title: Accelerating the Hybrid Monte Carlo algorithm with ILU preconditioning

abstract:
  The pseudofermion action of the Hybrid Monte Carlo (HMC) algorithm for
dynamical fermions is modified to directly incorporate Incomplete LU (ILU)
factorisation. This reduces the stochastic noise and allows a larger molecular
dynamics step-size to be taken, cutting the computational cost. Numerical tests
using the two-flavour Schwinger model are presented, where a two-step ILU
preconditioning of the even-odd fermion matrix allows the step-size to be
increased by a factor of two over the standard even-odd formulation.


title: Non-perturbative Renormalization in Lattice Field Theory

abstract:
  I review the strategies which have been developped in recent years to solve
the non-perturbative renormalization problem in lattice field theories.
Although the techniques are general, the focus will be on applications to
lattice QCD. I discuss the momentum subtraction and finite volume schemes, and
their application to scale dependent renormalizations. The problem of finite
renormalizations is illustrated with the example of explicit chiral symmetry
breaking, and I give a short status report concerning Symanzik's improvement
programme to O($a$).


title: Using a Fermionic Ensemble of Systems to Determine Excited States

abstract:
  We discuss a new numerical method for the determination of excited states of
a quantum system using a generalization of the Feynman-Kac formula. The method
relies on introducing an ensemble of non-interacting identical systems with a
fermionic statistics imposed on the systems as a whole, and on determining the
ground state of this fermionic ensemble by taking the large time limit of the
Euclidean kernel. Due to the exclusion principle, the ground state of an
$n$-system ensemble is realized by the set of individual systems occupying
successively the $n$ lowest states, all of which can therefore be sampled in
this way. To demonstrate how the method works, we consider a one-dimensional
oscillator and a chain of harmonically coupled particles.


title: Matrix Distributed Processing and FermiQCD

abstract:
  Matrix Distributed Processing is a collection of classes and functions
written in C++ for fast development of efficient parallel algorithms for the
most general lattice/grid application. FermiQCD is an Object Oriented Lattice
QCD application of MDP, under development at Fermilab.


title:
Effective Z(2) Spin Models of Deconfinement and Percolation in SU(2)
  Gauge Theory

abstract:
  Effective theories are helpful tools to gain an intuitive insight into
phenomena governed by complex laws. In this work we show by means of Monte
Carlo simulations that Z(2) spin models with only spin-spin interactions
approximate rather well the critical behavior of SU(2) gauge theory at finite
temperature. These models are then used to formulate an effective description
of Polyakov loop percolation, which is shown to reproduce the thermal critical
behaviour of SU(2) gauge theory.


title:
Study of Charmonia near the deconfining transition on an anisotropic
  lattice with O(a) improved quark action

abstract:
  We study hadron properties near the deconfining transition in the quenched
lattice QCD simulation. This paper focuses on the heavy quarkonium states, such
as $J/\psi$ meson. In order to treat heavy quarks at $T>0$, we adopt the $O(a)$
improved Wilson action on anisotropic lattice. We discuss $c\bar{c}$ bound
state observing the wave function and compare the meson correlators at above
and below $T_c$. Although we find a large change of correlator near the $T_c$,
the strong spatial correlation which is almost the same as confinement phase
survives even $T\sim 1.5T_c$.


title:
An improved random matrix model for the chiral phase transition in QCD
  at finite chemical potential

abstract:
  We consider a lattice-inspired random matrix model for the QCD chiral phase
transition at finite chemical potential. Useful features of the usual RMM for
QCD at finite chemical potential are reobtained, some being brought closer to
their lattice equivalent. The simple physical requirement of a vanishing quark
number density in the broken phase is fulfilled in the limit of a large number
of timeslices.
  It is argued that the suppression of the partition function at nonzero
chemical potential in the broken phase, seen in the usual RMM, is possibly
present in lattice simulations and is simply a result of the discretization in
time.


title:
The Combination of Wilson Loops into $J^{PC}$ Operators in Lattice Pure
  Gauge Theory

abstract:
  To calculate the mass of glueballs with quantum number $J^{PC}$ in lattice
gauge theory by using Wilson loops, we discuss their combinations of Wilson
loops into irreducible representation of $O^{PC}$ group for arbitry-link wilson
loops. We present a general computational procedure for this combination which
is suitable for any finite groups.


title: Light Hadron Weak Matrix Elements

abstract:
  I review this year's developments in the study of weak matrix elements of
light hadrons on the lattice, with emphasis on K^0-\bar K^0 mixing and K -> pi
pi decays.


title: Physical Results from Partially Quenched Simulation

abstract:
  We describe how one can use chiral perturbation theory to obtain results for
physical quantities, such as quark masses, using partially quenched
simulations.


title: Parallel Computing for QCD on a Pentium Cluster

abstract:
  Motivated by the computational demands of our research and budgetary
constraints which are common to many research institutions, we built a ``poor
man's supercomputer'', a cluster of PC nodes which together can perform
parallel calculations at a fraction of the price of a commercial supercomputer.
We describe the construction, cost, and performance of our cluster.


title:
A lattice calculation of the nucleon's spin-dependent structure function
  g_2 revisited

abstract:
  Our previous calculation of the spin-dependent structure function g_2 is
revisited. The interest in this structure function is to a great extent
motivated by the fact that it receives contributions from twist-two as well as
from twist-three operators already in leading order of 1/Q^2 thus offering the
unique possibility of directly assessing higher-twist effects. In our former
calculation the lattice operators were renormalized perturbatively and mixing
with lower-dimensional operators was ignored. However, the twist-three operator
which gives rise to the matrix element d_2 mixes non-perturbatively with an
operator of lower dimension. Taking this effect into account leads to a
considerably smaller value of d_2, which is consistent with the experimental
data.


title: Algebraic Multigrid for Disordered Systems and Lattice Gauge Theories

abstract:
  The construction of multigrid operators for disordered linear lattice
operators, in particular the fermion matrix in lattice gauge theories, by means
of algebraic multigrid and block LU decomposition is discussed. In this
formalism, the effective coarse-grid operator is obtained as the Schur
complement of the original matrix. An optimal approximation to it is found by a
numerical optimization procedure akin to Monte Carlo renormalization, resulting
in a generalized (gauge-path dependent) stencil that is easily evaluated for a
given disorder field. Applications to preconditioning and relaxation methods
are investigated.


title: Geometry of Reduced Supersymmetric 4D Yang-Mills Integrals

abstract:
  We study numerically the geometric properties of reduced supersymmetric
non-compact SU(N) Yang-Mills integrals in D=4 dimensions, for N = 2,3, ..., 8.
We show that in the range of large eigenvalues of the matrices A^mu, the
original D-dimensional rotational symmetry is spontaneously broken and the
dominating field configurations become one-dimensional, as anticipated by
studies of the underlying surface theory. We also discuss possible implications
of our results for the IKKT model.


title: Nonrelativistic Bound States in Quantum Field Theory

abstract:
  Nonrelativistic bound states are studied using an effective field theory.
Large logarithms in the effective theory can be summed using the velocity
renormalization group. For QED, one can determine the structure of the leading
and next-to-leading order series for the energy, and compute corrections up to
order alpha^8 ln^3 alpha, which are relevant for the present comparison between
theory and experiment. For QCD, one can compute the velocity renormalization
group improved quark potentials. Using these to compute the renormalization
group improved t-tbar production cross-section near threshold gives a result
with scale uncertainties of 2%, a factor of 10 smaller than existing fixed
order calculations.


title: Quark Masses on the Lattice: Light and Heavy

abstract:
  I review the current status of lattice calculations of light and heavy quark
masses. Significant progresses, in these studies, have been allowed by the
introduction of improved actions and non-perturbative renormalization
techniques. Current determinations of light quark masses are accurate at the
level of 20%, where the main source of uncertainty is represented by the
quenching error. The determination of the bottom quark mass is accurate at the
impressive level of 2%. As final averages of lattice results, I quote mud(2
GeV) = (4.5 +- 1.0) MeV, ms(2 GeV) = (110 +- 25) MeV and mb(mb) = (4.26 +-
0.09) GeV.


title: A derivation of Regge trajectories in large-N transverse lattice QCD

abstract:
  Large-N QCD is analysed in light-front coordinates with a transverse lattice
at strong coupling. The general formalism can be looked up on as a d+n
expansion with a stack of d-dimensional hyperplanes uniformly spaced in n
transverse dimensions. It can arise by application of the renormalisation group
transformations only in the transverse directions. At leading order in strong
coupling, the gauge field dynamics reduces to the constraint that only colour
singlet states can jump between the hyperplanes. With d=2, n=2 and large-N, the
leading order strong coupling results are simple renormalisations of those for
the 't Hooft model. The meson spectrum lies on a set of parallel trajectories
labeled by spin. This is the first derivation of the widely anticipated Regge
trajectories in a regulated systematic expansion in QCD.


title: Lattice Gauge Theory - A short Primer

abstract:
  In this contribution we give an introduction to the foundations and methods
of lattice gauge theory. Starting with a brief discussion of the quantum
mechanical path integral, we develop the main ingredients of lattice field
theory: functional integrals, Euclidean field theory and the space-time
discretization of scalar, fermion and gauge fields. Some of the methods used in
calculations are reviewed and illustrated by a collection of typical results.


title: Percolation and Deconfinement in SU(2) Gauge Theory

abstract:
  Cluster percolation and second order thermal phase transitions show an
amazing number of common features: power laws of the variables at criticality,
scaling relations of the critical exponents and universality of the critical
indices. Because of that, percolation theory seems to be an ideal framework to
devise a geometrical picture of a second order phase transition; the leading
characters of the phenomenon are ordered domains, whose size increases while
approaching the threshold until they fuse into a spanning structure, so that
the order from local becomes global. Such a geometrical picture is known to be
successful in the Ising model. The clusters are site-bond clusters, i.e. they
are built by joining nearest-neighbouring aligned spins with some
temperature-dependent bond probability. In this work we extend this result to a
wide variety of theories, from continuous Ising-like models to O(n) models. On
the grounds of these results, we devise a percolation picture for the confining
phase transition of SU(2) pure gauge theory, exploiting its analogies with the
Ising model. The cluster definition is obtained by constructing suitable
effective theories for SU(2), which admit an equivalent percolation
formulation.


title:
A Numerical Study of Spectral Flows of Hermitian Wilson-Dirac Operator
  and the Index Theorem in Abelian Gauge Theories on Finite Lattices

abstract:
  We investigate the index of the Neuberger's Dirac operator in abelian gauge
theories on finite lattices by numerically analyzing the spectrum of the
hermitian Wilson-Dirac operator for a continuous family of gauge fields
connecting different topological sectors. By clarifying the characteristic
structure of the spectrum leading to the index theorem we show that the index
coincides to the topological charge for a wide class of gauge field
configurations. We also argue that the index can be found exactly for some
special but nontrivial configurations in two dimensions by directly analyzing
the spectrum.


