title: Renormalization Group Flow of SU(3) Gauge Theory

abstract:
  We calculate numerically the renormalization group (RG) flow of lattice QCD
in two-coupling space, $(\beta_{1\times 1},\beta_{1\times 2})$. This is the
first explicit calculation of the RG flow of SU(3) gauge theory. From the RG
flow,a renormalized trajectory (RT) is revealed. Its behavior is consistent
with the strong coupling expansion near the high-temperature fixed point.
Actions with $(\beta_{1\times 1},\beta_{1\times 2})$ are studied; the lattice
spacing is evaluated by measuring the string tension from the heavy quark
potential. Recovery of the rotational symmetry is studied as a function of the
ratio $\beta_{1\times 2} / \beta_{1\times 1}$.


title: Resummation of Cactus Diagrams in Lattice QCD

abstract:
  We show how to perform a resummation, to all orders in perturbation theory,
of a certain class of gauge invariant diagrams in Lattice QCD. These diagrams
are often largely responsible for lattice artifacts. Our resummation leads to
an improved perturbative expansion. Applied to a number of cases of interest,
this expansion yields results remarkably close to corresponding nonperturbative
estimates.


title: Chiral Fermions on the Lattice

abstract:
  A recently proposed method for regularizing chiral gauge theories
non-perturbatively is discussed in detail. The result is an effective action
which can be computed from the lattice gauge field, and which is suited for
numerical simulations.


title:
Evidence for fractional topological charge in SU(2) pure Yang-Mills
  theory

abstract:
  We investigate the spectral flows of the hermitian Wilson-Dirac operator in
the fundamental and adjoint representations on two ensembles of pure SU(2)
gauge field configurations at the same physical volume. We find several
background gauge field configurations where the index of the hermitian
Wilson-Dirac operator in the adjoint representation is not four times the index
in the fundamental representation. This could imply a topological basis for the
gluino condensate in supersymmetric Yang-Mills theories.


title:
Critical Exponents of the 3D Ising Universality Class From Finite Size
  Scaling With Standard and Improved Actions

abstract:
  We propose a method to obtain an improved Hamiltonian (action) for the Ising
universality class in three dimensions. The improved Hamiltonian has suppressed
leading corrections to scaling. It is obtained by tuning models with two
coupling constants. We studied three different models: the +1,-1 Ising model
with nearest neighbour and body diagonal interaction, the spin-1 model with
states 0,+1,-1, and nearest neighbour interaction, and phi**4-theory on the
lattice (Landau-Ginzburg Hamiltonian). The remarkable finite size scaling
properties of the suitably tuned spin-1 model are compared in detail with those
of the standard Ising model. Great care is taken to estimate the systematic
errors from residual corrections to scaling. Our best estimates for the
critical exponents are nu= 0.6298(5) and eta= 0.0366(8), where the given error
estimates take into account the statistical and systematic uncertainties.


title:
Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion
  and axial U(1) anomaly

abstract:
  We discuss the weak coupling expansion of massless QCD with the Dirac
operator which is derived by Neuberger based on the overlap formalism and
satisfies the Ginsparg-Wilson relation. The axial U(1) anomaly associated to
the chiral transformation proposed by Luscher is calculated as an application
and is shown to have the correct form of the topological charge density for
perturbative backgrounds. The coefficient of the anomaly is evaluated as a
winding number related to a certain five-dimensional fermion propagator.


title:
Improved staggered quark actions with reduced flavour symmetry
  violations for lattice QCD

abstract:
  We introduce a new class of actions for staggered quarks in lattice QCD which
significantly reduce flavour symmetry violations in the pion mass spectrum. An
action introduced by the MILC collaboration for the same purpose is seen to be
a special case. We discus how such actions arise from a systematic attempt to
reduce flavour symmetry violations in the weak coupling limit. It is shown that
for quenched lattice QCD at 6/g^2=5.7, representative actions of this class
give a considerable reduction in flavour symmetry violation over the standard
staggered action, and a significant reduction over what is achieved by the MILC
action.


title:
Perturbative calculation of improvement coefficients to O(g^2a) for
  bilinear quark operators in lattice QCD

abstract:
  We calculate the O(g^2 a) mixing coefficients of bilinear quark operators in
lattice QCD using a standard perturbative evaluation of on-shell Green's
functions. Our results for the plaquette gluon action are in agreement with
those previously obtained with the Schr\"odinger functional method. The
coefficients are also calculated for a class of improved gluon actions having
six-link terms.


title: B-parameters for DeltaS = 2 Supersymmetric Operators

abstract:
  We present a calculation of the matrix elements of the most general set of
DeltaS=2 dimension-six four-fermion operators. The values of the matrix
elements are given in terms of the corresponding B-parameters. Our results can
be used in many phenomenological applications, since the operators considered
here give important contributions to K^0--K^0bar mixing in several extensions
of the Standard Model (supersymmetry, left-right symmetric models, multi-Higgs
models etc.). The determination of the matrix elements improves the accuracy of
the phenomenological analyses intended to put bounds on basic parameters of the
different models, as for example the pattern of the sfermion mass matrices. The
calculation has been performed on the lattice, using the tree-level improved
Clover action at two different values of the strong coupling constant
(beta=6/g_0^2(a)=6.0 and 6.2, corresponding to a^-1= 2.1 and 2.7 GeV
respectively), in the quenched approximation. The renormalization constants and
mixing coefficients of the lattice operators have been obtained
non-perturbatively.


title:
Critical behavior of 3D SU(2) gauge theory at finite temperature: exact
  results from universality

abstract:
  We show that universality arguments, namely the Svetitsky-Yaffe conjecture,
allow one to obtain exact results on the critical behavior of 3D SU(2) gauge
theory at the finite temperature deconfinement transition,through a mapping
into the 2D Ising model. In particular, we consider the finite-size scaling
behavior of the plaquette operator, which can be mapped into the energy
operator of the 2D Ising model. We obtain exact predictions for the dependence
of the plaquette expectation value on the size and shape of the lattice and we
compare them to Monte Carlo results, finding complete agreement. We discuss the
application of this method to the computation of more general correlators of
the plaquette operator at criticality, and its relevance to the study of the
color flux tube structure.


title: Theory of Abelian Projection

abstract:
  Analytic methods for Abelian projection are developed. A number of results
are obtained related to string tension measurements. It is proven that even
without gauge fixing, abelian projection yields string tensions of the
underlying non-Abelian theory. Strong arguments are given for similar results
in the case where gauge fixing is employed. The methods used emphasize that the
projected theory is derived from the underlying non-Abelian theory rather than
vice versa. In general, the choice of subgroup used for projection is not very
important, and need not be Abelian. While gauge fixing is shown to be in
principle unnecessary for the success of Abelian projection, it is
computationally advantageous for the same reasons that improved operators,
e.g., the use of fat links, are advantageous in Wilson loop measurements. Two
other issues, Casimir scaling and the conflict between projection and critical
universality, are also discussed.


title: Solutions of the Ginsparg-Wilson Relation

abstract:
  We analyze general solutions of the Ginsparg-Wilson relation for lattice
Dirac operators and formulate a necessary condition for such operators to have
non-zero index in the topologically nontrivial background gauge fields.


title: An Efficient Algorithm for QCD with Light Dynamical Quarks

abstract:
  A new approach to the inclusion of virtual quark effects in lattice QCD
simulations is presented. Infrared modes which build in the chiral physics in
the light quark mass limit are included exactly and in a gauge invariant way.
At fixed physical volume the number of relevant infrared modes does not
increase as the continuum limit is approached. The acceptance of our procedure
does not decrease substantially in the limit of small quark masses. Two
alternative approaches are discussed for including systematically the remaining
ultraviolet modes. In particular, we present evidence that these modes are
accurately described by an effective action involving only small Wilson loops.


title: Lattice study of Weak First Order Phase Transitions in D=4

abstract:
  The properties of several phase transitions relevant to the lattice study of
Quantum Field Theory are investigated.


title: Four Fermion Models at Non-Zero Density

abstract:
  I review the properties of the three-dimensional Gross-Neveu model formulated
with non-zero chemical potential and temperature, focussing on results obtained
by lattice Monte Carlo simulation.


title:
Calculation of the continuum--lattice HQET matching for the complete
  basis of four--fermion operators: reanalysis of the $B^{0}$-$\bar{B}^{0}$
  mixing

abstract:
  In this work, we find the expressions of continuum HQET four-fermion
operators in terms of lattice operators in perturbation theory. To do so, we
calculate the one--loop continuum--lattice HQET matching for the complete basis
of $\Delta B=2$ and $\Delta B=0$ operators (excluding penguin diagrams),
extending and completing previous studies. We have also corrected some errors
in previous evaluations of the matching for the operator $O_{LL}$. Our results
are relevant to the lattice computation of the values of unknown hadronic
matrix elements which enter in many very important theoretical predictions in
$B$--meson phenomenology: $B^{0}$-$\bar{B}^{0}$ mixing, $\tau_{B}$ and
$\tau_{B_{s}}$ lifetimes, SUSY effects in $\Delta B=2$ transitions and the
$B_{s}$ width difference $\Delta \Gamma_{B_{s}}$. We have reanalyzed our
lattice data for the $B_{B}$ parameter of the $B^{0}$-$\bar{B}^{0}$ mixing on
600 lattices of size $24^{3}\times 40$ at $\beta=6.0$ computed with the
SW-Clover and HQET lattice actions. We have used the correct lattice--continuum
matching factors and boosted perturbation theory with tadpole improved
heavy--light operators to reduce the systematic error in the evaluation of the
renormalization constants. Our best estimate of the renormalization scale
independent $B$--parameter is $\hat{B}_{B} = 1.29 \pm 0.08 \pm 0.06$, where the
first error is statistical and the second is systematic coming from the
uncertainty in the determination of the renormalization constants. Our result
is in good agreement with previous results obtained by extrapolating Wilson
data. As a byproduct, we also obtain the complete one--loop anomalous dimension
matrix for four--fermion operators in the HQET.


title:
Gauge Invariant SO(3) - Z2 Monopoles as Possible Source of Confinement
  in SU(2) Lattice Gauge Theory

abstract:
  A gauge invariant procedure for extracting combined SO(3)-Z2 monopoles in
positive-plaquette SU(2) lattice gauge theory is shown. When these monopoles
are eliminated through a constraint, the theory deconfines for all $\beta$ on
$12^4$ and $20^4$ lattices even in the strong coupling limit, despite a rather
strong average plaquette of around 0.64. This corresponds to an effective
Wilson $\beta$ of 2.45, at which Wilson-action lattices would be far into the
confining region. This suggests that Wilson-action confinement may be a
strong-coupling lattice artifact; the continuum limit may not confine.


