
In particular, string breaking is readily observed using only Wilson loops to
excite a static quark-antiquark pair. Improved actions on coarse lattices are
used, providing an extremely efficient means to access the quark separations
and propagation times at which string breaking occurs.


title: The Weak-Coupling Limit of Simplicial Quantum Gravity

abstract:
  In the weak-coupling limit, kappa_0 going to infinity, the partition function
of simplicial quantum gravity is dominated by an ensemble of triangulations
with the ratio N_0/N_D close to the upper kinematic limit. For a combinatorial
triangulation of the D--sphere this limit is 1/D. Defining an ensemble of
maximal triangulations, i.e. triangulations that have the maximal possible
number of vertices for a given volume, we investigate the properties of this
ensemble in three dimensions using both Monte Carlo simulations and a
strong-coupling expansion of the partition function, both for pure simplicial
gravity and a with a suitable modified measure. For the latter we observe a
continuous phase transition to a crinkled phase and we investigate the fractal
properties of this phase.


title:
Deconfinement and Chiral Symmetry Restoration in an SU(3) Gauge Theory
  with Adjoint Fermions

abstract:
  We analyze the finite temperature phase diagram of$QC$ with fermions in the
adjoint representation. The simulations performed with four dynamical Majorana
fermions show that the deconfinement and chiral phase transitions occur at two
distinct temperatures. While the deconfinement transition is first order at T_d
we find evidence for a continuous chiral transition at a higher temperature
$T_c ~ 8 T_d. We observe a rapid change of bulk thermodynamic observables at
T_d which reflects the increase in the number of degrees of freedom. However,
these show little variation at T_c, where the fermion condensate vanishes. We
also analyze the potential between static fundamental and adjoint charges in
all three phases and extract the corresponding screening masses above T_d.


title: Sea quark effects in B Spectroscopy and Decay Constants

abstract:
  We present comprehensive results for the spectrum and decay constants of
hadrons containing a single b quark. The heavy quark is simulated using an
$O(1/M)$ NRQCD action and the light quark using the $O(a)$ tadpole-improved
clover action on gauge configurations containing two degenerate flavours of sea
quarks at $\beta^{n_f=2}=5.6$ provided by the HEMCGC collaboration. We present
detailed results for the lower lying $S$ and $P$ wave $B$ meson states and the
$\Lambda_b$ baryon. We find broad agreement with experiment. In addition, we
present results for the pseudoscalar and, for the first time, the vector decay
constants fully consistent to $O(\alpha/M): f_B =
186(5)(stat)(19)(pert)(9)(disc)(13)(NRQCD)(+50)(a^{-1})MeV, f_B^* = 181(6)
(stat)(18)(pert)(9)(disc)(13)(NRQCD)(+55)(a^{-1})MeV$ and $f_{B_s}/f_B =
1.14(2)(stat)(-2)(\kappa_s)$. We present an investigation of sea quark effects
in the $B$ spectrum and decay constants. We compare our results with those from
similar quenched simulations at $\beta^{n_f=0}=6.0$. For the spectrum, the
quenched results reproduce the experimental spectrum well and there is no
significant difference between the quenched and $n_f=2$ results. For the decay
constants, our results suggest that sea quark effects may be large. We find
that $f_B$ increases by approximately 25% between $n_f=0$ and $n_f=2$.


title:
The three flavour chiral phase transition with an improved quark and
  gluon action in lattice QCD

abstract:
  The finite-temperature chiral phase transition is investigated for three
flavours of staggered quarks on a lattice of temporal extent N_t=4. In the
simulation we use an improved fermion action which reduces rotational symmetry
breaking of the quark propagator (p4-action), include fat-links to improve the
flavour symmetry and use the tree level improved (1,2) gluon action. We study
the nature of the phase transition for quark masses of ma=0.025, ma=0.05 and
ma=0.1 on lattices with spatial sizes of 8^3 and 16^3.


title: The overlap lattice Dirac operator and dynamical fermions

abstract:
  I show how to avoid a two level nested conjugate gradient procedure in the
context of Hybrid Monte Carlo with the overlap fermionic action. The resulting
procedure is quite similar to Hybrid Monte Carlo with domain wall fermions, but
is more flexible and therefore has some potential worth exploring.