title: Do we understand the unquenched value of fB?

abstract:
  I review our qualitative understanding of the increase in the value of the B
meson decay constant (fB), when dynamical fermions are included in lattice QCD
calculations.


title: An Estimate of the K0-K0bar Mixing Amplitude

abstract:
  We computed the B_K parameter on the lattice by using a non-perturbatively
improved Wilson action. From our quenched simulation, in the MSbar scheme and
at mu=2 GeV, we obtain B_K=0.73(7)^{+0.05}_{-0.01}. To gain some insight in the
systematic errors due to the use of the quenched approximation, we also made
the unquenched computation with Wilson fermions. We do not observe any
significant deviation with respect to the quenched result.


title: The Vacuum Polarization: Power Corrections beyond OPE ?

abstract:
  We compute the vacuum polarization on the lattice using non-perturbatively
O(a) improved Wilson fermions. The result is compared with the operator product
expansion (OPE).


title:
The residual mass in Lattice Heavy Quark Effective Theory to alpha^3
  order

abstract:
  We determine to order alpha^3 in the quenched approximation the so-called
residual mass in the lattice regularisation of the Heavy Quark Effective
Theory. We follow a gauge-invariant strategy which exploits the fact that this
mass term dominates the exponential decrease of perturbative Wilson loops at
large perimeters. Our computational tool is Numerical Stochastic Perturbation
Theory. The new coefficient we compute is crucial to improve the determination
of the (MS bar) mass of the b-quark from lattice simulations of the Heavy Quark
Effective Theory.


title: Lattice simulations of QCD-like theories at non-zero density

abstract:
  One way of avoiding the complex action problem in lattice QCD at non-zero
density is to simulate QCD-like theories with a real action, such as two-colour
QCD. The symmetries of two-colour QCD with quarks in the fundamental and in the
adjoint representation are described, and the status of lattice simulations is
reviewed, with particular emphasis on comparison with predictions from chiral
perturbation theory. Finally, we discuss how the lessons from two-colour QCD
may be carried over to physical QCD.


title: Topics in Non-Perturbative QCD

abstract:
  General aspects of non-perturbative field theory are discussed.The definition
of condensates is analysed.Mechanisms of color confinement are rewieved.


title: Low-Energy Effective Theories of Quantum Link and Quantum Spin Models

abstract:
  Quantum spin and quantum link models provide an unconventional regularization
of field theory in which classical fields arise via dimensional reduction of
discrete variables. This D-theory regularization leads to the same continuum
theories as the conventional approach. We show this by deriving the low-energy
effective Lagrangians of D-theory models using coherent state path integral
techniques. We illustrate our method for the $(2+1)$-d Heisenberg quantum spin
model which is the D-theory regularization of the 2-d O(3) model. Similarly, we
prove that in the continuum limit a $(2+1)$-d quantum spin model with
$SU(N)_L\times SU(N)_R\times U(1)_{L=R}$ symmetry is equivalent to the 2-d
principal chiral model. Finally, we show that $(4+1)$-d SU(N) quantum link
models reduce to ordinary 4-d Yang-Mills theory.


title: A nonlocal discretization of fields

abstract:
  A nonlocal method to obtain discrete classical fields is presented. This
technique relies on well-behaved matrix representations of the derivatives
constructed on a non--equispaced lattice. The drawbacks of lattice theory like
the fermion doubling or the breaking of chiral symmetry for the massless case,
are absent in this method.


title: Lattice supersymmetry with domain wall fermions

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


title: Colour Confinement in the Lattice Landau Gauge QCD Simulation

abstract:
  The colour confinement criterion proposed by Kugo and Ojima is tested in the
lattice Landau gauge QCD simulation. The renormalization effects are studied by
measuring the gluon propagator, ghost propagator, three gluon vertex and the
ghost-antighost-gluon vertex.


title:
Errata and Addenda to ``Anomaly Cancellation Condition in Lattice Gauge
  Theory''

abstract:
  We correct some intermediate expressions and arguments in hep-lat/0002009
(Nucl. Phys. B 585 (2000) 471--513). The main results do not change. We also
mention some additional observations, including a constraint on a coefficient
of the possible nontrivial anomaly which was not given in the paper.


title:
QCD with Adjoint Scalars in 2D: Properties in the Colourless Scalar
  Sector

abstract:
  We present a numerical study of an SU(3) gauged 2D model for adjoint scalar
fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high
temperature. In the symmetric phase of its global Z_2 symmetry, two colourless
boundstates, even and odd under Z_2, are identified. Their respective
contributions (poles) in correlation functions of local composite operators A_n
of degree n=2p and 2p+1 in the scalar fields (p=1,2) fulfill factorization. The
contributions of two particle states (cuts) are detected. Their size agrees
with estimates based on a meanfield-like decomposition of the p=2 operators
into polynomials in p=1 operators. No sizable signal in any A_n correlation can
be attributed to 1/n times a Debye screening length associated with n
elementary fields. These results are quantitatively consistent with the picture
of scalar ``matter'' fields confined within colourless boundstates whose
residual ``strong'' interactions are very weak.


title: Ginsparg-Wilson Fermions in Odd Dimensions

abstract:
  The Ginsparg-Wilson relation, if written in a suitable form, can be used as a
condition for lattice Dirac operators of massless fermions also in odd
dimensions. The fermion action with such a Dirac operator is invariant under a
generalized parity transformation, which reduces to the ordinary parity
transformation in the (naive) continuum limit. The fermion measure, however,
transforms non-trivially under the generalized parity transformation, and hence
the parity anomaly arises solely from the fermion measure. The analogy to the
lattice construction of chiral gauge theories in even dimensions is clarified
by considering a dimensional reduction. We also propose a natural definition of
a lattice Chern-Simons term, which is consistent with odd dimensional
Ginsparg-Wilson fermions.


title: Low-lying fermion modes, topology and light hadrons in quenched QCD

abstract:
  We explore the properties of low lying eigenmodes of fermions in the quenched
approximation of lattice QCD. The fermion action is a recently proposed overlap
action and has exact chiral symmetry. We find that chiral zero-eigenvalue modes
are localized in space and their positions correlate strongly with the
locations (as defined through the density of pure gauge observables) of
instantons of the appropriate charge. Nonchiral modes are also localized with
peaks which are strongly correlated with the positions of both charges of
instantons. These correlations slowly die away as the fermion eigenvalue rises.
Correlators made of quark propagators restricted to these modes closely
reproduce ordinary hadron correlators at small quark mass in many channels. Our
results are in qualitative agreement with the expectations of instanton liquid
models.


title: Dynamical Fermions with Fat Links

abstract:
  We present and test a new method for simulating dynamical fermions with fat
links. Our construction is based on the introduction of auxiliary but dynamical
gauge fields and works with any fermionic action and can be combined with any
fermionic updating. In our simulation we use an over-relaxation step which
makes it effective. For four flavors of staggered fermions first results
indicate that flavor symmetry at a lattice spacing a~0.2 fm is restored to a
few percent. With the standard action this amount of flavor symmetry
restoration is achieved at a~0.07 fm. We estimate that the overall
computational cost is reduced by at least a factor 10.


title: Quark Mass and Flavour Dependence of the QCD Phase Transition

abstract:
  We analyze the quark mass and flavour dependence of the QCD phase transition
temperature. When the lightest pseudo-scalar meson mass (m_PS) is larger than 2
GeV the critical temperature is controlled by the gluonic sector of QCD alone.
For smaller values of the lightest meson mass the pseudo-critical temperature
decreases slowly with m_PS. For a large regime of meson masses the
pseudo-critical temperature of 2-flavour QCD is about 10% larger than in the
3-flavour case. On lattices with temporal extent N_t=4 an extrapolation to the
chiral limit yields T_c = 173(8) MeV and 154(8) MeV for 2 and 3-flavour QCD,
respectively. We also analyze dynamical quark mass effects on the screening of
the heavy quark potential. A detailed analysis of the heavy quark free energy
in 3-flavour QCD shows that close to T_c screening effects are approximately
quark mass independent already for pseudo-scalar meson masses m_PS = 800 MeV
and screening sets in at distances r = 0.3 fm.


title: Fit to Gluon Propagator and Gribov Formula

abstract:
  We report a numerical study of SU(2) lattice gauge theory in the minimal
Coulomb gauge at beta = 2.2 and 9 different volumes. After extrapolation to
infinite volume, our fit agrees with a lattice discretization of Gribov's
formula for the transverse equal-time would-be physical gluon propagator, that
vanishes like |k| at k = 0, whereas the free equal-time propagator (2|k|)^{-1}
diverges. Our fit lends reality to a confinement scenario in which the would-be
physical gluons leave the physical spectrum while the long-range Coulomb force
confines color.


title: The k=2 string tension in four dimensional SU(N) gauge theories

abstract:
  We calculate the k=2 string tensions in SU(4) and SU(5) gauge theories in 3+1
dimensions, and compare them to the k=1 fundamental string tensions. We find,
from the continuum extrapolation of our lattice calculations, that
K(k=2)/K(k=1) = 1.40(8) in the SU(4) gauge theory, and that K(k=2)/K(k=1) =
1.56(10) in SU(5). We remark upon the way this might constrain the dynamics of
confinement and the intriguing implications it might have for the mass spectrum
of SU(N) gauge theories. We also note that these results agree closely with the
MQCD-inspired conjecture that the SU(N) string tensions satisfy K(k)/K(1) =
sin(k.pi/N)/sin(pi/N).


title: Recent Lattice QCD Results from the UKQCD Collaboration

abstract:
  The lattice technique of studying the strong interaction of matter is used to
obtain predictions of the hadronic spectrum. These simulations were performed
by the UKQCD collaboration using full (unquenched) QCD. Details of the results,
a comparison with quenched data, and novel methods of extracting spectral
properties are described.


title: Helicity modulus as renormalized coupling in the O(3) sigma-model

abstract:
  For the family of O(n) invariant nonlinear sigma-models we consider boundary
conditions that are periodic up to an O(n) rotation. The helicity modulus is
related to the change in free energy under variations of the corresponding
angle. It defines a nonperturbative finite volume running coupling similar to
the Schr"odinger functional for QCD. For the two-dimensional O(3)-model we
investigate this quantity by analytical and numerical techniques. We establish
its universal continuum relation to the finite volume massgap coupling at all
scales and coupling strengths.