abstract:
  A practical implementation of the Overlap-Dirac operator
${{1+\gamma_5\epsilon(H)}\over 2}$ is presented. The implementation exploits
the sparseness of $H$ and does not require full storage. A simple application
to parity invariant three dimensional SU(2) gauge theory is carried out to
establish that zero modes related to topology are exactly reproduced on the
lattice.


title: Instanton Content of the SU(3) Vacuum

abstract:
  We study the topological content of the SU(3) vacuum using the
renormalization group (RG) mapping method. RG mapping is a simple smoothing
algorithm, in which a series of APE-smearing steps are done while the
topological content of the configuration is carefully monitored. This
monitoring process makes it possible to separate true topological objects from
vacuum fluctuations and allows an extrapolation to zero smearing steps. Using
RG mapping we have measured the instanton distribution and topological
susceptibility for SU(3) gauge theory. We arrive at a value for the topological
susceptibily, ${\chi}^{1/4}$ of 203(5) MeV. The size distribution peaks at
$\rho=0.3$fm, and is in good agreement with the prediction of instanton liquid
models.


title: Light and Strange Hadron Spectroscopy with Dynamical Wilson Fermions

abstract:
  We present the final analysis of the light and strange hadron spectra from a
full QCD lattice simulation with two degenerate dynamical sea quark flavours at
$\beta = 5.6$ on a $16^3 \times 32$ lattice. Four sets of sea quark masses
corresponding to the range $.69 \leq m_\pi/m_\rho \leq .83$ are investigated.
  For reference we also ran a quenched simulation at $\beta_{\sf eff} = 6.0$,
which is the point of equal lattice spacing, $a_{\rho}^{-1}$. In the light
sector, we find the chiral extrapolation to physical u- and d- masses to
present a major source of uncertainty, comparable to the expected size of
unquenching effects. From linear and quadratic fits we can estimate the errors
on the hadron masses made from light quarks to be on a 15 % level prior to the
continuum extrapolation. For the hadrons with strange valence quark content,
the $N_F = 2$ approximation to QCD appears not to cure the well-known failure
of quenched QCD to reproduce the physical $K-K^*$ splitting.


title: Random Matrices and the Glasgow Method

abstract:
  A simple non-Hermitean random matrix (RM) model is used to study the Glasgow
method of finite-density lattice QCD. The zeros of the RM partition function
are evaluated through an averaging procedure, involving the zeros of the RM
'propagator matrix' in the complex chemical-potential plane. The nature of the
uncertainty affecting the results is similar to that produced by rounding
errors in computing the known analytic result. This similarity is exploited to
give quantitative estimates on the relationship between the size of the matrix
and the number of configurations needed to achieve a given precision. For the
quenched ensemble considered here, the relationship is exponential.


title: Phase Structure of lattice SU(2)xU_S(1) three-dimensional Gauge Theory

abstract:
  We discuss a phase diagram for a relativistic SU(2) x U_{S}(1) lattice gauge
theory, with emphasis on the formation of a parity-invariant chiral condensate,
in the case when the $U_{S}(1)$ field is infinitely coupled, and the SU(2)
field is moved away from infinite coupling by means of a strong-coupling
expansion. We provide analytical arguments on the existence of (and partially
derive) a critical line in coupling space, separating the phase of broken SU(2)
symmetry from that where the symmetry is unbroken. We review uncoventional
(Kosterlitz-Thouless type) superconducting properties of the model, upon
coupling it to external electromagnetic potentials. We discuss the r\^ole of
instantons of the unbroken subgroup U(1) of SU(2), in eventually destroying
superconductivity under certain circumstances. The model may have applications
to the theory of high-temperature superconductivity. In particular, we argue
that in the regime of the couplings leading to the broken SU(2) phase, the
model may provide an explanation on the appearance of a pseudo-gap phase, lying
between the antiferromagnetic and the superconducting phases. In such a phase,
a fermion mass gap appears in the theory, but there is no phase coherence, due
to the Kosterlitz-Thouless mode of symmetry breaking. The absence of
superconductivity in this phase is attributed to non-perturbative effects
(instantons) of the subgroup U(1) of SU(2).


title: Absence of confinement in the absence of vortices

abstract:
  We consider the Wilson loop expectation in SU(2) lattice gauge theory in the
presence of constraints. The constraints eliminate from the functional measure
gauge field configurations whose physical interpretation is that of thick
center vortices linking with the loop. We give a simple proof that, for
dimension $d \geq 3$, the so constrained Wilson loop follows perimeter law,
i.e. non-confining behavior, at weak coupling (low temperature). Thus the
presence of vortex configurations is a necessary condition for confinement.


title: Chiral structure of the solutions of the Ginsparg-Wilson relation

abstract:
  We analyse the structure of solutions of the Ginsparg-Wilson relation for
lattice Dirac operator in topologically trivial gauge sector. We show that the
properties of such solutions relating to the perturbative stability of the pole
of the fermion propagator as well as to the structure of the Yukawa models
based on these solutions are solely determined by the non-local chirally
invariant part of these Dirac operators. Depending on the structure of this
part, the pole in the fermion propagator may or may not be stable under
radiative corrections. We illustrate this by explicit examples.


title:
Clover improvement, spectrum and Atiyah-Singer index theorem for the
  Dirac operator on the lattice

abstract:
  We study the role of the O(a)-improving clover term for the spectrum of the
lattice Dirac operator using cooled and thermalized SU(2) gauge field
configurations. For cooled configurations we observe improvement of the
spectral properties when adding the clover term. For the thermalized case
(12^4, beta = 2.4) without clover term we find a rather bad separation of
physical and doubler branches making a probabilistic interpretation of the
Atiyah-Singer index theorem on the lattice questionable for this beta and
lattice size. Adding the clover term leads to the creation of additional real
eigenvalues which come in pairs of opposite chirality thus further worsening
the situation for the index theorem.


title: Lessons from the 3d U(1) Gross-Neveu Model

abstract:
  The effectiveness of the Glasgow algorithm is explored via implementation in
the 3d U(1) Gross-Neveu model and the realisation of the Goldstone mechanism in
this model is compared and contrasted with its realisation in QCD.


title:
Dimensional Reduction and Screening Masses in Pure Gauge Theories at
  Finite Temperature

abstract:
  We studied screening masses in the equilibrium thermodynamics of SU(2) and
SU(3) pure gauge theories on the lattice. At a temperature of 2 Tc we found
strong evidence for dimensional reduction in the non-perturbative spectrum of
screening masses. Mass ratios in the high temperature SU(3) theory are
consistent with those in the pure gauge theory in three dimensions. At the
first order SU(3) phase transition we report the first measurement of the true
scalar screening mass.


title:
Crumpled triangulations and critical points in 4D simplicial quantum
  gravity

abstract:
  This is an expanded and revised version of our geometrical analysis of the
strong coupling phase of 4D simplicial quantum gravity. The main differences
with respect to the former version is a full discussion of singular
triangulations with singular vertices connected by a subsingular edge. In
particular we provide analytical arguments which characterize the entropical
properties of triangulations with a singular edge connecting two singular
vertices. The analytical estimate of the location of the critical coupling at
k_2\simeq 1.3093 is presented in more details. Finally we also provide a model
for pseudo-criticality at finite N_4(S^4).


title: Phase structure of U(1) lattice gauge theory with monopole term

abstract:
  We investigate four-dimensional compact U(1) lattice gauge theory with a
monopole term added to the Wilson action. First we consider the phase structure
at negative $\beta$, revealing some properties of a third phase region there,
in particular the existence of a number of different states. Then our present
studies concentrate on larger values of the monopole coupling $\lambda$ where
the confinement-Coulomb phase transition turns out to become of second order.
Performing a finite-size analysis we find that the critical exponent $\nu$ is
close to, however, different from the gaussian value and that in the range
considered $\nu$ increases somewhat with $\lambda$.


title: Evaluating Grassmann Integrals

abstract:
  I discuss a simple numerical algorithm for the direct evaluation of multiple
Grassmann integrals. The approach is exact, suffers no Fermion sign problems,
and allows arbitrarily complicated interactions. Memory requirements grow
exponentially with the interaction range and the transverse size of the system.
Low dimensional systems of order a thousand Grassmann variables can be
evaluated on a workstation. The technique is illustrated with a spinless
fermion hopping along a one dimensional chain.


title:
Ehrenfest theorems and charge antiscreening in Abelian projected gauge
  theories

abstract:
  We derive exact relations for SU(2) lattice gauge theory in 3+1 dimensions.
In terms of Abelian projection, these are the expectation values of Maxwell
equations that define a new field strength operator and conserved, dynamic
electric currents formed from the charged matter and ghost fields. The effect
of gauge fixing is calculated, and in the maximally Abelian gauge we find
antiscreening of U(1) Wilson loop source charges. We discuss the importance of
these quantities in the dual superconducting vacuum mechanism of confinement.


title: Optimizing the Chiral Properties of Lattice Fermion Actions

abstract:
  We describe a way to optimize the chiral behavior of Wilson-type lattice
fermion actions by studying the low energy real eigenmodes of the Dirac
operator. We find a candidate action, the clover action with fat links with a
tuned clover term. We present a calculation of spectroscopy and matrix elements
at Wilson gauge coupling $\beta=5.7$. The action shows good scaling behavior.


title: Phase transition(s) in finite density QCD

abstract:
  The Grand Canonical formalism is generally used in numerical simulations of
finite density QCD since it allows free mobility in the chemical potential
$\mu$. We show that special care has to be used in extracting numerical results
to avoid dramatic rounding effects and spurious transition signals. If we
analyze data correctly, with reasonable statistics, no signal of first order
phase transition is present and results using the Glasgow prescription are
practically coincident with the ones obtained using the modulus of the
fermionic determinant.


title: Can a flavour-conserving treatment improve things ?

abstract:
  In this work I would like to present some ideas on how to improve on the
gauge sector in our lattice simulations at finite baryon density. The long
standing problem, that we obtain an onset in thermodynamic quantities at a much
smaller chemical potential than expected, could be related to an unphysical
proliferation of flavours due to hard gluons close to the Brillouin edges.
These hard gluons produce flavour non-conserving vertices to the fermion
sector. They also produce excessive number of small instantons due to lattice
dislocations. Both unphysical effects could increase the propagation in
(di)-quarks to give the early onset in $\mu$. Thus we will present here a
modified action that avoids large fields close to the lattice cutoff. Some of
these ideas have been tested for SU(2) and are being implemented for SU(3).