title: The glueball spectrum from an anisotropic lattice study

abstract:
  The spectrum of glueballs below 4 GeV in the SU(3) pure-gauge theory is
investigated using Monte Carlo simulations of gluons on several anisotropic
lattices with spatial grid separations ranging from 0.1 to 0.4 fm. Systematic
errors from discretization and finite volume are studied, and the continuum
spin quantum numbers are identified. Care is taken to distinguish single
glueball states from two-glueball and torelon-pair states. Our determination of
the spectrum significantly improves upon previous Wilson action calculations.


title: The Absence of Ultralocal Ginsparg-Wilson Fermions

abstract:
  It was shown recently by I. Horvath that lattice fermions obeying the
standard form of the Ginsparg-Wilson relation cannot be ultralocal. However,
there are more general forms of the Ginsparg-Wilson relation, which also
guarantee the physical properties related to chirality, but which are not
covered by Horvath's consideration. Here we present a proof which applies to
all Ginsparg-Wilson fermions, demonstrating that they can only be local in the
sense of an exponential decay of their couplings, but not ultralocal.


title: The Deconfinement Transition in SO(3) Gauge Theory

abstract:
  The SO(3) lattice gauge theory with a Villain form of action was investigated
by Monte Carlo techniques on asymmetric lattices with Nt = 2 and 4, where Nt is
the number of sites in the temporal extent. Unlike the results for higher Nt,
only one transition of second order was found for Nt = 2 . An extended action
with an irrelevant term to suppress Z_2 monopoles enabled us to get a better
view of the deconfinement transition as the effects of bulk transition could be
suppressed as well. Although the action has no global Z_2 symmetry for the
SO(3) theory, unlike the SU(2) theory at finite temperature, our study revealed
a second order deconfinement transition, with properties similar to the
deconfinement transition of SU(2).


title: Two heavy-light mesons on a lattice

abstract:
  The potential between two heavy-light mesons as a function of the heavy quark
separation is calculated in quenched SU(3) lattice QCD. We study the case of
heavy-light mesons with a static heavy quark and light quarks of mass close to
the strange quark mass. We explore the case of light quarks with the same and
with different flavours, classified according to the light quark isospin. We
evaluate the appropriate light quark exchange contributions and explore the
spin-dependence of the interaction. Comparison is made with meson exchange.


title:
The Euclidean two-point correlation function of the topological charge
  density

abstract:
  We study the Euclidean two-point correlation function $G_q(x)$ of the
topological charge density in QCD. A general statement based on reflection
positivity tells us that $G_q(x)<0$ for $x\neq 0 $. On the other hand the
topological susceptibility $\chi_q=\int d^d x G_q(x)$ is a positive quantity.
This indicates that $G_q(x)$ developes a positive contact term at $x=0$, that
contributes to the determination of the physical value of $\chi_q$. We show
explicitly these features of $G_q(x)$ in a solvable nontrivial continuum model,
the two-dimensional $CP^{N-1}$ model in the large-N limit. A similar analysis
is done on the lattice.


title:
Flavor Singlet Axial Vector Coupling of the Proton with Dynamical Wilson
  Fermions

abstract:
  We present the results of a full QCD lattice calculation of the flavor
singlet axial vector coupling $G_A^1$ of the proton. The simulation has been
carried out on a $16^3\times 32$ lattice at $\beta=5.6$ with $n_f=2$ dynamical
Wilson fermions. It turns out that the statistical quality of the connected
contribution to $G_A^1$ is excellent, whereas the disconnected part is
accessible but suffers from large statistical fluctuations. Using a 1st order
tadpole improved renormalization constant $Z_A$, we estimate $G_A^1 =
0.20(12)$.


title: Improved Staggered Fermion Actions for QCD Thermodynamics

abstract:
  We analyze the cut-off dependence of the fermion contribution to the finite
temperature free energy density in ${\cal O}(g^2)$ lattice perturbation theory
for several improved staggered fermion actions. Cut-off effects are drastically
reduced for the Naik action and an action with improved rotational symmetry of
the quark propagator. We show that improvement of rotational symmetry at ${\cal
O}(g^2)$ further reduces cut-off effects in thermodynamic observables. We also
show that the introduction of fat-links does not have a significant influence
on cut-off distortions at ${\cal O}(g^2)$.