title: Phase Structure of the 5D Abelian Higgs Model with Anisotropic Couplings

abstract:
  We establish the phase diagram of the five-dimensional anisotropic Abelian
Higgs model by mean field techniques and Monte Carlo simulations. The
anisotropy is encoded in the gauge couplings as well as in the Higgs couplings.
In addition to the usual bulk phases (confining, Coulomb and Higgs) we find
four-dimensional ``layered'' phases (3-branes) at weak gauge coupling, where
the layers may be in either the Coulomb or the Higgs phase, while the
transverse directions are confining.


title:
Chiral Lagrangians from lattice gauge theories in the strong coupling
  limit

abstract:
  We derive nonlinear sigma models (chiral Lagrangians) over symmetric spaces
U(n), U(2n)/Sp(2n), and U(2n)/O(2n) from U(N), O(N), and Sp(2N) lattice gauge
theories coupled to n flavors of staggered fermions, in the large-N and g^2 N
limit. To this end, we employ Zirnbauer's color-flavor transformation. We prove
the spatial homogeneity of the vacuum configurations of mesons by explicitly
solving the large-N saddle point equations, and thus establish the above
patterns of spontaneous chiral symmetry breaking without any assumptions.


title: Lattice QCD with a chirally twisted mass term

abstract:
  Lattice QCD with Wilson quarks and a chirally twisted mass term represents a
promising alternative regularization of QCD, which does not suffer from
unphysical fermion zero modes. We show how the correlation functions of the
renormalized theory are related to the theory with a standard parameterization
of the mass term. In particular we discuss the conditions under which these
relations take the same form as obtained from naive continuum considerations.
We discuss in detail some applications and comment on potential benefits and
problems of this framework.


title: An Observation of Autocorrelation of Wilson Loops on Lattice

abstract:
  An observation of autocorrelation of Wilson loops on lattice is presented,
especially for the small seperation in Markov chain. We give a possible
explanation for such behavior. We also present the dependence of
autocorrelation behavior on the chosen operators in this paper.


title: Lattice B-Physics

abstract:
  I review the status of lattice simulations relevant for phenomenological
studies of B-physics. Results for much-studied quantities such as f_B, B_B and
form-factors for semileptonic decays are presented as well as those for
quantities which have begun to be studied only recently (such as B-lifetimes).
The improvement in the precision of the determinations of the mass of the
b-quark, which has been made possible by new results for perturbative
coefficients, is discussed. Finally I describe new ideas being developed with
the aim of making computations of two-body non-leptonic decays possible.


title: Lattice instanton action from 3D SU(2) Georgi-Glashow model

abstract:
  3D Georgi-Glashow model is studied on the lattice in the London limit in an
infrared but an intermediate region before the screening appears. Abelian and
instanton dominances are observed after abelian projections in a unitary gauge
and roughly in the maximally abelian gauge. Using an inverse Monte-Carlo
method, we determine an effective instanton action in both gauges. When we
restrict ourselves to some regions of parameters $\beta$ and $\kappa$, we
obtain an almost perfect instanton action, performing a block-spin
transformation on the dual lattice. It takes a form of a Coulomb gas and
reproduces fairly well the string tension obtained analytically by Polyakov.
The almost perfect actions in both gauges look the same in the infrared region,
which suggests gauge independence.


title: The Structure of the Aoki Phase at Weak Coupling

abstract:
  A new method to determine the phase diagram of certain lattice fermionic
field theories in the weakly coupled regime is presented. This method involves
a new type of weak coupling expansion which is multiplicative rather than
additive in nature and allows perturbative calculation of partition function
zeroes. Application of the method to the single flavour Gross-Neveu model gives
a phase diagram consistent with the parity symmetry breaking scenario of Aoki
and provides new quantitative information on the width of the Aoki phase in the
weakly coupled sector.


title: Exact Chiral Symmetry on the Lattice

abstract:
  Developments during the last eight years have refuted the folklore that
chiral symmetries cannot be preserved on the lattice. The mechanism that
permits chiral symmetry to coexist with the lattice is quite general and may
work in Nature as well. The reconciliation between chiral symmetry and the
lattice is likely to revolutionize the field of numerical QCD.


title: Improvement and Renormalization Constants in O(a) Improved Lattice QCD

abstract:
  We present results at beta=6.0 and 6.2 for the O(a) improvement and
renormalization constants for bilinear operators using axial and vector Ward
identities. We discuss the extraction of the mass dependence of the
renormalization constants and the coefficients of the equation of motion
operators.


title:
Domain Wall Fermion Study of Scaling in Non-perturbative Renormalization
  of Quark Bilinears and $B_K$

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


title: Large pion pole in Z_{S}^{MOM}/Z_{P}^{MOM} from Wilson action data

abstract:
  We show that, contrarily to recent claims, data from the Wilson (unimproved)
fermionic action at three different beta values demonstrate the presence of a
large Goldstone boson contribution in the quark pseudoscalar vertex,
quantitatively close to our previous estimate based on the SW action with
c_{SW}=1.769. We show that discretisation errors on Z_{S}^{MOM}/Z_{P}^{MOM}
seem to be much smaller than the Goldstone pole contribution over a very large
range of momenta. The subtraction of this non perturbative contribution leads
to numbers close to one-loop BPT.


title:
Center vortex properties in the Laplace center gauge of SU(2) Yang-Mills
  theory

abstract:
  Resorting to the the Laplace center gauge (LCG) and to the Maximal-center
gauge (MCG), respectively, confining vortices are defined by center projection
in either case. Vortex properties are investigated in the continuum limit of
SU(2) lattice gauge theory. The vortex (area) density and the density of vortex
crossing points are investigated. In the case of MCG, both densities are
physical quantities in the continuum limit. By contrast, in the LCG the
piercing as well as the crossing points lie dense in the continuum limit. In
both cases, an approximate treatment by means of a weakly interacting vortex
gas is not appropriate.


title: QED$_3$ with Dynamical Fermions in an External Magnetic Field

abstract:
  In this paper, we present results of numerical lattice simulations of
two-flavor QED in three space-time dimensions. First, we provide evidence that
chiral symmetry is spontaneously broken in the chiral and continuum limit. Next
we discuss the role of an external magnetic field $B$ on the dynamically
generated fermion mass. We investigate the $B$-dependence of the condensate
through calculations with dynamical fermions using the non-compact formulation
of the gauge field, and compare the results with those of a comparable study
using the quenched approximation.


title: Solution of the Complex Action Problem in the Potts Model for Dense QCD

abstract:
  Monte Carlo simulations of lattice QCD at non-zero baryon chemical potential
$\mu$ suffer from the notorious complex action problem. We consider QCD with
static quarks coupled to a large chemical potential. This leaves us with an
SU(3) Yang-Mills theory with a complex action containing the Polyakov loop.
Close to the deconfinement phase transition the qualitative features of this
theory, in particular its Z(3) symmetry properties, are captured by the 3-d
3-state Potts model. We solve the complex action problem in the Potts model by
using a cluster algorithm. The improved estimator for the $\mu$-dependent part
of the Boltzmann factor is real and positive and is used for importance
sampling. We localize the critical endpoint of the first order deconfinement
phase transition line and find consistency with universal 3-d Ising behavior.
We also calculate the static quark-quark, quark-anti-quark, and
anti-quark-anti-quark potentials which show screening as expected for a system
with non-zero baryon density.


title:
Infinite Volume and Continuum Limits of the Landau-Gauge Gluon
  Propagator

abstract:
  We extend a previous improved action study of the Landau gauge gluon
propagator, by using a variety of lattices with spacings from $a = 0.17$ to
0.41 fm, to more fully explore finite volume and discretization effects. We
also extend a previously used technique for minimizing lattice artifacts, the
appropriate choice of momentum variable or ``kinematic correction'', by
considering it more generally as a ``tree-level correction''. We demonstrate
that by using tree-level correction, determined by the tree-level behavior of
the action being considered, it is possible to obtain scaling behavior over a
very wide range of momenta and lattice spacings. This makes it possible to
explore the infinite volume and continuum limits of the Landau-gauge gluon
propagator.


title: Studying Hadronic Structure of the Photon in Lattice QCD

abstract:
  We show that the matrix element of a local quark-gluon operator in the photon
state, $<\gamma(k\lambda)|\hat O| \gamma(k\lambda)>$, can be calculated in
lattice QCD. The result is generalized to other quantities involving space-like
photons, including the transition form factor $\gamma\gamma^*\to \pi^0$ and the
virtual-photon-nucleon Compton amplitude $<\gamma^*N |\gamma^*N>$ which can be
used to define the generalized Drell-Hearn-Gerasimov and Bjorken sum rules.


title:
Schwinger Model with the Overlap-Dirac Operator: exact results versus a
  physics motivated approximation

abstract:
  We propose new techniques for the numerical implementation of the
overlap-Dirac operator, which exploit the physical properties of the underlying
theory to avoid nested algorithms. We test these procedures in the
two-dimensional Schwinger model and the results are very promising. These
techniques can be directly applied to QCD simulations. We also present a
detailed computation of the spectrum and the chiral properties of the Schwinger
model in the overlap lattice formulation.


title:
Color-Flavor Transformation for the Special Unitary Group and
  Application to Low Energy QCD

abstract:
  The color-flavor transformation for the unitary group (Zirnbauer 1996) is
extended to the special unitary group. The resulting partition function is
represented as sum over disconnected sectors characterized by a U(1)-charge.
Application to low energy QCD on a lattice leads to a theory where the inverse
number of colors appears as expansion parameter. We use a saddle point
approximation to estimate the partition function both in the pure mesonic
sector and in the case of a single baryon on a mesonic background.


title:
Abelian chromomagnetic background field at finite temperature on the
  lattice

abstract:
  The vacuum dynamics of SU(2) and SU(3) lattice gauge theories is studied by
means of a gauge-invariant effective action defined using the lattice
Schr\"odinger functional at finite temperature. In the case of the SU(3) gauge
theory numerical simulations are performed both at zero and finite temperature.
The vacuum is probed using an external constant Abelian chromomagnetic field.
At zero temperature, in agreement with our previous studies for the SU(2)
theory, the external field is totally screened in the continuum limit. At
finite temperature numerical data suggest that confinement is restored by
increasing the strength of the applied field.


title:
How to calculate the bubble nucleation rate in first order transitions
  non-perturbatively

abstract:
  We present a new method for calculating the bubble nucleation rate in first
order phase transitions non-perturbatively on the lattice. The method takes
into account all fluctuations and the full dynamical pre-factor. We also
present results from applying it to the cubic anisotropy model, which has a
radiatively induced, strongly first order phase transition.


title:
Comparison Studies of Finite Momentum Correlators on Anisotropic and
  Isotropic Lattices

abstract:
  We study hadronic two- and three-point correlators relevant for heavy to
light pseudoscalar meson semi-leptonic decays, using Symanzik improved glue,
D234 light quark and NRQCD heavy quark actions. Detailed comparisons are made
between simulations on anisotropic and isotropic lattices involving finite
momentum hadrons. We find evidence that having an anisotropy helps in
extracting better signals at higher momenta. Initial results for the form
factors f_+(q^2) and f_0(q^2) are presented with tree-level matching of the
lattice heavy-light currents.