title:
Large-$q$ expansion of the specific heat for the two-dimensional
  $q$-state Potts model

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


title: Dual Higgs Theory for Color Confinement

abstract:
  We study theoretical bases of the dual Higgs theory for confinement physics
in QCD in terms of monopoles and the gluon configuration in the maximally
abelian (MA) gauge. Abelian dominance for the confinement force can be
analytically proved by regarding the off-diagonal angle variable as a random
variable in the lattice formalism. In the long-distance scale, the contribution
of off-diagonal gluons to the Wilson loop cancels each other and exhibits a
perimeter law behavior, which leads to exact abelian dominance on the string
tension if the finite size effect of the Wilson loop is removed. We investigate
the appearance of the monopole in the QCD vacuum, considering the role of
off-diagonal gluons. The monopole carries a large fluctuation of the gluon
field and provides a large abelian action in abelian projected QCD. Due to the
partial cancellation between the abelian part and the off-diagonal part of the
QCD action, the monopole can appear in QCD without large cost of the QCD
action. The off-diagonal gluon is necessary for existence of the monopole at
the short-distance scale. We study monopole condensation, which is the
requirement of the dual Higgs theory, by comparing the QCD vacuum with the
monopole-current system. We find that ``entropy'' of monopole-current dominates
than its ``energy'', and the monopole seems to be condensed at the infrared
scale in the QCD vacuum.


title: Monte Carlo simulations and field transformation: the scalar case

abstract:
  We describe a new method in lattice field theory to compute observables at
various values of the parameters lambda_i in the action S[phi,lambda_i].
Firstly one performs a single simulation of a ``reference action'' S[phi^r,
lambda_i^r] with fixed lambda_i^r. Then the phi^r-configurations are
transformed into those of a field phi distributed according to S[phi,lambda_i],
apart from a ``remainder action'' which enters as a \break weight. In this way
we measure the observables at values of lambda_i different from lambda_i^r. We
study the performance of the algorithm in the case of the simplest
renormalizable model, namely the phi^4 scalar theory on a four dimensional
lattice and compare the method with the ``histogram'' technique of which it is
a generalization.


title: Evidence for a Center Vortex Origin of the Adjoint String Tension

abstract:
  Wilson loops in the adjoint representation are evaluated on cooled lattices
in SU(2) lattice gauge theory. It is found that the string tension of an
adjoint Wilson loop vanishes, if the loop is evaluated in a sub-ensemble of
configurations in which no center vortex links the loop. This result supports
our recent proposal that the adjoint string tension, in the Casimir-scaling
regime, can be attributed to a center vortex mechanism.


title: Lattice Chirality

abstract:
  The external fermion propagator and the internal fermion propagator in the
overlap are given by different matrices. A generic problem (formulated by
Pelissetto) faced by all chiral, non-local, propagators of Rebbi type is
avoided in this manner. Nussinov-Weingarten-Witten mass inequalities are
exactly preserved. It is sketched how to obtain simple lattice chiral Yukawa
models and simple expressions for covariant currents. Going beyond my oral
presentation, I have added to the write-up several comments on Niedermayer's
talk. His transparencies are available on the internet.


title: Exact Supersymmetry on the Lattice

abstract:
  We discuss the possibility of representing supersymmetry exactly in a lattice
discretized system. In particular, we construct a perfect supersymmetric action
for the Wess-Zumino model.


title: The lattice Schwinger model with the SW action

abstract:
  We perform a model study on the 2-flavor lattice Schwinger model using
standard Wilson and ${\cal O}(a)$ improved Sheikholeslami-Wohlert (SW) action.
We find, that the phase diagram is altered, the critical line shifted closer
towards its continuum value $\kappa_c=0.25$. We find no improvement in the
rotation invariance of meson propagators; the scaling of the Schwinger mass is
considerably improved, high momentum states are not. The additional cost of
$\approx 30 %$ CPU-time is highly justified when calculating masses, but not
for high momentum observables.


title:
Reducing Chiral Symmetry Violations in Lattice QCD with Domain-Wall
  Fermions

abstract:
  The inverse of the fermion matrix squared is used to define a transfer matrix
for domain-wall fermions. When the domain-wall height $M$ is bigger than one,
the transfer matrix is complex. Slowly suppressed chiral symmetry violations
may then arise from all eigenvalues of the transfer matrix which are located
near the unit circle. Using a variable lattice spacing for the fifth coordinate
we enforce the strict positivity of the transfer matrix for any $M$. We
furthermore propose a modified pseudo-fermion action, aimed to decrease the
density of close-to-unity eigenvalues of the (positive) transfer matrix, at the
price of a small renormalization of the coupling constant. We explain why these
changes may reduce chiral symmetry violations in lattice QCD simulations.


title: Preconditioning of Improved and ``Perfect'' Fermion Actions

abstract:
  We construct a locally-lexicographic SSOR preconditioner to accelerate the
parallel iterative solution of linear systems of equations for two improved
discretizations of lattice fermions: the Sheikholeslami-Wohlert scheme where a
non-constant block-diagonal term is added to the Wilson fermion matrix and
renormalization group improved actions which incorporate couplings beyond
nearest neighbors of the lattice fermion fields. In case (i) we find the block
llssor-scheme to be more effective by a factor about 2 than odd-even
preconditioned solvers in terms of convergence rates, at beta=6.0. For type
(ii) actions, we show that our preconditioner accelerates the iterative
solution of a linear system of hypercube fermions by a factor of 3 to 4.


title: The QCD Chiral Condensate from the Lattice

abstract:
  We determine the chiral condensate from simulations of quenched lattice QCD
with Wilson fermions. Our measurements have been obtained with high statistics
at three values of the gauge coupling, corresponding to UV cutoffs in the range
2 - 4 GeV. Several improvements have been made with respect to earlier lattice
computations. The most important are the non-perturbative renormalization of
the condensate, the use of the tree-level improved Clover action and the
reduction of the systematic error due to uncertainties in the lattice
calibration. Our result for the chiral condensate in the $\msbar$ scheme is
  (\bar\psi \psi)^{\msbar}(mu = 2 GeV)
  = - 0.0147(8)(16)(12) GeV^3
  = - [245(4)(9)(7) MeV]^3
  where the first error is statistical, the second is due to the
non-perturbative renormalization and the third due to the lattice calibration.


title: Tuning Actions and Observables in Lattice QCD

abstract:
  We propose a strategy for conducting lattice QCD simulations at fixed volume
but variable quark mass so as to investigate the physical effects of dynamical
fermions. We present details of techniques which enable this to be carried out
effectively, namely the tuning in bare parameter space and efficient stochastic
estimation of the fermion determinant. Preliminary results and tests of the
method are presented. We discuss further possible applications of these
techniques.


title: Z-Vortex Percolation in the Electroweak Crossover Region

abstract:
  We study the statistical properties of Z-vortices and Nambu monopoles in the
3D SU(2) Higgs model for a Higgs mass M_H \approx 100 GeV near and above the
crossover temperature, where these defects are thermally excited. Although
there is no phase transition at that strong selfcoupling, we observe that the
Z-vortices exhibit the percolation transition that has been found recently to
accompany the first order thermal transition that exists at smaller Higgs mass.
Above the crossover temperature percolating networks of Z-vortex lines are
ubiquitous, whereas vortices form a dilute gas of closed vortex loops and
(Nambu) monopolium states on the low-temperature side of the crossover. The
percolation temperature turns out to be roughly independent of the lattice
spacing. We find that the Higgs modulus is smaller (the gauge action is larger)
inside the vortices, compared to the bulk average. This correlation becomes
very strong on the low-temperature side. The percolation transition is a
prerequisite of some string mediated baryon number generation scenarios.


title:
A Study of Practical Implementations of the Overlap-Dirac Operator in
  Four Dimensions

abstract:
  We study three practical implementations of the Overlap-Dirac operator $D_o=
(1/2) [1 + \gamma_5\epsilon(H_w)]$ in four dimensions. Two implementations are
based on different representations of $\epsilon(H_w)$ as a sum over poles. One
of them is a polar decomposition and the other is an optimal fit to a ratio of
polynomials. The third one is obtained by representing $\epsilon(H_w)$ using
Gegenbauer polynomials and is referred to as the fractional inverse method.
After presenting some spectral properties of the Hermitian operator
$H_o=\gamma_5 D_o$, we study its spectrum in a smooth SU(2) instanton
background with the aim of comparing the three implementations of $D_o$. We
also present some results in SU(2) gauge field backgrounds generated at
$\beta=2.5$ on an $8^4$ lattice. Chiral properties have been numerically
verified.


title: Anomalous Chiral Symmetry Breaking above the QCD Phase Transition

abstract:
  We study the anomalous breaking of U_A(1) symmetry just above the QCD phase
transition for zero and two flavors of quarks, using a staggered fermion,
lattice discretization. The properties of the QCD phase transition are expected
to depend on the degree of U_A(1) symmetry breaking in the transition region.
For the physical case of two flavors, we carry out extensive simulations on a
16^3 x 4 lattice, measuring a difference in susceptibilities which is sensitive
to U_A(1) symmetry and which avoids many of the staggered fermion
discretization difficulties. The results suggest that anomalous effects are at
or below the 15% level.


title:
Wilson loop distributions, higher representations and centre dominance
  in SU(2)

abstract:
  To help understand the centre dominance picture of confinement, we look at
Wilson loop distributions in pure SU(2) lattice gauge theory. A strong coupling
approximation for the distribution is developed to use for comparisons. We
perform a Fourier expansion of the distribution: centre dominance here
corresponds to suppression of odd terms beyond the first. The Fourier terms
correspond to SU(2) representations; hence Casimir scaling behaviour leads to
centre dominance. We examine the positive plaquette model, where only thick
vortices are present. We show that a simple picture of random, non-interacting
centre vortices gives a string tension about 3/4 of the measured value.
Finally, we attempt to limit confusion about the adjoint representation.


title:
String Breaking in Non-Abelian Gauge Theories with Fundamental Matter
  Fields

abstract:
  We present clear numerical evidence for string breaking in three-dimensional
SU(2) gauge theory with fundamental bosonic matter through a mixing analysis
between Wilson loops and meson operators representing bound states of a static
source and a dynamical scalar. The breaking scale is calculated in the
continuum limit. In units of the lightest glueball we find $r_{\rm b}
m_G\approx13.6$. The implications of our results for QCD are discussed.