title: Perturbation calculation of the axial anomaly of Ginsparg-Wilson fermion

abstract:
  We evaluate the axial anomaly for the general Ginsparg-Wilson fermion
operator $D = D_c (\Id + R D_c)^{-1}$ with $R = r \Id$. For any chirally
symmetric $D_c$ which in the free fermion limit, is free of species doubling
and behaves like $i \gamma_\mu p_\mu$ as $p \to 0$, the axial anomaly
$\tr[\gamma_5 (R D) (x,x)]$ for U(1) lattice gauge theory with single fermion
flavor is equal to $e^2/(32 \pi^2) \epsilon_{\mu\nu\lambda\sigma} F_{\mu\nu}(x)
F_{\lambda\sigma}(x+\hat\mu+\hat\nu)$ plus terms which are higher orders and/or
non-perturbative contribtuons. The $F \tilde{F}$ term is r-invariant and has
the correct continuum limit.


title:
Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the
  Lattice

abstract:
  L\"uscher's recent formulation of Abelian chiral gauge theories on the
lattice, in the vacuum (or perturbative) sector in infinite volume, is
reinterpreted in terms of the lattice covariant regularization. The gauge
invariance of the effective action and the integrability of the gauge current
in anomaly-free cases become transparent. The real part of the effective action
is simply one-half that of the Dirac fermion and, when the Dirac operator
behaves properly in the continuum limit, the imaginary part in this limit
reproduces the $\eta$-invariant.


title: Random Matrix Theory and Chiral Logarithms

abstract:
  Recently, the contributions of chiral logarithms predicted by quenched chiral
perturbation theory have been extracted from lattice calculations of hadron
masses. We argue that a detailed comparison of random matrix theory and lattice
calculations allows for a precise determination of such corrections. We
estimate the relative size of the m*log(m), m, and m^2 corrections to the
chiral condensate for quenched SU(2).


title: Ginsparg-Wilson-Luscher Symmetry and Ultralocality

abstract:
  Important recent discoveries suggest that Ginsparg-Wilson-Luscher (GWL)
symmetry has analogous dynamical consequences for the theory on the lattice as
chiral symmetry does in the continuum. While it is well known that inherent
property of lattice chiral symmetry is fermion doubling, we show here that
inherent property of GWL symmetry is that the infinitesimal symmetry
transformation couples fermionic degrees of freedom at arbitrarily large
lattice distances (non-ultralocality). The consequences of this result for
ultralocality of symmetric actions are discussed.


title:
Approach to the Continuum Limit of the Quenched Hermitian Wilson-Dirac
  Operator

abstract:
  We investigate the approach to the continuum limit of the spectrum of the
Hermitian Wilson-Dirac operator in the supercritical mass region for pure gauge
SU(2) and SU(3) backgrounds. For this we study the spectral flow of the
Hermitian Wilson-Dirac operator in the range $0\le m\le 2$. We find that the
spectrum has a gap for $0 < m \le m_1$ and that the spectral density at zero,
$\rho(0;m)$, is non-zero for $m_1\le m\le 2$. We find that $m_1\to 0$ and, for
$m \ne 0, \rho(0;m)\to 0$ (exponential in the lattice spacing) as one goes to
the continuum limit. We also compute the topological susceptibility and the
size distribution of the zero modes. The topological susceptibility scales well
in the lattice spacing for both SU(2) and SU(3). The size distribution of the
zero modes does not appear to show a peak at a physical scale.


title:
Universal continuum limit of non-perturbative lattice non-singlet moment
  evolution

abstract:
  We present evidence for the universality of the continuum limit of the scale
dependence of the renormalization constant associated with the operator
corresponding to the average momentum of non-singlet parton densities. The
evidence is provided by a non-perturbative computation in quenched lattice QCD
using the Schr\"odinger Functional scheme. In particular, we show that the
continuum limit is independent of the form of the fermion action used, i.e. the
Wilson action and the non-perturbatively improved clover action.


title: Mesons Above The Deconfining Transition

abstract:
  We analyze temporal and spatial meson correlators in quenched lattice QCD at
T>0. Above T_c we find different masses and (spatial) screening masses, signals
of plasma formation, and indication of persisting mesonic excitations.