title:
Structure and Representation Theory for Double Group of Four-Dimensional
  Cubic Group

abstract:
  Hypercubic groups in any dimension are defined and their conjugate
classifications and representation theories are derived. Double group and
spinor representation are introduced. A detailed calculation is carried out on
the structures of four-dimensional cubic group $O_4$ and its double group, as
well as all inequivalent single-valued representations and spinor
representations of $O_4$. All representations are derived adopting Clifford
theory of decomposition of induced representations. Based on these results,
single-valued and spinor representations of the orientation-preserved subgroup
of $O_4$ are calculated.


title: Quark mass effects on the topological susceptibility in QCD

abstract:
  We investigate topology in lattice simulations of QCD with two flavours of
dynamical Wilson fermions. At various sea quark masses we find reasonable
agreement between results for the topological charge from fermionic and gluonic
definitions, the latter with cooling. We study correlations of the topological
charge with light hadronic observables and find effects in the flavour singlet
pseudoscalar channel. The quark mass dependence of the topological
susceptibility, $\chi$, is in agreement with the leading order small m_pi
expectation, chi=(f_pi m_pi)^2/4.


title:
Evidence Against Instanton Dominance of Topological Charge Fluctuations
  in QCD

abstract:
  The low-lying eigenmodes of the Dirac operator associated with typical gauge
field configurations in QCD encode, among other low-energy properties, the
physics behind the solution to the $U_A(1)$ problem (i.e. the origin of the
$\eta'$ mass), the nature of spontaneous chiral symmetry breaking, and the
physics of string-breaking, quark-antiquark pair production, and the OZI rule.
Moreover, the space-time chiral structure of these eigenmodes reflects the
space-time topological structure of the underlying gauge field. We present
evidence from lattice QCD on the local chiral structure of low Dirac eigenmodes
leading to the conclusion that topological charge fluctuations of the QCD
vacuum are not instanton-dominated. The result supports Witten's arguments that
topological charge is produced by confinement-related gauge fluctuations rather
than instantons.


title: Finite-size scaling and the deconfinement transition in gauge theories

abstract:
  We introduce a new method for determining the critical indices of the
deconfinement transition in gauge theories. The method is based on the finite
size scaling behavior of the expectation value of simple lattice operators,
such as the plaquette. We test the method for the case of SU(3) pure gauge
theory in (2+1) dimensions and obtain a precise determination of the critical
index $\nu$, in agreement with the prediction of the Svetitsky-Yaffe
conjecture.


title:
Non-perturbative Renormalisation of Domain Wall Fermions: Quark
  Bilinears

abstract:
  We find the renormalisation coefficients of the quark field and the flavour
non-singlet fermion bilinear operators for the domain wall fermion action, in
the regularisation independent (RI) renormalisation scheme. Our results are
from a quenched simulation, on a 16^3x32 lattice, with beta=6.0 and an extent
in the fifth dimension of 16. We also discuss the expected effects of the
residual chiral symmetry breaking inherent in a domain wall fermion simulation
with a finite fifth dimension, and study the evidence for both explicit and
spontaneous chiral symmetry breaking effects in our numerical results. We find
that the relations between different renormalisation factors predicted by
chiral symmetry are, to a good approximation, satisfied by our results and that
systematic effects due to the (low energy) spontaneous chiral symmetry breaking
and zero-modes can be controlled. Our results are compared against the
perturbative predictions for both their absolute value and renormalisation
scale dependence.


title:
A New Solution to Ginsparg-Wilson Relation from Generalized Staggered
  Fermion

abstract:
  A generalized anti-hermitian staggered Dirac operator is formulated. Its
relation with noncommutative geometry is briefly reviewed. Once this
anti-hermitian operator is modified to be ``$\gamma^5$-hermitian'', it will
provide a new solution to Ginsparg-Wilson relation, basing on an abstract
algebraic analysis of Neuberger's overlap construction and a redefinition of
chirality.


title: Possible Color Octet Quark-Anti-Quark Condensate in the Instanton Model

abstract:
  Inspired by a recent proposal for a Higgs description of QCD we study the
possible formation of a color-octet/flavor-octet quark-anti-quark condensate in
the instanton liquid model. For this purpose we calculate two-point correlation
functions of color-singlet and octet quark-anti-quark operators. We find long
range order in the standard $<\bar{\psi}\psi>$ channel, but not in the
color-octet channel. We emphasize that similar calculations in lattice QCD can
check whether or not a color-flavor locked Higgs phase is realized in QCD at
zero temperature and baryon density.


title: Understanding CP violation in lattice QCD

abstract:
  It is pointed out that any CP violation which may be found in lattice QCD
with a chiral phase in the fermion mass term cannot be relevant for the
continuum theory. CP is classically conserved in the corresponding continuum
theory and is non-anomalous.


title: Monopoles and vortices in pure gauge theories and in Higgs theories

abstract:
  Smeared Abelian and center gauges are introduced in pure non-Abelian lattice
gauge theories. Popular Abelian and center gauges are limits of smeared gauges.
Smeared gauges are also shown to be equivalent to Higgs theories. As a result,
distributions and interactions of monopoles and vortices, which are objects
responsible for confinement in pure gauge theories, can be studied by
investigating classical solutions of Higgs theories.


title: A Lattice Study of the Nucleon Excited States with Domain Wall Fermions

abstract:
  We present results of our numerical calculation of the mass spectrum for
isospin one-half and spin one-half non-strange baryons, i.e. the ground and
excited states of the nucleon, in quenched lattice QCD. We use a new lattice
discretization scheme for fermions, domain wall fermions, which possess almost
exact chiral symmetry at non-zero lattice spacing. We make a systematic
investigation of the negative-parity $N^*$ spectrum by using two distinct
interpolating operators at $\beta=6/g^2=6.0$ on a $16^3 \times 32 \times 16$
lattice. The mass estimates extracted from the two operators are consistent
with each other. The observed large mass splitting between this state,
$N^*(1535)$, and the positive-parity ground state, the nucleon N(939), is well
reproduced by our calculations. We have also calculated the mass of the first
positive-parity excited state and found that it is heavier than the
negative-parity excited state for the quark masses studied.


title: apenext: A Multi-Tflops LQCD Computing Project

abstract:
  This paper is a slightly modified and reduced version of the proposal of the
{\bf apeNEXT} project, which was submitted to DESY and INFN in spring 2000. .It
presents the basic motivations and ideas of a next generation lattice QCD
(LQCD) computing project, whose goal is the construction and operation of
several large scale Multi-TFlops LQCD engines, providing an integrated peak
performance of tens of TFlops, and a sustained (double precision) performance
on key LQCD kernels of about 50% of peak speed.


title: Locality Properties of a New Class of Lattice Dirac Operators

abstract:
  A new class of lattice Dirac operators $D$ which satisfy the index theorem
have been recently proposed on the basis of the algebraic relation
$\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} =
2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands for a non-negative integer and
$k=0$ corresponds to the ordinary Ginsparg-Wilson relation. We analyze the
locality properties of Dirac operators which solve the above algebraic
relation.
  We first show that the free fermion operator is analytic in the entire
Brillouin zone for a suitable choice of parameters $m_{0}$ and $r$, and there
exists a well-defined ``mass gap'' in momentum space, which in turn leads to
the exponential decay of the operator in coordinate space for any finite $k$.
This mass gap in the free fermion operator suggests that the operator is local
for sufficiently weak background gauge fields. We in fact establish a finite
locality domain of gauge field strength for
$\Gamma_{5}=\gamma_{5}-(a\gamma_{5}D)^{2k+1}$ for any finite $k$, which is
sufficient for the cohomological analyses of chiral gauge theory. We also
present a crude estimate of the localization length defined by an exponential
decay of the Dirac operator, which turns out to be much shorter than the one
given by the general Legendre expansion.


title:
Nonperturbative improvement and tree-level correction of the quark
  propagator

abstract:
  We extend an earlier study of the Landau gauge quark propagator in quenched
QCD where we used two forms of the O(a)-improved propagator with the
Sheikholeslami-Wohlert quark action. In the present study we use the
nonperturbative value for the clover coefficient c_sw and mean-field
improvement coefficients in our improved quark propagators. We compare this to
our earlier results which used the mean-field c_sw and tree-level improvement
coefficients for the propagator. We also compare three different
implementations of tree-level correction: additive, multiplicative, and hybrid.
We show that the hybrid approach is the most robust and reliable and can
successfully deal even with strong ultraviolet behavior and zero-crossing of
the lattice tree-level expression. We find good agreement between our improved
quark propagators when using the appropriate nonperturbative improvement
coefficients and hybrid tree-level correction. We also present a simple
extrapolation of the quark mass function to the chiral limit.


title: Chiral Symmetry Versus the Lattice

abstract:
  After mentioning some of the difficulties arising in lattice gauge theory
from chiral symmetry, I discuss one of the recent attempts to resolve these
issues using fermionic surface states in an extra space-time dimension. This
picture can be understood in terms of end states on a simple ladder molecule.


title:
Comment on ``Evidence Against Instanton Dominance of Topological Charge
  Fluctuations in QCD''

abstract:
  We comment on the recent paper (hep-lat/0102003) by Horvath, Isgur, McCune,
and Thacker, which concludes that the local chiral structure of fermionic
eigenmodes is not consistent with instanton dominance. Our calculations, done
with an overlap action, suggest the opposite conclusion.


title: Understanding Color Confinement

abstract:
  An updated review is presented of our understanding of color confinement.
Lattice results on condensation of magnetic charges are discussed. The role of
vortices is analysed.


title: A Regularization of Quantum Gravity

abstract:
  We re-examine results of the Liouville theory and provide arguments that a
{\it negative} bare cosmological constant is essential to define
two-dimensional quantum gravity. From this we are naturally led to a
regularization of quantum gravity within the Regge approach such that it is
described by small fluctuations around equilateral triangles, whose average
link length approaches zero in the continuum limit. We investigate a model
based on this idea numerically and present evidence for the desired long-range
correlations. Interestingly, the approach might generalize to higher
dimensions. The picture of an inflated balloon, which is often used to
demonstrate the properties of an expanding classical universe, seems to be
valuable to understand quantum gravity as well.


title: Color confinement and dual superconductivity of the vacuum. III

abstract:
  It is demonstrated that monopole condensation in the confined phase of SU(2)
and SU(3) gauge theories is independent of the specific Abelian projection used
to define the monopoles. Hence the dual excitations which condense in the
vacuum to produce confinement must have magnetic U(1) charge in all the Abelian
projections. Some physical implications of this result are discussed.