title: The strength of the electroweak phase transition at $m_H \approx$ 80 GeV

abstract:
  In this letter we present the results of our numerical simulations for the
finite temperature electroweak phase transition using the SU(2)-Higgs model on
four-dimensional lattices at $m_H \approx 80$ GeV. The temporal extension
$L_t=2$ is used for asymmetric lattice spacings with an asymmetry parameter
$a_s/a_t \approx 4$. The measured thermodynamical quantities (interface
tension, jump of the order parameter and latent heat) suggest that the phase
transition is of very weakly first order.


title: String breaking in SU(2) gauge theory with scalar matter fields

abstract:
  We investigate the static potential in the confinement phase of the SU(2)
Higgs model on the lattice, where this model is expected to have properties
similar to QCD. We observe that Wilson loops are inadequate to determine the
potential at large distances, where the formation of two color-neutral mesons
is expected. Introducing smeared fields and a suitable matrix correlation
function, we are able to overcome this difficulty. We observe string breaking
at a distance $r_b \approx 1.8 r_0$, where the length scale $r_0$ has a value
$r_0 \approx 0.5 fm$ in QCD. The method presented here may lead the way towards
a treatment of string breaking in QCD.


title:
Wave Functions and Spectrum in Hot Electroweak Matter for Large Higgs
  Masses

abstract:
  We present results for the wave functions and the screening mass spectrum for
quantum numbers $0^{++}$, $1^{--}$ and $2^{++}$ in the three-dimensional
SU(2)-Higgs model near to the phase transition line below the endpoint and in
the crossover region. Varying the 3D gauge couplings we study the behaviour
along a line of constant physics towards the continuum limit in both phases. In
the crossover region the changing spectrum of screening states versus
temperature is examined showing the aftermath of the phase transition at lower
Higgs mass. Different to smearing concepts we used large sets of operators with
various extensions allowing to identify wave functions in position space.


title:
Possible Consequences of Conjectural Periodicity of Spectrum of Lattice
  Dirac Operator

abstract:
  Some consequences which follow from the periodicity assumption for spectral
density of Wilson--Dirac operator are studied. Such an assumption allows to
obtain simple representations for quark propagator, which reveals an important
role of $m\leftrightarrow -m$ symmetry. It is argued that this symmetry is
restored when the mirror fermion mass $m_r$ tended to infinity. The constrains
on zero modes of Wilson--Dirac operator in a toy model approximation are also
discussed.


title:
Semi-analytical Proof of Abelian Dominance on Confinement in the
  Maximally Abelian Gauge

abstract:
  We study abelian dominance for confinement in terms of the local gluon
properties in the maximally abelian (MA) gauge in a semi-analytical manner with
the help of the lattice QCD. The global Weyl symmetry persistently remains as
the relic of SU($N_c$) in the MA gauge, and provides the ambiguity on the
electric and magnetic charges. We derive the criterion on the SU($N_c$)-gauge
invariance in terms of the residual symmetry in the abelian gauge. In the
lattice QCD, we find microscopic abelian dominance on the link variable for the
whole region of $\beta$ in the MA gauge. The off-diagonal angle variable, which
is not constrained by the MA-gauge fixing condition, tends to be random besides
the residual gauge degrees of freedom. Within the random-variable approximation
for the off-diagonal angle variable, we prove that off-diagonal gluon
contribution to the Wilson loop obeys the perimeter law in the MA gauge, and
show exact abelian dominance for the string tension, although small deviation
is brought by the finite size effect of the Wilson loop in the actual lattice
QCD simulation.


title: Three-Dimensional Simplicial Gravity and Degenerate Triangulations

abstract:
  I define a model of three-dimensional simplicial gravity using an extended
ensemble of triangulations where, in addition to the usual combinatorial
triangulations, I allow degenerate triangulations, i.e. triangulations with
distinct simplexes defined by the same set of vertexes. I demonstrate, using
numerical simulations, that allowing this type of degeneracy substantially
reduces the geometric finite-size effects, especially in the crumpled phase of
the model, in other respect the phase structure of the model is not affected.


title: Vortices and the SU(3) string tension

abstract:
  We present simulation results comparing the SU(3) heavy quark potential
extracted from the full Wilson loop expectation to that extracted from the
expectation of the Wilson loop fluctuation solely by elements of Z(3). The two
potentials are found to coincide. This agreement is stable under multiple
smoothings of the configurations which remove short distance fluctuations, and
thus reflects long-distance physics. It strongly indicates that the asymptotic
string tension arises from thick center vortices linking with the Wilson loop.


title: Introduction to Lattice QCD

abstract:
  These notes aim to provide a pedagogical introduction to Lattice QCD. The
topics covered include the scope of LQCD calculations, lattice discretization
of gauge and fermion (naive, Wilson, and staggered) actions, doubling problem,
improved gauge and Dirac actions, confinement and strong coupling expansions,
phase transitions in the lattice theory, lattice operators, a general
discussion of statistical and systematic errors in simulations of LQCD, the
analyses of the hadron spectrum, glueball masses, the strong coupling constant,
and the quark masses.


title: Domain wall fermion zero modes on classical topological backgrounds

abstract:
  The domain wall approach to lattice fermions employs an additional dimension,
in which gauge fields are merely replicated, to separate the chiral components
of a Dirac fermion. It is known that in the limit of infinite separation in
this new dimension, domain wall fermions have exact zero modes, even for gauge
fields which are not smooth. We explore the effects of finite extent in the
fifth dimension on the zero modes for both smooth and non-smooth topological
configurations and find that a fifth dimension of around ten sites is
sufficient to clearly show zero mode effects. This small value for the extent
of the fifth dimension indicates the practical utility of this technique for
numerical simulations of QCD.


title:
Simulation of an Abelian Higgs theory in world line (polymer)
  representation

abstract:
  In World Line Path Integral representation Abelian Higgs theories admit a
curvature term in the Hamiltonian. Using Monte Carlo simulations we show that
the curvature term drives a phase transition at sufficiently strong coupling.
In quenched approximation this phase transition is smooth, with implications
that the model reduces to a Goldstone theory. Critical properties of the system
near the transition are investigated and found to be consistent with mean field
behavior.


title: Speeding up finite step-size updating of full QCD on the lattice

abstract:
  We propose various improvements of finite step-size updating for full QCD on
the lattice that might turn finite step-size updating into a viable alternative
to the hybrid Monte Carlo algorithm. These improvements are noise reduction of
the noisy estimator of the fermion determinant, unbiased inclusion of the
hopping parameter expansion and a multi-level Metropolis scheme. First
numerical tests are performed for the 2 dimensional Schwinger model with two
flavours of Wilson fermions and for QCD two flavours of Wilson fermions and
Schr"odinger functional boundary conditions.


title: Towards a lattice determination of the $B^\ast B \pi$ coupling

abstract:
  The coupling $g_{B^\ast B \pi}$ is related to the form factor at zero
momentum of the axial current between $B^\ast$- and $B$-states. This form
factor is evaluated on the lattice using static heavy quarks and light quark
propagators determined by a stochastic inversion of the fermionic bilinear. The
$\gBBP$ coupling is related to the coupling $g$ between heavy mesons and
low-momentum pions in the effective heavy meson chiral lagrangian. The coupling
of the effective theory can therefore be computed by numerical simulations. We
find the value $g = 0.42(4)(8)$. Besides its theoretical interest, the
phenomenological implications of such a determination are discussed.


title: Lattice Simulation of Diquark Condensation in Dense Matter

abstract:
  We present results of a Monte Carlo simulation of a three dimensional
Gross-Neveu model with SU(2)xSU(2) chiral symmetry at non-zero baryon chemical
potential mu, corresponding to non-zero baryon density. For mu sufficiently
large there is a sharp transition between a phase where the chiral symmetry is
broken by a condensate <qbar q> and one where the global U(1) baryon number
symmetry appears to be broken by a scalar diquark condensate <qq>. There is
also tentative evidence for the formation of a weaker pseudoscalar diquark
condensate in the high density phase, which violoates parity.


title: Confinement Physics in Quantum Chromodynamics

abstract:
  We study the confinement physics in QCD in the maximally abelian (MA) gauge
using the SU(2) lattice QCD, based on the dual-superconductor picture. In the
MA gauge, off-diagonal gluon components are forced to be small, and the
off-diagonal angle variable $\chi_\mu(s)$ tends to be random. Within the
random-variable approximation for $\chi_\mu(s)$, we analytically prove the
perimeter law of the off-diagonal gluon contribution to the Wilson loop in the
MA gauge, which leads to abelian dominance on the string tension. To clarify
the origin of abelian dominance for the long-range physics, we study the
charged-gluon propagator in the MA gauge using the lattice QCD, and find that
the effective mass $m_{ch} \simeq 0.9 {\rm GeV}$ of the charged gluon is
induced by the MA gauge fixing. In the MA gauge, there appears the macroscopic
network of the monopole world-line covering the whole system, which would be
identified as monopole condensation at a large scale. To prove monopole
condensation in the field-theoretical manner, we derive the inter-monopole
potential from the dual Wilson loop in the monopole part of QCD, which carries
the nonperturbative QCD aspects, in the MA gauge. The dual gluon mass is
evaluated as $m_B \simeq $0.5GeV in the monopole part in the infrared region,
which is the evidence of the dual Higgs mechanism by monopole condensation.


title:
Screening Masses of Hot SU(2) Gauge Theory from the 3d Adjoint Higgs
  Model

abstract:
  We study the Landau gauge propagators of the lattice SU(2) 3d adjoint Higgs
model, considered as an effective theory of high temperature 4d SU(2) gauge
theory. From the long distance behaviour of the propagators we extract the
screening masses. The propagators are studied both in the symmetric and the
broken phases of the 3d Higgs model. It is shown that the pole masses extracted
from the propagators in the symmetric phase agree well with the screening
masses obtained recently in finite temperature SU(2) theory, while propagators
measured in the broken phase show quite a different behaviour. This suggest
that the symmetric phase of the 3d model corresponds to the deconfined phase of
the 4d SU(2) gauge theory. The relation of the propagator masses to the masses
extracted from gauge invariant correlators and the mass gap of pure 3d SU(2)
gauge theory is also discussed.


title:
Z_2 Monopoles and Deconfinement Phase Transition in SU(2) Lattice Gauge
  Theory

abstract: The paper has been withdrawn


title:
Critical correlators of three-dimensional gauge theories at finite
  temperature: exact results from universality

abstract:
  According to the Svetitsky-Yaffe conjecture, a three-dimensional gauge theory
undergoing a continuous deconfinement transition is in the same universality
class as a two-dimensional statistical model with order parameter taking values
in the center of the gauge group. This allows us to use conformal field theory
techniques to evaluate exactly various correlation functions at the critical
point. In particular, we show that the plaquette operator of the gauge theory
is mapped into the energy operator of the dimensionally reduced model. The
plaquette expectation value in presence of static sources for three-dimensional
SU(2) and SU(3) theories at the deconfinement temperature can be exactly
evaluated, providing some new insight about the structure of the color flux
tube in mesons and baryons.