title:
The Kaon B-parameter with the Wilson Quark Action using Chiral Ward
  Identities

abstract:
  A lattice QCD calculation of the kaon $B$ parameter $B_K$ is carried out with
the Wilson quark action in the quenched approximation at $\beta=6/g^2=5.9-6.5$.
The mixing problem of the $\Delta s=2$ four-quark operators is solved
non-perturbatively with full use of chiral Ward identities employing four
external quarks with an equal off-shell momentum in the Landau gauge. This
method, without invoking any effective theory, enables us to construct the weak
four-quark operators exhibiting good chiral behavior. Our results for $B_K$
with the non-perturbative mixing coefficients show small scaling violation
beyond the lattice cut-off $a^{-1}\sim 2.5 $GeV. Our estimate concludes
$B_K(NDR, 2 GeV)=0.69(7)$ at $a^{-1}=2.7-4.3$GeV, which agrees with the value
obtained with the Kogut-Susskind quark action. For comparison we also calculate
$B_K$ with one-loop perturbative mixing coefficients. While this yields
incorrect values at finite lattice spacing, a linear extrapolation to the
continuum limit as a function of $a$ leads to a result consistent with those
obtained with the Ward identity method.


title:
Non-perturbative determination of quark masses in quenched lattice QCD
  with the Kogut-Susskind fermion action

abstract:
  We report results of quark masses in quenched lattice QCD with the
Kogut-Susskind fermion action, employing the Reguralization Independent scheme
(RI) of Martinelli et al. to non-perturbatively evaluate the renormalization
factor relating the bare quark mass on the lattice to that in the continuum.
Calculations are carried out at \beta=6.0, 6.2, and 6.4, from which we find
$m^{\bar{MS}}_{ud} (2 GeV)= 4.23(29) MeV$ for the average up and down quark
mass and, with the $\phi$ meson mass as input, $m^{\bar{MS}}_{s} (2 GeV)=
129(12) MeV$ for the strange mass in the continuum limit. These values are
about 20% larger than those obtained with the one-loop perturbative
renormalization factor.


title: On the relevance of center vortices to QCD

abstract:
  In a numerical experiment, we remove center vortices from an ensemble of
lattice SU(2) gauge configurations. This removal adds short-range disorder.
Nevertheless, we observe long-range order in the modified ensemble: confinement
is lost and chiral symmetry is restored (together with trivial topology),
proving that center vortices are responsible for both phenomena. As for the
Abelian monopoles, they survive but their percolation properties are lost.


title:
The endpoint of the first-order phase transition of the SU(2)
  gauge-Higgs model on a 4-dimensional isotropic lattice

abstract:
  We study the first-order finite-temperature electroweak phase transition of
the SU(2) gauge-Higgs model defined on a 4-dimensional isotropic lattice with
temporal extension N_t=2. Finite-size scaling study of Lee-Yang zeros yields
the value of the Higgs self coupling of the endpoint at lambda_c=0.00116(16).
An independent analysis of Binder cumulant gives a consistent value for the
endpoint. Combined with our zero-temperature measurement of Higgs and W boson
masses, this leads to M_{H,c}=73.3 +- 6.4 GeV for the critical Higgs boson mass
beyond which the electroweak transition turns into a crossover.


title:
Dual Wilson Loop and Infrared Monopole Condensation in Lattice QCD in
  the Maximally Abelian Gauge

abstract:
  Using the SU(2) lattice QCD, we formulate the dual Wilson loop and study the
dual Higgs mechanism induced by monopole condensation in the maximally abelian
(MA) gauge, where QCD is reduced into an abelian gauge theory including the
electric current $j_\mu$ and the monopole current $k_\mu$. After the abelian
projection in the MA gauge, the system can be separated into the photon part
and the monopole part corresponding to the separation of $j_\mu$ and $k_\mu$,
respectively. We study here the monopole part (the monopole-current system),
which is responsible to the electric confinement. Owing to the absence of
electric currents, the monopole part is naturally described using the dual
gluon field $B_\mu$ without the Dirac-string singularity. Defining the dual
Wilson loop from the dual gluon $B_\mu$, we find the perimeter law of the dual
Wilson loop in the lattice QCD simulation. In the monopole part in the MA
gauge, the inter-monopole potential is found to be flat, and can be fitted as
the Yukawa potential in the infrared region after the subtraction of the
artificial finite-size effect on the dual Wilson loop. From more detailed
analysis of the inter-monopole potential considering the monopole size, we
estimate the effective dual-gluon mass $m_B \simeq 0.5$GeV and the effective
monopole size $R \simeq 0.2$fm. The effective mass of the dual gluon field at
the long distance can be regarded as an evidence of ``infrared monopole
condensation''.