title: Chiral extrapolation of lattice moments of proton quark distributions

abstract:
  We present the resolution of a long-standing discrepancy between the moments
of parton distributions calculated from lattice QCD and their experimental
values. We propose a simple extrapolation formula for the moments of the
nonsinglet quark distribution u-d, as a function of quark mass, which embodies
the general constraints imposed by the chiral symmetry of QCD. The inclusion of
the leading nonanalytic behavior leads to an excellent description of both the
lattice data and the experimental values of the moments.


title: Photon Structure Functions from Quenched Lattice QCD

abstract:
  We calculate the first moment of the photon structure function,
$<x>^{\gamma}=\int^1_0 dx F^{\gamma}_2(x,Q^2)$, on the quenched lattices with
$\beta=6.0$ using the formalism developed by the authors recently. In this
exploratory study, we take into account only the connected contractions. The
result is compared with the experimental data as well as model predictions.


title: From Surface Roughening to QCD String Theory

abstract:
  Surface critical phenomena and the related onset of Goldstone modes represent
fundamental properties of the confining flux in Quantum Chromodynamics. New
ideas on surface roughening and their implications for lattice studies of quark
confinement and string formation are presented. Problems with a simple string
description of the large Wilson surface are discussed.


title: Propagators and Dimensional Reduction of Hot SU(2) Gauge Theory

abstract:
  We investigate the large distance behavior of the electric and magnetic
propagators of hot SU(2) gauge theory in different gauges using lattice
simulations of the full 4d theory and the effective, dimensionally reduced 3d
theory. Comparison of the 3d and 4d propagators suggests that dimensional
reduction works surprisingly well down to the temperature T=2 T_c. Within
statistical uncertainty the electric screening mass is found to be gauge
independent. The magnetic propagator, on the other hand, exhibits a complicated
gauge dependent structure at low momentum.


title: Cluster Percolation and Pseudocritical Behaviour in Spin Models

abstract:
  The critical behaviour of many spin models can be equivalently formulated as
percolation of specific site-bond clusters. In the presence of an external
magnetic field, such clusters remain well-defined and lead to a percolation
transition, even though the system no longer shows thermal critical behaviour.
We investigate the 2-dimensional Ising model and the 3-dimensional O(2) model
by means of Monte Carlo simulations. We find for small fields that the line of
percolation critical points has the same functional form as the line of thermal
pseudocritical points.


title:
Topological susceptibility in full QCD: lattice results versus the
  prediction from the QCD partition function with granularity

abstract:
  Recent lattice data from CP-PACS, UKQCD, SESAM/TXL and the Pisa group
regarding the quark mass dependence of the topological susceptibility in
2-flavour QCD are compared to each other and to theoretical expectations. The
latter get specified by referring to the QCD finite-volume partition function
with ``granularity'' which accounts for the entropy brought by instantons and
anti-instantons. The chiral condensate in $N_f=2$ QCD, if determined by this
method, turns out surprisingly large.


title: Zero temperature string breaking in lattice quantum chromodynamics

abstract:
  The separation of a heavy quark and antiquark pair leads to the formation of
a tube of flux, or "string", which should break in the presence of light
quark-antiquark pairs. This expected zero-temperature phenomenon has proven
elusive in simulations of lattice QCD. We study mixing between the string state
and the two-meson decay channel in QCD with two flavors of dynamical sea
quarks. We confirm that mixing is weak and find that it decreases at level
crossing. While our study does not show direct effects of internal quark loops,
our results, combined with unitarity, give clear confirmation of string
breaking.


title: Quark number susceptibilities, strangeness and dynamical confinement

abstract:
  We report first results on the strange quark number susceptibility, chi_s,
over a large range of temperatures, mainly in the plasma phase of QCD. Chi_s
jumps across the phase transition temperature, T_c, and grows rapidly with
temperature above but close to T_c. For all quark masses and susceptibilities
in the entire temperature range studied, we found significant departures from
ideal-gas values. We also observed a strong correlation between these
quantities and the susceptibility in the scalar/pseudo-scalar channel,
supporting ideas of ``dynamical confinement'' in the high temperature phase of
the QCD plasma.


title: The Weakly Coupled Gross-Neveu Model with Wilson Fermions

abstract:
  The nature of the phase transition in the lattice Gross-Neveu model with
Wilson fermions is investigated using a new analytical technique. This involves
a new type of weak coupling expansion which focuses on the partition function
zeroes of the model. Its application to the single flavour Gross-Neveu model
yields a phase diagram whose structure is consistent with that predicted from a
saddle point approach. The existence of an Aoki phase is confirmed and its
width in the weakly coupled region is determined. Parity, rather than chiral
symmetry breaking naturally emerges as the driving mechanism for the phase
transition.


title: Hybrid Quarkonia with Dynamical Sea Quarks

abstract:
  We present a dynamical lattice calculation with 2 flavours for bottomonium
states with an additional gluonic excitation. Using improved actions for the
quarks and gauge fields at a lattice spacing of $a \approx 0.1$ fm, we find
10.977(61)(62) GeV for the energy of the lowest lying $b\bar bg$-hybrid, where
the first error is statistical and the second denotes the systematic
uncertainty due to the determination of scale. In a parallel quenched
simulation we demonstrate explicitly that vacuum polarisation effects are less
than 10% of the splitting with the ground state.


title: CP(N-1) Models with Theta Term and Fixed Point Action

abstract:
  The topological charge distribution P(Q) is calculated for lattice ${\rm
CP}^{N-1}$ models. In order to suppress lattice cut-off effects we employ a
fixed point (FP) action. Through transformation of P(Q) we calculate the free
energy $F(\theta)$ as a function of the $\theta$ parameter. For N=4, scaling
behavior is observed for P(Q), $F(\theta)$ as well as the correlation lengths
$\xi(Q)$. For N=2, however, scaling behavior is not observed as expected. For
comparison, we also make a calculation for the ${\rm CP}^{3}$ model with
standard action. We furthermore pay special attention to the behavior of P(Q)
in order to investigate the dynamics of instantons. For that purpose, we
carefully look at behavior of $\gamma_{\it eff}$, which is an effective power
of P(Q)($\sim \exp(-CQ^{\gamma_{\it eff}})$), and reflects the local behavior
of P(Q) as a function of Q. We study $\gamma_{\it eff}$ for two cases, one of
which is the dilute gas approximation based on the Poisson distribution of
instantons and the other is the Debye-H\"uckel approximation of instanton
quarks. In both cases we find similar behavior to the one observed in numerical
simulations.


title: Asymptotically free models and discrete non-Abelian groups

abstract:
  We study the two-dimensional renormalization-group flow induced by
perturbations that reduce the global symmetry of the O(3) sigma-model to the
discrete symmetries of Platonic solids. We estimate the value of the
correlation length at which differences in the behaviour of the various models
should be expected. For the icosahedron model, we find xi > 200. We provide an
explanation for the recent numerical results of Patrascioiu and Seiler and of
Hasenfratz and Niedermayer.


title:
A New Approach to Construct the Operator on Lattice for the Calculation
  of Glueball Masses

abstract:
  We develop a new approach to construct the operator on lattice for the
calculation of glueball mass, which is based on the connection between the
continuum limit of the chosen operator and the quantum number $J^{PC}$ of the
state studied. The spin of the state studied is then determined uniquely and
directly in numerical simulation. Furthermore, the approach can be applied to
calculate the mass of glueball states (ground or excited states) with any spin
$J$ including $J\geq 4$. Under the quenched approximation, we present
pre-calculation results for the masses of $0^{++}$ state and $2^{++}$ state,
which are $1754(85)(86)MeV$ and $2417(56)(117)MeV$, respectively.


title: Abelian monopole and vortex condensation in lattice gauge theories

abstract:
  We study Abelian monopole and vortex condensation in lattice pure gauge
theories. Condensation is detected by means of a disorder parameter defined in
terms of a gauge-invariant effective action introduced using the lattice
Schr\"odinger functional. Dirac monopoles condense in the confined phase of
U(1) lattice gauge theory. Abelian monopoles and Abelian vortices condense in
the confined phase of SU(2) and SU(3) lattice gauge theories.


title:
B meson decay constant from two-flavor lattice QCD with non-relativistic
  heavy quarks

abstract:
  We present a study of leptonic $B$ meson decay constants in lattice QCD with
two flavors ($N_f=2$) of light dynamical quarks using NRQCD for the heavy
quark. Gauge configurations are generated with a renormalization-group improved
gauge action and a meanfield-improved clover light quark action. Measurements
are carried out at two values of $\beta=6/g^2$, each for four sea quark masses,
corresponding to the inverse lattice spacing $a^{-1}\approx 1.3$ and 1.8 GeV in
the chiral limit of sea quark. The continuum values of the decay constants are
derived by evaluating the discretization errors at each finite lattice spacing.
We find $f_B^{N_f=2}=204(8)(29)(+44) $ MeV, $f_{B_s}^{N_f=2} = 242(9)(34)(+38)$
MeV, and $f_{B_s}^{N_f=2}/f_B^{N_f=2} = 1.179(18)(23)$, where the errors listed
are statistical, systematic and uncertainty due to choice of the physical
quantity used to fix the scale. Comparison is made to quenched results
($N_f=0$) obtained with the same action combination and matching lattice
spacings. We find $f_B^{N_f=2}/f_B^{N_f=0}=1.07(5)$,
$f_{B_s}^{N_f=2}/f_{B_s}^{N_f=0}=1.10(5)$ and
$(f_{B_s}/f_B)^{N_f=2}/(f_{B_s}/f_B)^{N_f=0}=1.03(2)$, which indicates a 5--10%
increase in the values of the decay constants, but no appreciable change in the
ratio $f_{B_s}/f_B$, due to sea quarks.


title:
Comment on ``Lattice QCD analysis of the strangeness magnetic moment of
  the nucleon''

abstract:
  The recent chirally extrapolated result of Leinweber and Thomas [Phys. Rev. D
{\bf 62}, 074505 (2000), or LT] for the nucleon strangeness form factor
G_M^s(0)= -0.16 \pm 0.18 \mu_N differs markedly from the earlier result -0.75
\pm 0.30 \mu_N obtained by Leinweber [Phys. Rev. D {\bf 53}, 5115 (1996)] from
the same lattice data. An unresolved problem in the LT analysis of lattice data
is identified and addressed. A value of G_M^s(0) = -0.55 \pm 0.37 \mu_N is
obtained at R^s_d = 0.55 by extrapolating only the nucleon isoscalar lattice
data.


title: Exact Zero-Modes of the Compact QED Dirac Operator

abstract:
  We calculate the low-lying eigenmodes of the Neuberger overlap-Dirac operator
for $4d$ compact lattice QED in the quenched approximation. In the strong
coupling phase we find exact zero-modes, quite similar as in non-Abelian
lattice QCD. Subsequently we make an attempt to identify responsible
topological excitations of the U(1) lattice gauge theory.