title: Strong Coupling Model for String Breaking on the Lattice (LATTICE'98)

abstract:
  A model for string breaking on the lattice is formulated using strong
coupling ideas. It gives an explicit picture of string breaking, in the
presence of dynamical quarks, as a mixing process between a string state and a
two-meson state. An analysis of the Wilson loop shows that the evolution of the
mixing angle as a function of separation may obscure the expected crossover
effect. If a sufficiently extensive mixing region exists then an appropriate
combination of transition amplitudes may help reveal the effect. The
sensitivity of the mixing region to the values of the meson energy and the
dynamical quark mass is explored.


title: Imaginary chemical potential and finite fermion density on the lattice

abstract:
  Standard lattice fermion algorithms run into the well-known sign problem at
real chemical potential. In this paper we investigate the possibility of using
imaginary chemical potential, and argue that it has advantages over other
methods, particularly for probing the physics at finite temperature as well as
density. As a feasibility study, we present numerical results for the partition
function of the two-dimensional Hubbard model with imaginary chemical
potential.
  We also note that systems with a net imbalance of isospin may be simulated
using a real chemical potential that couples to I_3 without suffering from the
sign problem.


title: Lattice QCD with Exponentially Small Chirality Breaking

abstract:
  A new multifermion formulation of lattice QCD is proposed. The model is free
of spectrum doubling and preserves all nonanomalous chiral symmetries up to
exponentially small corrections. It is argued that a small number of fermion
fields may provide a good approximation making computer simulations feasible.


title: Lattice Models of Quantum Gravity

abstract:
  Standard Regge Calculus provides an interesting method to explore quantum
gravity in a non-perturbative fashion but turns out to be a CPU-time demanding
enterprise. One therefore seeks for suitable approximations which retain most
of its universal features. The $Z_2$-Regge model could be such a desired
simplification. Here the quadratic edge lengths $q$ of the simplicial complexes
are restricted to only two possible values $q=1+\epsilon\sigma$, with
$\sigma=\pm 1$, in close analogy to the ancestor of all lattice theories, the
Ising model. To test whether this simpler model still contains the essential
qualities of the standard Regge Calculus, we study both models in two
dimensions and determine several observables on the same lattice size. In order
to compare expectation values, e.g. of the average curvature or the Liouville
field susceptibility, we employ in both models the same functional integration
measure. The phase structure is under current investigation using mean field
theory and numerical simulation.


title: Vortices in equilibrium scalar electrodynamics

abstract:
  Scalar electrodynamics can be used to investigate the formation of cosmic
strings in the early universe. We present the results of lattice Monte Carlo
simulations of an effective three-dimensional U(1)+Higgs theory that describes
the equilibrium properties of finite-temperature scalar electrodynamics near
the transition. A gauge-invariant criterion for the existence of a vortex is
used in measuring the properties of the vortex network in the equilibrium state
both in the Coulomb and in the Higgs phase of the system. The naive definition
of the vortex density becomes meaningless in the continuum limit and special
care is needed in extracting physical quantities. Numerical evidence for a
physical discontinuity in the vortex density is given.


title: Finite size analysis of the 3D gonihedric Ising model with k=0

abstract: This paper has been withdrawn


title: Nonperturbative Renormalisation of Composite Operators in Lattice QCD

abstract:
  We investigate the nonperturbative renormalisation of composite operators in
lattice QCD restricting ourselves to operators that are bilinear in the quark
fields. These include operators which are relevant to the calculation of
moments of hadronic structure functions. The computations are based on Monte
Carlo simulations using quenched Wilson fermions.


title:
Finite Size Analysis of the U(1) Phase Transition using the World-sheet
  Formulation

abstract:
  We present a high statistics analysis of the pure gauge compact U(1) lattice
theory using the the world-sheet or Lagrangian loop representation. We have
applied a simulation method that deals directly with (gauge invariant) integer
variables on plaquettes. As a result we get a significant amelioration of the
simulation that allows to work with large lattices avoiding the metaestability
problems that appear using the standard Wilson formulation.


title: Non-perturbatively Renormalized Light-Quark Masses with the Alpha Action

abstract:
  We have computed the light quark masses using the O(a^2) improved Alpha
action, in the quenched approximation. The renormalized masses have been
obtained non-perturbatively. By eliminating the systematic error coming from
the truncation of the perturbative series, our procedure removes the
discrepancies, observed in previous calculations, between the results obtained
using the vector and the axial-vector Ward identities. It also gives values of
the quark masses larger than those obtained by computing the renormalization
constants using (boosted) perturbation theory. Our main results, in the RI
(MOM) scheme and at a renormalization scale \mu=2 GeV, are m^{RI}_s= 138(15)
MeV and m^{RI}_l= 5.6(5) MeV, where m^{RI}_s is the mass of the strange quark
and m^{RI}_l=(m^{RI}_u+m^{RI}_d)/2 the average mass of the up-down quarks. From
these results, which have been obtained non-perturbatively, by using continuum
perturbation theory we derive the \bar{MS} masses, at the same scale, and the
renormalization group invariant (m^{RGI}) masses. We find m^{NLO \bar{MS}}_s=
121(13)$ MeV and m^{NLO\bar{MS}}_l= 4.9(4) MeV at the next-to-leading order;
m^{N^2LO \bar{MS}}_s= 111(12) MeV, m^{N^2LO \bar{MS}}_l= 4.5(4) MeV, m_s^{RGI}=
177(19) MeV and m^{RGI}_l= 7.2(6) MeV at the next-to-next-to-leading order.


title: Genetic Algorithm for SU(N) gauge theory on a lattice

abstract:
  An Algorithm is proposed for the simulation of pure SU(N) lattice gauge
theories based on Genetic Algorithms(GAs). Main difference between GAs and
Metropolis methods(MPs) is that GAs treat a population of points at once, while
MPs treat only one point in the searching space. This provides GAs with
information about the assortment as well as the fitness of the evolution
function and producting a better solution. We apply GAs to SU(2) pure gauge
theory on a 2 dimensional lattice and show the results are consistent with
those given by MP and Heatbath methods(HBs). Thermalization speed of GAs is
especially faster than the simple MPs.


title: Ginsparg-Wilson Relation and Ultralocality

abstract:
  It is shown that it is impossible to construct a free theory of fermions on
infinite hypercubic Euclidean lattice in four dimensions that is: (a)
ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding
kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation),
(d) describes single species of massless Dirac fermions in the continuum limit.


title: Testing fixed points in the 2D O(3) non-linear sigma model

abstract:
  Using high statistic numerical results we investigate the properties of the
O(3) non-linear 2D sigma-model. Our main concern is the detection of an
hypothetical Kosterlitz-Thouless-like (KT) phase transition which would
contradict the asymptotic freedom scenario. Our results do not support such a
KT-like phase transition.


title: Topological properties of full QCD at the phase transition

abstract:
  We investigate the topological properties of the QCD vacuum with 4 flavours
of dynamical staggered fermions at finite temperature. To calculate the
topological susceptibility we use the field-theoretical method. As in the
quenched case, a sharp drop is observed for the topological susceptibility
across the phase transition.


title:
Moments of parton evolution probabilities on the lattice within the
  Schroedinger functional scheme

abstract:
  We define, within the Schroedinger functional scheme (SF), the matrix
elements of the twist-2 operators corresponding to the first two moments of
non-singlet parton densities. We perform a lattice one-loop calculation that
fixes the relation between the SF scheme and other common schemes and shows the
main source of lattice artefacts. This calculation sets the basis for a
numerical evaluation of the non-perturbative running of parton densities.


title:
Phase diagram of three-dimensional dynamical triangulations with a
  boundary

abstract:
  We use Monte Carlo simulation to study the phase diagram of three-dimensional
dynamical triangulations with a boundary. Three phases are indentified and
characterized. One of these phases is a new, boundary dominated phase; a simple
argument is presented to explain its existence. First-order transitions are
shown to occur along the critical lines separating phases.


title:
Computation of the improvement coefficient $c_{\rm sw}$ to 1-loop with
  improved gluon actions

abstract:
  The coefficient $c_{\rm sw}$ appearing in the Sheikholeslami-Wohlert improved
action is computed to one loop perturbation theory for improved gluon actions
including six-link loops. The O($a$) improvement coefficients for the dimension
three isovector composite operators bilinear in the quark fields are also
computed to one loop order of perturbation theory with degenerate non-vanishing
quark masses.


title: Simplicial Quantum Gravity on a Randomly Triangulated Sphere

abstract:
  We study 2D quantum gravity on spherical topologies employing the Regge
calculus approach with the dl/l measure. Instead of the normally used fixed
non-regular triangulation we study random triangulations which are generated by
the standard Voronoi-Delaunay procedure. For each system size we average the
results over four different realizations of the random lattices. We compare
both types of triangulations quantitatively and investigate how the difference
in the expectation value of the squared curvature, $R^2$, for fixed and random
triangulations depends on the lattice size and the surface area A. We try to
measure the string susceptibility exponents through finite-size scaling
analyses of the expectation value of an added $R^2$-interaction term, using two
conceptually quite different procedures. The approach, where an ultraviolet
cut-off is held fixed in the scaling limit, is found to be plagued with
inconsistencies, as has already previously been pointed out by us. In a
conceptually different approach, where the area A is held fixed, these problems
are not present. We find the string susceptibility exponent $\gamma_{str}'$ in
rough agreement with theoretical predictions for the sphere, whereas the
estimate for $\gamma_{str}$ appears to be too negative. However, our results
are hampered by the presence of severe finite-size corrections to scaling,
which lead to systematic uncertainties well above our statistical errors. We
feel that the present methods of estimating the string susceptibilities by
finite-size scaling studies are not accurate enough to serve as testing grounds
to decide about a success or failure of quantum Regge calculus.


title: Condensation of vortices and disorder parameter in 3d Heisenberg model

abstract:
  The 3d Heisenberg model is studied from a dual point of view. It is shown
that the disordered phase corresponds to condensation of vortices in the
vacuum, and the critical indices are computed from the corresponding disorder
parameter.