title: Overview from lattice QCD

abstract:
  I review recent Lattice results. In particular, the confinement mechanism and
string breaking, glueballs and hybrid mesons as well as light hadron
spectroscopy are discussed.


title: Chiral Gauge Models on a Lattice

abstract:
  Chiral gauge groups acting on a lattice fermion field are constructed such
that all fermion modes (doublers) have the same charge. Details are given for
an abelian axial gauge group within a perturbative framework. An action based
on this group correctly reproduces the continuum gauge-current anomaly, while
preserving global chiral symmetry, locality, rotational symmetry and
hermiticity. A Wess-Zumino-like scalar field enters naturally to enforce exact
chiral gauge invariance. The degeneracy amongst the doublers can be lifted as
in a vector model.


title: Hypercubic Random Surfaces with Extrinsic Curvature

abstract:
  We analyze a model of hypercubic random surfaces with an extrinsic curvature
term in the action. We find a first order phase transition at finite coupling
separating a branched polymer from a stable flat phase.


title: Breaking of the adjoint string in 2+1 dimensions

abstract:
  The roughly linear rise of the potential found between adjoint sources in
SU(N) in lattice simulations is expected to saturate into a state of two
`gluelumps' due to gluonic screening. We examine this in SU(2) in 2+1
dimensions. Crossover between string-like and broken states is clearly seen by
the mixing-matrix technique, using different operators to probe the two states;
the breaking behaviour is rather abrupt. Furthermore, we are able to show that
both types of operator have a finite overlap with both states; in the case of
the Wilson loops the overlap with the broken string is, as predicted, very
small.


title: String Breaking in SU(2) Yang Mills Theory with Adjoint Sources

abstract:
  We compute the static potential in three-dimensional SU(2) Yang Mills Theory
with adjoint sources using numerical simulations. By employing a variational
approach involving string and gluelump operators, we obtain clear evidence for
string breaking in the adjoint potential. The breaking scale r_b is computed
and extrapolated to the continuum limit. The result in units of the scalar
glueball mass is r_b*m_G = 10.3 +/- 1.5. We also resolve the structure of
higher excitations of the flux-tube and gluelumps. Furthermore we discuss the
implications of our findings for the case of the four-dimensional theory.


title: Gauge Fixing on the Lattice and the Gibbs Phenomenon

abstract:
  We discuss global gauge fixing on the lattice, specifically to the lattice
Landau gauge, with the goal of understanding the question of why the process
becomes extremely slow for large lattices. We construct an artificial
"gauge-fixing" problem which has the essential features encountered in
actuality. In the limit in which the size of the system to be gauge fixed
becomes infinite, the problem becomes equivalent to finding a series expansion
in functions which are related to the Jacobi polynomials. The series converges
slowly, as expected. It also converges non-uniformly, which is an observed
characteristic of gauge fixing. In the limiting example, the non-uniformity
arises through the Gibbs phenomenon.


title: Monopole Clustering and Color Confinement in the Multi-Instanton System

abstract:
  We study color confinement properties of the multi-instanton system, which
seems to carry an essence of the nonperturbative QCD vacuum. Here we assume
that the multi-instanton system is characterized by the infrared suppression of
instantons as $f(\rho)\sim \rho^{-5}$ for large size $\rho$. We first
investigate a monopole-clustering appearing in the maximally abelian (MA) gauge
by considering the correspondence between instantons and monopoles. In order to
clarify the infrared monopole properties, we make the ``block-spin''
transformation for monopole currents. The feature of monopole trajectories
changes drastically with the instanton density. At a high instanton density,
there appears one very long and highly complicated monopole loop covering the
entire physical vacuum. Such a global network of long-monopole loops resembles
the lattice QCD result in the MA gauge. Second, we observe that the SU(2)
Wilson loop obeys an area law and the static quark potential is approximately
proportional to the distance $R$ between quark and anti-quark in the
multi-instanton system using the SU(2) lattice with a total volume of $V=(10
fm)^4$ and a lattice spacing of $a=0.05 fm$. We extract the string tension from
the $5 \times 10^{6}$ measurements of Wilson loops. With an instanton density
of $(N/V)=(1/fm)^4$ and a average instanton size of $\bar{\rho}=0.4 fm$, the
multi-instanton system provides the string tension of about $0.4 GeV/fm$.