title:
Determination of $\Lambda_{\overline{MS}}$ from quenched and $N_f = 2$
  dynamical QCD

abstract:
  The scale parameter $\Lambda_{\overline{MS}}$ is computed on the lattice in
the quenched approximation and for $N_f = 2$ flavors of light dynamical quarks.
The dynamical calculation is done with non-perturbatively $O(a)$ improved
Wilson fermions. In the continuum limit we obtain
$\Lambda_{\overline{MS}}^{N_f=0} = 243(1)(10)$ MeV and
$\Lambda_{\overline{MS}}^{N_f=2} = 217(16)(11)$ MeV, respectively.


title: General Ginsparg-Wilson fermions and index

abstract:
  We show rigorously that for general Ginsparg-Wilson fermions the dimensions
of the geometric eigenspace and of the algebraic one for zero modes agree so
that the index theorem on the lattice is not spoiled by unwanted additional
terms.


title: Measurement of hybrid content of heavy quarkonia using lattice NRQCD

abstract:
  Using lowest-order lattice NRQCD to create heavy meson propagators and
applying the spin-dependent interaction, $c_B^{}
\frac{-g}{2m_q}\vec\sigma\cdot\vec{B}$, at varying intermediate time slices, we
compute the off-diagonal matrix element of the Hamiltonian for the
quarkonium-hybrid two-state system. Thus far, we have results for one set of
quenched lattices with an interpolation in quark mass to match the bottomonium
spectrum. After diagonalization of the two-state Hamiltonian, we find the
ground state of the $\Upsilon$ to show a $0.0035(1)c_B^2$ (with $c_B^2 \sim
1.5-3.1$) probability admixture of hybrid, $|b\bar{b}g>$.


title:
O(a)-improved quark action on anisotropic lattices and perturbative
  renormalization of heavy-light currents

abstract:
  We investigate the Symanzik improvement of the Wilson quark action on
anisotropic lattices. Taking first a general action with nearest-neighbor and
clover interactions, we study the mass dependence of the ratio of the hopping
parameters, the clover coefficients, and an improvement coefficient for
heavy-light vector and axial vector currents. We show how tree-level
improvement can be achieved. For a particular choice of the spatial Wilson
coupling, the results simplify, and $O(m_0a_\tau)$ improvement is possible.
(Here $m_0$ is the bare quark mass and $a_\tau$ the temporal lattice spacing.)
With this choice we calculate the renormalization factors of heavy-light
bilinear operators at one-loop order of perturbation theory employing the
standard plaquette gauge action.


title:
SU(N) gauge theories in four dimensions: exploring the approach to N =
  infinity

abstract:
  We calculate the string tension, K, and some of the lightest glueball masses,
M, in 3+1 dimensional SU(N) lattice gauge theories for N=2,3,4,5 . From the
continuum extrapolation of the lattice values, we find that the mass ratios,
M/sqrt(K), appear to show a rapid approach to the large-N limit, and, indeed,
can be described all the way down to SU(2) using just a leading O(1/NxN)
correction. We confirm that the smooth large-N limit we find, is obtained by
keeping a constant 't Hooft coupling. We also calculate the topological charge
of the gauge fields. We observe that, as expected, the density of small-size
instantons vanishes rapidly as N increases, while the topological
susceptibility appears to have a non-zero N=infinity limit.


title:
Equation of state in finite-temperature QCD with two flavors of improved
  Wilson quarks

abstract:
  We present results of a first study of equation of state in
finite-temperature QCD with two flavors of Wilson-type quarks. Simulations are
made on lattices with temporal size $N_t=4$ and 6, using an RG-improved action
for the gluon sector and a meanfield-improved clover action for the quark
sector. The lines of constant physics corresponding to fixed values of the
ratio $m_{\rm PS}/m_{\rm V}$ of the pseudo-scalar to vector meson masses at
zero temperature are determined, and the beta functions which describe the
renormalization-group flow along these lines are calculated. Using these
results, the energy density and the pressure are calculated as functions of
temperature along the lines of constant physics in the range $m_{\rm PS}/m_{\rm
V} = 0.65$--0.95. The quark mass dependence in the equation of state is found
to be small for $m_{\rm PS}/m_{\rm V} \simlt 0.8$. Comparison of results for
$N_t=4$ and $N_t=6$ lattices show significant scaling violation present in the
$N_t=4$ results. At high temperatures the results for $N_t=6$ are quite close
to the continuum Stefan-Boltzmann limit, suggesting the possibility of a
precise continuum extrapolation of thermodynamic quantities from simulations at
$N_t\simgt 6$.


title: Flavor Symmetry and the Static Potential with Hypercubic Blocking

abstract:
  We introduce a new smearing transformation, the hypercubic (HYP) fat link.
The hypercubic fat link mixes gauge links within hypercubes attached to the
original link only. Using quenched lattices at beta = 5.7 and 6.0 we show that
HYP fat links improve flavor symmetry by an order of magnitude relative to the
thin link staggered action. The static potential measured on HYP smeared
lattices agrees with the thin link potential at distances r/a >= 2 and has
greatly reduced statistical errors. These quenched results will be used in
forthcoming dynamical simulations of HYP staggered fermions.


title: Remarks on the Gribov Problem in Direct Maximal Center Gauge

abstract:
  We review the equivalence of maximal center gauge fixing to the problem of
finding the best fit, to a given lattice gauge field, by a thin vortex
configuration. This fit is necessarily worst at the location of P-plaquettes.
We then compare the fits achieved in Gribov copies generated by (i)
over-relaxation; (ii) over-relaxation after Landau gauge preconditioning; and
(iii) simulated annealing. Simulated annealing yields the best fit if all links
on the lattice are included, but the situation changes if we consider only the
lattice volume exterior to P-plaquettes. In this exterior region, the fit is
best for Gribov copies generated by over-relaxation, and worst for Gribov
copies generated after Landau gauge preconditioning. The two fitting criteria
(including or not including the P-plaquettes) yield string tensions differing
by -34% to +20% respectively, relative to the full string tension. Our usual
procedure (``quenched minimization'') seems to be a compromise between these
criteria, and yields string tensions at an intermediate value close to the full
string tension.


title: Calorons and localization of quark eigenvectors in lattice QCD

abstract:
  We analyze the localization properties for eigenvectors of the Dirac operator
in quenched lattice QCD in the vicinity of the deconfinement phase transition.
Studying the characteristic differences between the Z_3 sectors above the
critical temperature T_c, we find indications for the presence of calorons.


title: Anatomy of the lattice magnetic monopoles

abstract:
  We study the Abelian and non-Abelian action densitynear the monopole in the
maximal Abelian gauge of SU(2) lattice gauge theory. We find that the
non-Abelian action density near the monopoles belonging to the percolating
cluster decreases when we approach the monopole center. Our estimate of the
monopole radius is R_mon ~ 0.04 fm.


title: Monopoles and Confining Strings in QCD

abstract:
  We review the recent results in the physics of the magnetic monopoles in
gluodynamics and a dual formulation of non-Abelian theories, relevant to the
physics of the confinement. It occurs that the dual gluon is a U(1) gauge
boson, despite of the fact that usual gluons are non-Abelian. The effective
infrared Lagrangian for gluodynamics is suggested which leads to the Casimir
scaling of the string tension for quarks in various representations. We also
show that the results of the calculations in lattice gauge theories confirm our
theoretical predictions.


title: Lattice calculation of medium effects at short and long distances

abstract:
  We investigate medium effects in QCD like chromoelectric screening and
quasi-particle mass generation by calculating the heavy quark potential as well
as the temporal quark and gluon Coulomb gauge propagators in quenched
approximation.


title: The Local Bosonic Algorithm applied to the massive Schwinger model

abstract:
  We investigate various variants of the Hermitean version of the Local Bosonic
Algorithm proposed by M. L\"uscher. The model used is two-dimensional Quantum
Electrodynamics (QED) with two flavours of massive Wilson fermions. The
simplicity of the model allows high statistics simulations close to the chiral
and continuum limit.
  To find optimal CPU cost behaviour, we vary the approximation polynomial
parameters $n$ and \epsilon$ as well as the number of over-relaxation steps
within each trajectory. We find flat behaviour around the optimum and a modest
gain with respect to the Hybrid Monte Carlo algorithm for all variants.
  On the technical side, we demonstrate that a noisy Metropolis acceptance step
is possible also for the Hermitean variant. The numerical instabilities
appearing in the evaluation Chebyshev polynomial are investigated. We propose a
quantitative criterion for these instabilities and a reordering scheme of the
roots reducing the problem.
  The more physical problem of topological charge sectors and metastability is
addressed. We find no plateau in the effective pion mass if metastabilities
become too large.


title:
Non-perturbative computation of the bubble nucleation rate in the cubic
  anisotropy model

abstract:
  At first order phase transitions the transition proceeds through droplet
nucleation and growth. We discuss a lattice method for calculating the droplet
nucleation rate, including the complete dynamical factors. The method is
especially suitable for very strongly suppressed droplet nucleation, which is
often the case in physically interesting transitions. We apply the method to
the 3-dimensional cubic anisotropy model in a parameter range where the model
has a radiatively induced strong first order phase transition, and compare the
results with analytical approaches.


title:
Meson Screening Masses at high Temperature in quenched QCD with improved
  Wilson Quarks

abstract:
  We report on a lattice investigation of improved quenched Wilson fermions
above and below the confinement-deconfinement phase transition. Results on
meson screening masses as well as spatial wave functions are presented.
Moreover, the meson dispersion relation is studied. Below the critical
temperature we do not observe any significant temperature effect while above
$T_c$ the data are consistent with a leading free quark behavior.


title: A lattice evaluation of four-quark operators in the nucleon

abstract:
  Nucleon matrix elements of various four-quark operators are evaluated in
quenched lattice QCD using Wilson fermions. Some of these operators give rise
to twist-four contributions to nucleon structure functions. Furthermore, they
bear valuable information about the diquark structure of the nucleon. Mixing
with lower-dimensional operators is avoided by considering appropriate
representations of the flavour group. We find that for a certain flavour
combination of baryon structure functions, twist-four contributions are very
small. This suggests that twist-four effects for the nucleon might be much
smaller than m_p^2/Q^2.


title:
A new method to study lattice QCD at finite temperature and chemical
  potential

abstract:
  Due to the sign problem, it is exponentially difficult to study QCD on the
lattice at finite chemical potential. We propose a method --an overlap
improving multi-parameter reweighting technique-- to alleviate this problem. We
apply this method and give the phase diagram of four-flavor QCD obtained on
lattices 4^4 and 4\cdot6^3. Our results are based on {\cal{O}}(10^3-10^4)
configurations.