title: Locality properties of Neuberger's lattice Dirac operator

abstract:
  The gauge covariant lattice Dirac operator D which has recently been proposed
by Neuberger satisfies the Ginsparg-Wilson relation and thus preserves chiral
symmetry. The operator also avoids a doubling of fermion species, but its
locality properties are not obvious. We now prove that D is local (with
exponentially decaying tails) if the gauge field is sufficiently smooth at the
scale of the cutoff. Further analytic and numerical studies moreover suggest
that the locality of the operator is in fact guaranteed under far more general
conditions.


title:
The PHMC algorithm for simulations of dynamical fermions: I --
  description and properties

abstract:
  We give a detailed description of the so-called Polynomial Hybrid Monte Carlo
(PHMC) algorithm. The effects of the correction factor, which is introduced to
render the algorithm exact, are discussed, stressing their relevance for the
statistical fluctuations and (almost) zero mode contributions to physical
observables. We also investigate rounding-error effects and propose several
ways to reduce memory requirements.


title: Distinguishing J=4 from J=0 on a cubic lattice

abstract:
  We discuss the problem of constructing operators of arbitrary continuum
angular momentum on a spatial lattice. We illustrate one simple approach and
estimate the lightest J=4 glueball mass in the D=2+1 SU(2) gauge theory.


title:
The running quark mass in the SF scheme and its two-loop anomalous
  dimension

abstract:
  The non-perturbatively defined running quark mass introduced by the ALPHA
collaboration is based on the PCAC relation between correlation functions
derived from the Schr\"odinger functional (SF). In order to complete its
definition it remains to specify a number of parameters, including the ratio of
time to spatial extent, $T/L$, and the angle $\theta$ which appears in the
spatial boundary conditions for the quark fields. We investigate the running
mass in perturbation theory and propose a choice of parameters which attains
two desired properties: firstly the two-loop anomalous dimension $\d1SF$ is
reasonably small. This is needed in order to ease matching with the
non-perturbative computations and to achieve a precise determination of the
renormalization group invariant quark mass. Secondly, to one-loop order of
perturbation theory, cut-off effects in the step-scaling function are small in
O($a$) improved lattice QCD.


title: Mixing Scenarios for Lattice String Breaking

abstract:
  We present some simple scenarios for string breaking on the lattice based on
a crude strong coupling model introduced previously. We review the dependence
of the model on lattice spacing and extend it to include degenerate dynamical
quarks and also meson exchange diagrams. A comparison is made between quenched
and unquenched calculations. We examine string breaking in the presence of a
static quark-diquark system, a situation that is specific to SU(3).


title: Constituent monopoles without gauge fixing

abstract:
  We discuss the recent construction of new exact finite temperature instanton
solutions with a non-trivial value of the Polyakov loop at infinity. They can
be shown, in a precise and gauge invariant way, to be formed by the
superposition of n BPS monopoles for an SU(n) gauge group.


title: Light hadron spectroscopy with O(a) improved dynamical fermions

abstract:
  We present the first results for the static quark potential and the light
hadron spectrum using dynamical fermions at $\beta=5.2$ using an O(a) improved
Wilson fermion action together with the standard Wilson plaquette action for
the gauge part. Sea quark masses were chosen such that the pseudoscalar-vector
mass ratio, m_PS/m_V$, varies from 0.86 to 0.67. Finite-size effects are
studied by using three different volumes, 8^3\cdot 24, 12^3\cdot 24 and
16^3\cdot 24. Comparing our results to previous ones obtained using the
quenched approximation, we find evidence for sea quark effects in quantities
like the static quark potential and the vector-pseudoscalar hyperfine
splitting.


title:
Chiral symmetry breaking, instantons and the ultimate quenched
  calculation

abstract:
  We calculate the spectral density of the Dirac operator over an ensemble of
configurations composed of overlapping instantons and anti-instantons. We find
evidence that the spectral density diverges in the limit of small eigenvalues.
This indicates the breaking of chiral symmetry and also provides evidence that
quenched QCD may be pathological in nature.


title:
The generating functional for hadronic weak interactions and its
  quenched approximation

abstract:
  We derive the generating functional of $|\Delta S| =1, 2$ hadronic weak
interactions at one loop for a generic number of flavours and its counterpart
in the quenched approximation. A systematic analysis of the ultraviolet
divergences in the full theory (with and without a singlet dynamical field) and
in the quenched case is performed. We show that the quenched chiral logarithms
in the presence of weak interactions amount to a redefinition of the weak mass
term in the $\Delta S=\pm 1$ weak effective Lagrangian at leading order.
Finally, we apply the results to $B_K$ and $K\to\pi\pi$ matrix elements with
$\Delta I=1/2,3/2$ to analyze the modifications induced by quenching on the
coefficients of chiral logarithms in the one-loop corrections.


title:
A Conclusive Test of Abelian Dominance Hypothesis for Topological Charge
  in the QCD Vacuum

abstract:
  We study the topological feature in the QCD vacuum based on the hypothesis of
abelian dominance. The topological charge $Q_{\rm SU(2)}$ can be explicitly
represented in terms of the monopole current in the abelian dominated system.
To appreciate its justification, we directly measure the corresponding
topological charge $Q_{\rm Mono}$, which is reconstructed only from the
monopole current and the abelian component of gauge fields, by using the Monte
Carlo simulation on SU(2) lattice. We find that there exists a one-to-one
correspondence between $Q_{\rm SU(2)}$ and $Q_{\rm Mono}$ in the maximally
abelian gauge. Furthermore, $Q_{\rm Mono}$ is classified by approximately
discrete values.


title: The spectral dimension of non-generic branched polymers

abstract:
  We show that the spectral dimension on non-generic branched polymers with
positive susceptibility exponent is given by $d_s=2/(1+\gamma)$. For those
models with $\gamma<0$ we find that $d_s=2$.


title: Topology and the axial anomaly in abelian lattice gauge theories

abstract:
  The axial anomaly in abelian lattice gauge theories is shown to be equal to a
simple quadratic expression in the gauge field tensor plus a removable
divergence term if the lattice Dirac operator satisfies the Ginsparg-Wilson
relation. The theorem is a consequence of the locality, the gauge invariance
and the topological nature of the anomaly and does not refer to any other
properties of the lattice theory.


title: SU(4) pure-gauge string tensions

abstract:
  In response to recently renewed interests in SU(N) pure-gauge dynamics with
large N, both from M/string duality and from finite-temperature QCD phase
structure, we calculate string tensions acting between the fundamental 4,
diquark 6 and other color charges in SU(4) pure-gauge theory at temperatures
below the deconfining phase change and above the bulk phase transition. Our
results suggest 4 and 6 representations have different string tensions, with a
ratio of about 1.3. We also found the deconfining phase change is not strong.


title: Matter near to the Endpoint of the Electroweak Phase Transition

abstract:
  Wave functions and the screening mass spectrum in the 3D SU(2)-Higgs model
near to the phase transition line below the endpoint and in the crossover
region are calculated. In the crossover region the changing spectrum versus
temperature is examined showing the aftermath of the phase transition at lower
Higgs mass. Large sets of operators with various extensions are used allowing
to identify wave functions in position space.


title:
Numerical simulation of dynamical gluinos: experience with a
  multi-bosonic algorithm and first results

abstract:
  We report on our experience with the two-step multi-bosonic algorithm in a
large scale Monte Carlo simulation of the SU(2) Yang-Mills theory with
dynamical gluinos. First results are described on the low lying spectrum of
bound states, the string tension and the gluino condensate.


title: Chiral symmetry restoration of QCD and the Gross-Neveu model

abstract:
  Two flavour massless QCD has a second order chiral transition which has been
argued to belong to the universality class of the $3d$ O(4) spin model. The
arguments have been questioned recently, and the transition was claimed to be
mean field behaved. We discuss this issue at the example of the $3d$
Gross-Neveu model. A solution is obtained by applying various well established
analytical methods.


title: Axial vector current of exact chiral symmetry on the lattice

abstract:
  We discuss the exact chiral symmetry and its spontaneous breakdown in lattice
QCD with the Dirac operators satisfying the Ginsparg-Wilson relation. The axial
vector current, which turns out to be related to the vector current simply by
the insertion of the operator \gamma_5 (1-aD), is explicitly constructed in the
case of the Neuberger-Dirac operator. We also consider an Euclidean proof of
the Nambu-Goldstone theorem using the Ward-Takahashi identity of this symmetry.


title: Quantum Geometry and Diffusion

abstract:
  We study the diffusion equation in two-dimensional quantum gravity, and show
that the spectral dimension is two despite the fact that the intrinsic
Hausdorff dimension of the ensemble of two-dimensional geometries is very
different from two. We determine the scaling properties of the quantum gravity
averaged diffusion kernel.


title: 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 present simulation results that show
that the string does break in the confining phase at nonzero temperature.


title:
Eigenmodes of the Dirac Operator and Chiral Properties of QCD with Sea
  Quarks

abstract:
  I describe a mechanism to understand the relation between chiral-symmetry
breaking and eigenmodes of the Dirac operator in lattice QCD with
Kogut-Susskind sea quarks. It can be shown that if chiral symmetry is
spontaneously broken, the eigenvalues $\lambda_i$ should behave as $z(i)/V$ for
large volume $V$, where $z(i)$ is the i-th zero of the Bessel function. With
neither chiral nor $\lambda$ extrapolation, one can precisely calculate the
chiral condensate using only a small set of eigenvalues. Therefore, it is
economical and free of systematic uncertainties. I present the first QCD data
to support this mechanism and encourage the lattice community to test and use
it.


title:
Investigation of the Critical Behavior of the Critical Point of the Z2
  Gauge Lattice

abstract:
  We investigate, through Monte-Carlo simulations, the nature of the second
order point in a $Z_2$ (Bosonic) + $Z_2$ gauge theory in four dimensions.
Detailed analysis of the critical exponents point to the Ising universality
class. Relevancy to extended models and possible Non-Gaussian behavior is
discussed.


title: The Nonperturbative Broken Phase Sphaleron Rate

abstract:
  I present a technique for measuring the broken phase sphaleron rate
nonperturbatively. There are three parts to the calculation: determination of
the probability distribution of Chern-Simons number NCS; measurement of <|
d\NCS/dt |> at NCS=1/2, the mean rate of change of NCS at the barrier; and
measurement of the ``dynamical prefactor,'' the fraction of barrier crossings
which result in a permanent integer change in NCS.