title: The QCD spectrum with three quark flavors

abstract:
  We present results from a lattice hadron spectrum calculation using three
flavors of dynamical quarks - two light and one strange, and quenched
simulations for comparison. These simulations were done using a one-loop
Symanzik improved gauge action and an improved Kogut-Susskind quark action. The
lattice spacings, and hence also the physical volumes, were tuned to be the
same in all the runs to better expose differences due to flavor number. Lattice
spacings were tuned using the static quark potential, so as a byproduct we
obtain updated results for the effect of sea quarks on the static quark
potential. We find indications that the full QCD meson spectrum is in better
agreement with experiment than the quenched spectrum. For the 0++ (a0) meson we
see a coupling to two pseudoscalar mesons, or a meson decay on the lattice.


title: SU(2) gluon propagators from the lattice - a preview

abstract:
  High accuracy numerical results for the SU(2) gluonic form factor are
previewed for the case of Landau gauge. I focus on the information of quark
confinement encoded in the gluon propagator.


title: Topological Susceptibility of Yang-Mills Center Projection Vortices

abstract:
  The topological susceptibility induced by center projection vortices
extracted from SU(2) lattice Yang-Mills configurations via the maximal center
gauge is measured. Two different smoothing procedures, designed to eliminate
spurious ultraviolet fluctuations of these vortices before evaluating the
topological charge, are explored. They result in consistent estimates of the
topological susceptibility carried by the physical thick vortices
characterizing the Yang-Mills vacuum in the vortex picture. This susceptibility
is comparable to the one obtained from the full lattice Yang-Mills
configurations. The topological properties of the SU(2) Yang-Mills vacuum can
thus be accounted for in terms of its vortex content.


title: Non-Perturbative Renormalization in Lattice Field Theory

abstract:
  Non-perturbative renormalization of lattice composite operators plays a
crucial role in many applications of lattice field theory. We sketch the
general problems involved in this task and the methods which are currently used
to cope with them. We present a detailed investigation of a new approach based
on the operator product expansion. We test the new method on the
two-dimensional O(3) sigma-model and discuss its advantages and limitations.
Ph.D. thesis at Scuola Normale Superiore, Pisa, Italy.


title: $K \to \pi\pi$ Decays in a Finite Volume

abstract:
  We discuss finite-volume computations of two-body hadronic decays below the
inelastic threshold (e.g. $K\to\pi\pi$ decays). The relation between
finite-volume matrix elements and physical amplitudes, recently derived by
Lellouch and L\"uscher, is extended to all elastic states under the inelastic
threshold. We present a detailed comparison of our approach with that of
Lellouch and L\"uscher and discuss the possible limitations of the method which
could arise due to the presence of inelastic thresholds. We also examine a
standard alternative method which can be used to extract the real part of the
decay amplitude from correlators of the form $< 0 |T[\pi\pi{\cal H}_WK ]| 0 >$.
We show that in this case there are finite-volume corrections which vanish as
inverse powers of the volume, which cannot be removed by a multiplicative
factor.


title: The Calculation of the Perturbative Expansion of Wilson Loops on Lattice

abstract:
  We introduce an approach to expand gauge-invariant Wilson operators on
lattice. This approach is based on non-abelian Stokes theorem and overcomes
some shortage of some former methods. It is also suitable for expanding any
Wilson operators on lattice.


title: SU(2) vortex configuration in Laplacian Center Gauge

abstract:
  We study how Laplacian Center Gauge identifies the vortex content of a thick
SU(2) vortex configuration on the lattice. This configuration is a solution of
the Yang-Mills classical equations of motion having vortex properties. We find
that this gauge fixing procedure cleanly identifies the underlying vortex
properties. We also study the monopole content of this configuration detected
with this procedure. We obtain two monopole curves lying on the surface of the
vortex.


title: Contents of Lattice 2000 Proceedings

abstract:
  We give here a compilation of papers presented at Lattice 2000 (XVIII Intl.
Symposium on Lattice Field Theory, Bangalore, India, 17-22 August 2000). The
table of contents provides links to papers on the e-print arXiv.


title: Diquark Condensation at Nonzero Chemical Potential and Temperature

abstract:
  SU(2) lattice gauge theory with four flavors of quarks is studied at nonzero
chemical potential $\mu$ and temperature $T$ by computer simulation and
Effective Lagrangian techniques. Simulations are done on $8^4$, $8^3 \times 4$
and $12^3 \times 6$ lattices and the diquark condensate, chiral order
parameter, Wilson line, fermion energy and number densities are measured.
Simulations at a fixed, nonzero quark mass provide evidence for a tricritical
point in the $\mu$-$T$ plane associated with diquark condensation. For low $T$,
increasing $\mu$ takes the system through a line of second order phase
transitions to a diquark condensed phase. Increasing $T$ at high $\mu$, the
system passes through a line of first order transitions from the diquark phase
to the quark-gluon plasma phase. Using Effective Lagrangians we estimate the
position of the tricritical point and ascribe its existence to trilinear
couplings that increase with $\mu$ and $T$.


title:
Scaling behaviour at the $N_t=6$ chiral phase transition for 2-flavour
  lattice QCD with massless staggered quarks, and an irrelevant 4-fermion
  interaction

abstract:
  We have simulated lattice QCD with 2 flavours of massless staggered quarks.
An irrelevant chiral 4-fermion interaction was added to the standard quark
action to allow us to simulate at zero quark mass. Thermodynamics was studied
on lattices of temporal extent 6. Clear evidence for a second order chiral
transition was observed and the critical exponents $\beta_{mag}$, $\delta$,
$\nu$ and $\gamma_{mag}$ were measured. These exponents did not agree with
those expected by standard universality arguments. They were, however,
consistent with tricritical behaviour. The $\pi$ and $\sigma$ screening masses
were measured and showed clear evidence for chiral symmetry restoration at this
transition.


title: Problems in Lattice Gauge Fixing

abstract: We review many topics and results about numeric gauge fixing in lattice QCD.


title: Chiral Behaviour of the Rho Meson in Lattice QCD

abstract:
  In order to guide the extrapolation of the mass of the rho meson calculated
in lattice QCD with dynamical fermions, we study the contributions to its
self-energy which vary most rapidly as the quark mass approaches zero; from the
processes $\rho \to \omega \pi$ and $\rho \to \pi \pi$. It turns out that in
analysing the most recent data from CP-PACS it is crucial to estimate the
self-energy from $\rho \to \pi \pi$ using the same grid of discrete momenta as
included implicitly in the lattice simulation. The correction associated with
the continuum, infinite volume limit can then be found by calculating the
corresponding integrals exactly. Our error analysis suggests that a factor of
10 improvement in statistics at the lowest quark mass for which data currently
exists would allow one to determine the physical rho mass to within 5%.
Finally, our analysis throws new light on a long-standing problem with the
J-parameter.


title: O(a) improved twisted mass lattice QCD

abstract:
  Lattice QCD with Wilson quarks and a chirally twisted mass term (tmQCD) has
been introduced in refs. [1,2]. We here apply Symanzik's improvement programme
to this theory and list the counterterms which arise at first order in the
lattice spacing a. Based on the generalised transfer matrix, we define the
tmQCD Schrodinger functional and use it to derive renormalized on-shell
correlation functions. By studying their continuum approach in perturbation
theory we then determine the new O(a) counterterms of the action and of a few
quark bilinear operators to one-loop order.


title: Topological Susceptibility on Dynamical Staggered Fermion Configurations

abstract:
  The topological susceptibility is one of the few physical quantities that
directly measure the properties of the QCD vacuum. Chiral perturbation theory
predicts that in the small quark mass limit the topological susceptibility
depends quadratically on the pion mass, approaching zero in the chiral limit.
Lattice calculations have difficulty reproducing this behavior. In this paper
we study the topological susceptibility on dynamical staggered fermion
configurations. Our results indicate that the lattice spacing has to be small,
around a~0.1fm for thin link staggered fermion actions to show the expected
chiral behavior. Our preliminary result indicates that fat link fermions, on
the other hand, reproduce the theoretical expectations even on lattices with
a~0.17fm. We argue that this is due to the improved flavor symmetry of fat link
fermionic actions.


title:
The masses of the mesons and baryons. Part V. The neutrino branch
  particles

abstract:
  We have determined theoretically the rest mass of the muon neutrino at 50
milli-eV and the rest mass of the electron neutrino at 5 meV, as well as, to 1%
accuracy, the ratio of the masses of the stable elementary particles which
decay by weak decays. We assume that the particles of the neutrino branch
consist of a cubic, isotropic nuclear lattice, held together by the weak
nuclear force. The eigenfrequencies of the lattice are calculated with Born's
theory of cubic lattices. Only neutrinos are required to explain the so-called
stable particles of the neutrino branch.


title: Instanton dominance of topological charge fluctuations in QCD?

abstract:
  We consider the local chirality of near-zero eigenvectors from Wilson-Dirac
and clover improved Wilson-Dirac lattice operators as proposed recently by
Horv\'ath et al. We studied finer lattices and repaired for the loss of
orthogonality due to the non-normality of the Wilson-Dirac matrix. As a result
we do see a clear double peak structure on lattices with resolutions higher
than 0.1 fm. We found that the lattice artifacts can be considerably reduced by
exploiting the biorthogonal system of left and right eigenvectors. We conclude
that the dominance of instantons on topological charge fluctuations is not
ruled out by local chirality measurements.


title:
The Ising Model on a Dynamically Triangulated Disk with a Boundary
  Magnetic Field

abstract:
  We use Monte Carlo simulations to study a dynamically triangulated disk with
Ising spins on the vertices and a boundary magnetic field. For the case of zero
magnetic field we show that the model possesses three phases. For one of these
the boundary length grows linearly with disk area, while the other two phases
are characterized by a boundary whose size is on the order of the cut-off. A
line of continuous magnetic transitions separates the two small boundary
phases. We determine the critical exponents of the continuous magnetic phase
transition and relate them to predictions from continuum 2-d quantum gravity.
This line of continuous transitions appears to terminate on a line of
discontinuous phase transitions dividing the small boundary phases from the
large boundary phase. We examine the scaling of bulk magnetization and boundary
magnetization as a function of boundary magnetic field in the vicinity of this
tricritical point.


title: First results on the running coupling in QCD with two massless flavours

abstract:
  We report on the non-perturbative computation of the running coupling of
two-flavour QCD in the Schr"odinger functional scheme. The corresponding
Lambda-parameter, which describes the coupling strength at high energy, is
related to a low energy scale which still remains to be connected to a hadronic
``experimentally'' observable quantity. We find the non-perturbative evolution
of the coupling indispensable to avoid untolerable errors in the estimated
Lambda-parameter.