title:
A calculation of the Lepage-Mackenzie scale for the lattice axial and
  vector currents

abstract:
  We calculate the perturbative scales (q*) for the axial and vector currents
for the Wilson action, with and without tadpole improvement, using Lepage and
Mackenzie's formalism. The scale for the pseudoscalar density (times the mass)
is computed as well. Contrary to naive expectation, tadpole improvement reduces
q* by only a small amount for the operators we consider. We also discuss the
use of a nonperturbative coupling to calculate the perturbative scale.


title: The infrared behaviour of the gluon propagator from lattice QCD

abstract:
  The gluon propagator in the Landau gauge is calculated in quenched QCD on a
large lattice (32^3x64) at beta=6.0. In order to assess finite volume and
finite lattice spacing artefacts, we also calculate the propagator on a smaller
volume for two different values of the lattice spacing. New structure seen in
the infrared region survives conservative cuts to the lattice data, and serves
to exclude a number of models that have appeared in the literature.


title:
Non-perturbative determination of anisotropy coefficients and pressure
  gap at the deconfining transition of QCD

abstract:
  We propose a new non-perturbative method to compute derivatives of gauge
coupling constants with respect to anisotropic lattice spacings (anisotropy
coefficients). Our method is based on a precise measurement of the finite
temperature deconfining transition curve in the lattice coupling parameter
space extended to anisotropic lattices by applying the spectral density method.
We determine the anisotropy coefficients for the cases of SU(2) and SU(3) gauge
theories. A longstanding problem, when one uses the perturbative anisotropy
coefficients, is a non-vanishing pressure gap at the deconfining transition
point in the SU(3) gauge theory. Using our non-perturbative anisotropy
coefficients, we find that this problem is completely resolved.


title: The QCD Dirac Operator Spectrum and Finite-Volume Scaling

abstract:
  Random matrix theory and chiral Lagrangians offer a convenient tool for the
exact calculation of microscopic spectral correlators of the Dirac operator in
a well-defined finite-volume scaling regime.


title: Chirality on the Lattice

abstract:
  During the last several years a non-perturbative formulation of exact chiral
symmetry on the lattice has been developed. I shall outline the main ideas of
these developments and discuss prospects for the future. The focus will be on
the basic concepts enciphered in a new jargon consisting of terms like
``infinite number of fermions'', ``domain wall fermions'', ``the overlap'',
``the Ginsparg-Wilson relation''. Technical details will be omitted.


title: Lattice gauge theory studies of the gluon propagator

abstract:
  The gluon propagator in Landau gauge is calculated in quenched QCD on a large
(32^3X64) lattice at beta=6.0. In order to assess finite volume and finite
lattice spacing artefacts, we also calculate the propagator on a smaller volume
for two different values of the lattice spacing. New structure seen in the
infrared region survives conservative cuts to the lattice data, and serves to
exclude a number of models that have appeared in the literature.


title:
The PHMC algorithm for simulations of dynamical fermions: II -
  Performance analysis

abstract:
  We compare the performance of the PHMC algorithm with the one of the HMC
algorithm in practical simulations of lattice QCD. We show that the PHMC
algorithm can lead to an acceleration of numerical simulations. It is
demonstrated that the PHMC algorithm generates configurations carrying small
isolated eigenvalues of the lattice Dirac operator and hence leads to a
sampling of configuration space that is different from that of the HMC
algorithm.


title: Determination of constant lattice spacing trajectories in lattice QCD

abstract:
  We argue that lattice simulations of full QCD with varying quark mass are
best conducted at fixed lattice spacing rather than at fixed $\beta$. We
present techniques which enable this to be carried out effectively, namely the
tuning in bare parameter space and efficient stochastic estimation of the
fermion determinant. Results and tests of the method are presented. We discuss
other applications of such techniques.


title: Properties of U(1) lattice gauge theory with monopole term

abstract:
  In 4D compact U(1) lattice gauge theory with a monopole term added to the
Wilson action we first reveal some properties of a third phase region at
negative $\beta$. Then at some larger values of the monopole coupling $\lambda$
by a finite-size analysis we find values of the critical exponent $\nu$ close
to, however, different from the Gaussian value.


title:
Corrections to Scaling and Critical Amplitudes in SU(2) Lattice Gauge
  Theory

abstract:
  We calculate the critical amplitudes of the Polyakov loop and its
susceptibility at the deconfinement transition of SU(2) gauge theory. To this
end we carefully study the corrections to the scaling functions of the
observables coming from irrelevant exponents. As a guiding line for determining
the critical amplitudes we use envelope equations derived from the finite size
scaling formulae for the observables. The equations are then evaluated with new
high precision data obtained on N^3 x 4 lattices for N=12,18,26 and 36. We find
different correction-to-scaling behaviours above and below the transition. Our
result for the universal ratio of the susceptibility amplitudes is
C_+/C_-=4.72(11) and agrees perfectly with a recent measurement for the 3d
Ising model.


title: Debye mass from domainwalls and dimensionally reduced phase diagram

abstract:
  To measure the Debye mass in dimensionally reduced QCD for $N_c\le 3$ we
replace in the correlator of two Polyakov loops one of the loops by a wall
triggered by a dimensionally reduced twist. The phase diagram for $N_c=3$ has
R-parity broken in part of the Higgs phase.


title: The U(1) phase transition on toroidal and spherical lattices

abstract:
  We have studied the properties of the phase transition in the U(1) compact
pure gauge model paying special atention to the influence of the topology of
the boundary conditions. From the behavior of the energy cumulants and the
observation of an effective \nu -> 1/d on toroidal and spherical lattices, we
conclude that the transition is first order.


title: The dual sector of the \phi^4 Theory in 4D

abstract:
  The one-component $\lambda\phi^4$ theory in four dimensions in the
spontaneously broken symmetry phase has a non-trivial, non-perturbative sector
which can be studied by means of a duality transformation of its Ising limit.
Duality maps this theory to a model of interacting membranes. Physical states
correspond to membrane excitations. The way this non-perturbative behaviour can
be reconciled with the triviality of the theory in its continuum limit is
discussed.


title: In search of a scaling scalar glueball

abstract:
  Anisotropic lattices are an efficient means of studying the glueballs of QCD,
however problems arise with simulations of the lightest, scalar state. The mass
is strongly dependent on the lattice spacing, even when a mean-field improved
gluon action is used. The nature and cause of these errors are discussed and
the scaling properties of the scalar from different lattice actions are
presented.


title: SU(3) string tension and the presence of vortices

abstract:
  Lattice simulations are presented showing the expectation of the fluctuation
of the Wilson loop solely by elements of the center to fully reproduce the
SU(3) heavy quark potential. The results are stable under smoothing, and point
to thick vortices as being responsible for the full SU(3) tension. An analytic
result on the necessary presence of thick vortices for confinement at weak
coupling is also presented.


title: Predicting the Aoki Phase using the Chiral Lagrangian

abstract:
  This work is concerned with the phase diagram of Wilson fermions in the mass
and coupling constant plane for two-flavor (unquenched) QCD. We show that as
the continuum limit is approached, one can study the lattice theory using the
continuum chiral Lagrangian, supplemented by additional terms proportional to
powers of the lattice spacing. We find two possible phase structures at
non-zero lattice spacing: (1) There is an Aoki phase of spontaneously broken
flavor and parity, with two massless Goldstone-pions, and a width $\Delta m_0
\sim a^3$; (2) There is no spontaneous symmetry breaking, and all three pions
have equal mass of order $a$. Present numerical simulations suggest that the
former option is realized.


title:
Probing finite size effects in $(\lambda \Phi^4)_4$ MonteCarlo
  calculations

abstract:
  The Constrained Effective Potential (CEP) is known to be equivalent to the
usual Effective Potential (EP) in the infinite volume limit. We have carried
out MonteCarlo calculations based on the two different definitions to get
informations on finite size effects. We also compared these calculations with
those based on an Improved CEP (ICEP) which takes into account the finite size
of the lattice. It turns out that ICEP actually reduces the finite size effects
which are more visible near the vanishing of the external source.


title:
Universality of the gauge-ball spectrum of the four-dimensional pure
  U(1) gauge theory

abstract:
  We continue numerical studies of the spectrum of the pure U(1) lattice gauge
theory in the confinement phase, initiated in our previous work. Using the
extended Wilson action $ S = -\sum_P [\beta \cos(\Theta_P) + \gamma
\cos(2\Theta_P)] $ we address the question of universality of the phase
transition line in the ($\beta,\gamma$) plane between the confinement and the
Coulomb phases. Our present results at $\gamma= -0.5$ for the gauge-ball
spectrum are fully consistent with the previous results obtained at $\gamma=
-0.2$. Again, two different correlation length exponents, $\nu_{ng} = 0.35(3)$
and $\nu_{g} = 0.49(7)$, are obtained in different channels. We also confirm
the stability of the values of these exponents with respect to the variation of
the distance from the critical point at which they are determined. These
results further demonstrate universal critical behaviour of the model at least
up to correlation lengths of 4 lattice spacings when the phase transition is
approached in some interval at $\gamma\leq -0.2$.


title: The string tension in the maximally Abelian gauge after smoothing

abstract:
  We apply smoothing to SU(2) lattice field configurations in 3+1 dimensions
before fixing to the maximally Abelian gauge. The Abelian projected string
tension is shown to be stable under this, whilst the monopole string tension
declines by O(30%). Blocking of the SU(2) fields reduces this effect, but the
use of extended monopole definitions does not. We discuss these results in the
context of additional confining excitations in the U(1) vacuum.


title:
Dynamically generated electric charge distributions in Abelian projected
  SU(2) lattice gauge theories

abstract:
  We show in the maximal Abelian gauge the dynamical electric charge density
generated by the coset fields, gauge fixing and ghosts shows antiscreening as
in the case of the non-Abelian charge. We verify that with the completion of
the ghost term all contributions to flux are accounted for in an exact lattice
Ehrenfest relation.


title: Results From The UKQCD Parallel Tempering Project

abstract:
  We present results from our study of the Parallel Tempering algorithm. We
examine the swapping acceptance rate of a twin subensemble PT system. We use
action matching technology in an attempt to maximise the swap acceptance rate.
We model the autocorrelation times within Parallel Tempering ensembles in terms
of autocorrelation times from Hybrid Monte Carlo. We present estimates for the
autocorrelation times of the plaquette operator.


title: Electric and magnetic U(1) currents in lattice confinement studies

abstract:
  Making use of an Ehrenfest-Maxwell relation we show that in Abelian projected
SU(2), in the maximal Abelian gauge, the dynamical electric charge density
generated by the coset fields, gauge fixing and ghosts shows antiscreening as
in the case of the non-Abelian charge.