title: Are Topological Charge Fluctuations in QCD Instanton Dominated?

abstract:
  We consider a recent proposal by Horv\'ath {\em et al.} to address the
question whether topological charge fluctuations in QCD are instanton dominated
via the response of fermions using lattice fermions with exact chiral symmetry,
the overlap fermions. Considering several volumes and lattice spacings we find
strong evidence for chirality of a finite density of low-lying eigenvectors of
the overlap-Dirac operator in the regions where these modes are peaked. This
result suggests instanton dominance of topological charge fluctuations in
quenched QCD.


title:
A No-Go Theorem for the Compatibility between Involutions of the First
  Order Differentials on a Lattice and the Continuum Limit

abstract:
  We prove that the following three properties can not match each other on a
lattice, that differentials of coordinate functions are algebraically dependent
to their involutive conjugates, that the involution on a lattice is an
antihomomorphism and that differential calculus has a natural continuum limit.


title:
Chirality Correlation within Dirac Eigenvectors from Domain Wall
  Fermions

abstract:
  In the dilute instanton gas model of the QCD vacuum, one expects a strong
spatial correlation between chirality and the maxima of the Dirac eigenvectors
with small eigenvalues. Following Horvath, {\it et al.} we examine this
question using lattice gauge theory within the quenched approximation. We
extend the work of those authors by using weaker coupling, $\beta=6.0$, larger
lattices, $16^4$, and an improved fermion formulation, domain wall fermions. In
contrast with this earlier work, we find a striking correlation between the
magnitude of the chirality density, $|\psi^\dagger(x)\gamma^5\psi(x)|$, and the
normal density, $\psi^\dagger(x)\psi(x)$, for the low-lying Dirac eigenvectors.


title:
Fermion propagator at finite temperatures on extremely anisotropic
  lattice

abstract:
  Fermion propagator is computed in a simple model on an extremely anisotropic
lattice $\xi\gg1$. Fermion determinant is evaluated up to $\xi^{-4}$ order.
Chiral condensate is estimated in mean field approximation.


title: A new way to deal with fermions in Monte Carlo simulations

abstract:
  An exact, nonlocal, finite step-size algorithm for Monte Carlo simulation of
theories with dynamical fermions is proposed. The algorithm is based on
obtaining the new configuration U' from the old one U by solving the equation $
M(U') \eta = \omega M(U) \eta$, where $M$ is fermionic operator, $\eta$ is
random Gaussian vector, and $\omega$ is random real number close to unity. This
algorithm can be used for the acceleration of current simulations in theories
with Grassmann variables. A first test was done for SU(3) QCD with purely
fermionic term in the action.


title: Monopoles Vortices and Confinement

abstract: The status of our understanding of colour confinement is reviewed.


title: Quenched Finite Volume Logarithms

abstract:
  Quenched chiral perturbation theory is used to compute the first finite
volume correction to the chiral condensate. The correction diverges
logarithmically with the four-volume $V$. We point out that with dynamical
quarks one can obtain both the chiral condensate and the pion decay constant
from the distributions of the lowest Dirac operator eigenvalues.


title:
Spectrum of the SU(3) Dirac operator on the lattice: Transition from
  random matrix theory to chiral perturbation theory

abstract:
  We calculate complete spectra of the Kogut-Susskind Dirac operator on the
lattice in quenched SU(3) gauge theory for various values of coupling constant
and lattice size. From these spectra we compute the connected and disconnected
scalar susceptibilities and find agreement with chiral random matrix theory up
to a certain energy scale, the Thouless energy. The dependence of this scale on
the lattice volume is analyzed. In the case of the connected susceptibility
this dependence is anomalous, and we explain the reason for this. We present a
model of chiral perturbation theory that is capable of describing the data
beyond the Thouless energy and that has a common range of applicability with
chiral random matrix theory.


title: Thermodynamics of SU(3) gauge theory on anisotropic lattices

abstract:
  Finite temperature SU(3) gauge theory is studied on anisotropic lattices
using the standard plaquette gauge action. The equation of state is calculated
on $16^{3} \times 8$, $20^{3} \times 10$ and $24^{3} \times 12$ lattices with
the anisotropy $\xi \equiv a_s / a_t = 2$, where $a_s$ and $a_t$ are the
spatial and temporal lattice spacings. Unlike the case of the isotropic lattice
on which $N_t=4$ data deviate significantly from the leading scaling behavior,
the pressure and energy density on an anisotropic lattice are found to satisfy
well the leading $1/N_t^2$ scaling from our coarsest lattice, $N_t/\xi=4$. With
three data points at $N_t/\xi=4$, 5 and 6, we perform a well controlled
continuum extrapolation of the equation of state. Our results in the continuum
limit agree with a previous result from isotropic lattices using the same
action, but have smaller and more reliable errors.


title:
Bound states for Overlap and Fixed Point Actions close to the chiral
  limit

abstract:
  We study the overlap and the fixed point Dirac operators for massive fermions
in the two-flavor lattice Schwinger model. The masses of the triplet (pion) and
singlet (eta) bound states are determined down to small fermion masses and the
mass dependence is compared with various continuum model approximations. Near
the chiral limit, at very small fermion masses the fixed point operator has
stability problems, which in this study are dominated by finite size effects,


title: Multi--Layer Structure in the Strongly Coupled 5D Abelian Higgs Model

abstract:
  We explore the phase diagram of the five-dimensional anisotropic Abelian
Higgs model by Monte Carlo simulations. In particular, we study the transition
between the confining phase and the four dimensional layered Higgs phase. We
find that, in a certain region of the lattice parameter space, this transition
can be first order and that each layer moves into the Higgs phase independently
of the others (decoupling of layers). As the Higgs couplings vary, we find,
using mean field techniques, that this transition may probably become second
order.


title:
Light Hadron Spectroscopy with Two Flavors of Dynamical Quarks on the
  Lattice

abstract:
  We present results of a numerical calculation of lattice QCD with two
degenerate flavors of dynamical quarks, identified with up and down quarks, and
with a strange quark treated in the quenched approximation. The lattice action
and simulation parameters are chosen with a view to carrying out an
extrapolation to the continuum limit as well as chiral extrapolations. Gauge
configurations are generated with a renormalization-group improved gauge action
and a mean field improved clover quark action at three values of $\beta$ and
four sea quark masses. The sizes of lattice are chosen so that the physical
spatial size is kept constant. Hadron masses, light quark masses and meson
decay constants are measured at five valence quark masses. We also carry out
complementary quenched simulations with the same improved actions. The quenched
spectrum from this analysis agrees well in the continuum limit with the one of
our earlier work using the standard action. We find the two-flavor full QCD
meson masses in the continuum limit to be much closer to experimental meson
masses than those from quenched QCD. We take these results as manifestations of
sea quark effects in two-flavor full QCD. For baryon masses full QCD values for
strange baryons are in agreement with experiment, while they differ
increasingly with decreasing strange quark content, resulting in a nucleon mass
higher than experiment. The pattern suggests finite size effects as a possible
origin for this deviation. For light quark masses in the continuum limit we
obtain values which are reduced by about 25% compared to the values in quenched
QCD. We also present results for decay constants where large scaling violations
obstruct a continuum extrapolation. Need for a non-perturbative estimate of
renormalization factors is discussed.


title: Effective Lagrangian for strongly coupled domain wall fermions

abstract:
  We derive the effective Lagrangian for mesons in lattice gauge theory with
domain-wall fermions in the strong-coupling and large-N_c limits. We use the
formalism of supergroups to deal with the Pauli-Villars fields, needed to
regulate the contributions of the heavy fermions. We calculate the spectrum of
pseudo-Goldstone bosons and show that domain wall fermions are doubled and
massive in this regime. Since we take the extent and lattice spacing of the
fifth dimension to infinity and zero respectively, our conclusions apply also
to overlap fermions.


title: Geometric Origin of Staggered Fermion: Direct Product K-Cycle

abstract:
  Staggered formalism of lattice fermion can be cast into a form of direct
product K-cycle in noncommutative geometry. The correspondence between this
staggered K-cycle and a canonically defined K-cycle for finitely generated
abelian group where lattice appears as a special case is proved.


title: Direct Improvement of Hamiltonian Lattice Gauge Theory

abstract:
  We demonstrate that a direct approach to improving Hamiltonian lattice gauge
theory is possible. Our approach is to correct errors in the Kogut-Susskind
Hamiltonian by incorporating additional gauge invariant terms. The coefficients
of these terms are chosen so that the order $a^2$ classical errors vanish. We
conclude with a brief discussion of tadpole improvement in Hamiltonian lattice
gauge theory.


title:
The First Calculation for the Mass of the Ground $4^{++}$ Glueball State
  on Lattice

abstract:
  Under the quenched approximation, we perform a lattice calculation for the
mass of the ground $4^{++}$ glueball state in $E^{++}$ channel on a $D=3+1$
lattice. Our calculation shows that the mass of this state is
$M_G(4^{++})=3.65(6)(18)GeV$, which rules out the $4^{++}$ or mainly $4^{++}$
glueball interpretation for $\xi(2230)$.


title: Kaon B parameter from quenched domain-wall QCD

abstract:
  We report on a calculation of $B_K$ with domain wall fermion action in
quenched QCD. Simulations are made with a renormalization group improved gauge
action at $\beta=2.6$ and 2.9 corresponding to $a^{-1}\approx 2$GeV and 3GeV.
Effects due to finite fifth dimensional size $N_5$ and finite spatial size
$N_\sigma$ are examined in detail. Matching to the continuum operator is made
perturbatively at one loop order. We obtain $B_K(\mu = 2 GeV)=
0.5746(61)(191)$, where the first error is statistical and the second error
represents an estimate of scaling violation and ${\cal O}(\alpha^2)$ errors in
the renormalization factor added in quadrature, as an estimate of the continuum
value in the $\msbar$ scheme with naive dimensional regularization. This value
is consistent, albeit somewhat small, with $B_K(\mu = 2 {GeV})= 0.628(42)$
obtained by the JLQCD Collaboration using the Kogut-Susskind quark action.
Results for light quark masses are also reported.


title: A lattice study of 3D compact QED at finite temperature

abstract:
  We study the deconfinement phase transition and monopole properties in the
finite temperature 3D compact Abelian gauge model on the lattice. We predict
the critical coupling as function of the lattice size in a simplified model to
describe monopole binding. We demonstrate numerically that the monopoles are
sensitive to the transition. In the deconfinement phase the monopoles appear in
the form of a dilute gas of magnetic dipoles. In the confinement phase both
monopole density and string tension differ from semiclassical estimates if
monopole binding is neglected. However, the analysis of the monopole clusters
shows that the relation between the string tension and the density of monopoles
in charged clusters is in reasonable agreement with those predictions. We study
the cluster structure of the vacuum in both phases of the model.