title: Monopoles and Gluon Fields in QCD in the Maximally Abelian Gauge

abstract:
  We study monopoles and gluon fields in QCD in the maximally abelian (MA)
gauge in the context of the dual superconductor picture for confinement. In the
abelian gauge, unit-charge magnetic monopoles appear, but multi-charge
monopoles do not in general cases. The appearance of the monopole is studied
using the gauge-connection formalism in relation to the SU($N_c$) singular
gauge transformation. The relevant role of off-diagonal gluons is found for the
appearance of monopoles in the abelian gauge in QCD. We study the gluon-field
properties around the monopole in the MA gauge in terms of the action density
using the lattice QCD. The monopole provides infinitely large field
fluctuations in the abelian sector. In the MA gauge, off-diagonal gluons are
strongly suppressed but largely remain around the monopole, which indicates the
effective size and the structure of monopoles. We find the large cancellation
between the abelian part and the off-diagonal part of the action density around
the monopole in the MA gauge. Owing to this cancellation, the monopole can
appear in QCD without large cost of the QCD action. Finally, we generalize the
framework of the abelian projection, {\it i.e.} the extraction of the abelian
gauge manifold from QCD, by introducing the `gluonic Higgs field' $\vec
\phi_D[A_\mu(x)]$ defined from the ${\rm SU}(N_c)$ covariant derivative $\hat
D_\mu$. By way of $\vec \phi_D[A_\mu(x)]$, the maximally abelian projection can
be performed in the gauge-covariant manner without the notion of gauge fixing
in principle.


title: Dual lattice simulations of flux tubes

abstract:
  Abelian gauge theories formulated on a space-time lattice can be used as a
prototype for investigating the confinement mechanism. In U(1) lattice gauge
theory it is possible to perform a dual transformation of the path integral.
Simulating the obtained dual theory (which corresponds to a certain limit of a
dual Higgs model) including external sources, we perform a very accurate
analysis of flux tubes with respect to the dual superconductor picture. Dual
flux tube simulations are also performed in the full Abelian Higgs model, in
order to obtain non-perturbative control over quantum and string fluctuations,
and for a comparison to the results of dual QCD.


title: Gauge invariant Field Strength Correlators in QCD

abstract:
  Gauge invariant correlators in QCD are studied on the lattice.A Systematic
determination of the correlation lengths for gluon field strength correlators
and quark correlators is made.The measurement of the gluon and quark
condensates is discussed.


title: The Calculation of Critical Amplitudes in SU(2) Lattice Gauge Theory

abstract:
  We calculate the critical amplitudes of the Polyakov loop and its
susceptibility at the deconfinement transition of (3+1) dimensional SU(2) gauge
theory. To this end we study the corrections due to irrelevant exponents in the
scaling functions. As a guiding line for determining the critical amplitudes we
use envelope equations which we derive from the finite size scaling formulae of
the observables. We have produced new high precision data on N^3 x 4 lattices
for N=12,18,26 and 36. With these data we find different corrections to the
asymptotic scaling behaviour above and below the transition. Our result for the
universal ratio of the susceptibility amplitudes is C_+/C_-=4.72(11) and thus
in excellent agreement with a recent measurement for the 3d Ising model.


title: Composite operators in lattice QCD: nonperturbative renormalization

abstract:
  We investigate the nonperturbative renormalization of composite operators in
lattice QCD restricting ourselves to operators that are bilinear in the quark
fields. These include operators which are relevant to the calculation of
moments of hadronic structure functions. The computations are based on Monte
Carlo simulations using quenched Wilson fermions.


title: Scaling tests in $\Or(a)$--improved quenched lattice QCD

abstract:
  We present a scaling investigation of renormalized correlation functions in
$\Or(a)$--improved quenched lattice QCD. As one observable the renormalized
PCAC quark mass is considered, others are constructed such that they become the
vector meson mass, and the pseudoscalar and vector meson decay constants in
large volume. Presently, we remain in intermediate volume, $(0.75^3\times1.5)
{fm}^4$, and study the approach to the continuum limit.


title: Confinement and the vortex vacuum of SU(2) lattice gauge theory

abstract:
  The vortex theory which emerges from SU(2) lattice gauge theory by center
projection is briefly reviewed. In this vortex picture, quark confinement is
due to percolating (closed) vortices which are randomly linked to the Wilson
loop. The deconfinement phase transition appears as a de-percolation phase
transition.


title: The Electroweak Phase Transition in a Magnetic Field

abstract:
  We study the finite temperature electroweak phase transition in an external
hypercharge U(1) magnetic field H_Y, using lattice Monte Carlo simulations. For
sufficiently small fields, H_Y/T^2 < 0.3, the magnetic field makes the first
order transition stronger, but it still turns into a crossover for Higgs masses
m_H ~ 80 GeV. For larger fields, we observe a mixed phase analogous to a type I
superconductor, where a single macroscopic tube of the symmetric phase,
parallel to H_Y, penetrates through the broken phase. For the magnetic fields
and Higgs masses studied, we did not see indications of the expected
Ambjorn-Olesen phase, which should be similar to a type II superconductor.


title: How the PHMC algorithm samples configuration space

abstract:
  We show that in practical simulations of lattice QCD with two dynamical light
fermion species the PHMC algorithm samples configuration space differently from
the commonly used HMC algorithm.


title:
Intersection between Microscopic and Macroscopic Abelian Dominance in
  the Confinement Physics of QCD

abstract:
  We study abelian dominance for confinement in terms of the local gluon
properties in the maximally abelian (MA) gauge, where the diagonal component of
the gluon is maximized by the gauge transformation. We find microscopic abelian
dominance on the link-variable for the whole region of $\beta$ in the lattice
QCD in the MA gauge. The off-diagonal angle variable, which is not constrained
by the MA-gauge fixing condition, tends to be random besides the residual gauge
degrees of freedom. Within the random-variable approximation for the
off-diagonal angle variable, we analytically prove that off-diagonal gluon
contribution $W^{\rm off}$ to the Wilson loop obeys the perimeter law in the MA
gauge. The perimeter-law behavior of $W^{\rm off}$ is also confirmed using the
lattice QCD simulation. This indicates macroscopic abelian dominance for the
string tension.


title:
Resummation of Cactus Diagrams in the Clover Improved Lattice
  Formulation of QCD

abstract:
  We extend to the clover improved lattice formulation of QCD the resummation
of cactus diagrams, i.e. a certain class of tadpole-like gauge invariant
diagrams. Cactus resummation yields an improved perturbative expansion. We
apply it to the lattice renormalization of some two-fermion operators improving
their one-loop perturbative estimates.


title: Effective spin models for the confinement phase transition

abstract:
  Spatial correlations - bubbles, domain walls, etc. - can best be studied by
concentrating on the degrees of freedom most relevant to the problem. For the
finite temperature confinement transition, I integrate out all gauge degrees of
freedom, leaving only spins - Ising or Potts - related to the Wilson line. I
present problems that arise in the course of this transformation and some
results for the effective spin action.


title:
Non-perturbative running of the average momentum of non-singlet parton
  densities

abstract:
  We determine non-perturbatively the anomalous dimensions of the second moment
of non-singlet parton densities from a continuum extrapolation of results
computed in quenched lattice simulations at different lattice spacings. We use
a Schr\"odinger functional scheme for the definition of the renormalization
constant of the relevant twist-2 operator. In the region of renormalized
couplings explored, we obtain a good description of our data in terms of a
three-loop expression for the anomalous dimensions. The calculation can be used
for exploring values of the coupling where a perturbative expansion of the
anomalous dimensions is not valid a priori. Moreover, our results provide the
non-perturbative renormalization constant that connects hadron matrix elements
on the lattice, renormalized at a low scale, with the experimental results,
renormalized at much higher energy scales.


title: Running Coupling in the SU(2) Lattice Gauge Theory

abstract:
  Scenario according to which the SU(2)-gluodynamics is a theory with a
nontrivial fixed point is analyzed from the point of view of the modern
Monte-Carlo (MC) lattice data. It is found that an assumption of the first
order fixed point g=g_f of the beta function has no contradictions with
existing MC lattice data. The beta function parameters are found from the
requirement of constant values for critical temperature and string tension in
MC lattice calculations at 4/g^2 >= 2.30.


title: Constituent Quarks, Diquarks and the N-Delta Mass Splitting

abstract:
  We analyze hadron as well as quark and diquark correlation functions in
Landau gauge in order to extract information on the spin dependence of the
quark-quark interaction. We find evidence that the N-Delta mass splitting can
be attributed to the spin dependence of the interaction between quarks in a
colour anti-triplet state with spin 0 and 1, respectively. The lightest
excitations are observed in the S=0 channel. However, no evidence for a deeply
bound diquark state is found.


title: Scaling and Quantum Geometry in 2d Gravity

abstract:
  We review the status of understanding of the fractal structure of the quantum
spacetime of 2d gravity coupled to conformal matter with c <= 1, with emphasis
put on the results obtained last year.


abstract:
  The axial anomaly of Ginsparg-Wilson fermion operator $D$ is discussed in
general for the operator $R$ which enters the chiral symmetry breaking part in
the Ginsparg-Wilson relation. The axial anomaly and the index of $D$ as well as
the exact realization of the Atiyah-Singer index theorem on the lattice are
determined solely by the topological characteristics of the chirally symmetric
operator $D_c$ in the chiral limit $ R \to 0 $.


title: Progress in understanding colour confinement

abstract:
  New results from lattice are presented,which demonstrate that monopoles
condense in the vacuum of confined phase of QCD, which is thus a dual
superconductor. Monopoles defined by different abelian projections appear to be
physically equivalent.


title: Gluon excitations of the static-quark potential

abstract:
  The spectrum of gluon excitations in the presence of a static quark-antiquark
pair is presented. Our results are obtained from computer simulations of gluons
on anisotropic space-time lattices using an improved gauge-field action.
Measurements for quark-antiquark separations r ranging from 0.1 fm to 4 fm and
for various orientations on the lattice are made. Discretization errors and
finite volume effects are taken into account. Surprisingly, the spectrum does
not exhibit the expected onset of the universal pi/r Goldstone excitations of
the effective QCD string, even for r as large as 4 fm.


title:
Wilson, fixed point and Neuberger's lattice Dirac operator for the
  Schwinger model

abstract:
  We perform a comparison between different lattice regularizations of the
Dirac operator for massless fermions in the framework of the single and two
flavor Schwinger model. We consider a) the Wilson-Dirac operator at the
critical value of the hopping parameter; b) Neuberger's overlap operator; c)
the fixed point operator. We test chiral properties of the spectrum, dispersion
relations and rotational invariance of the mesonic bound state propagators.


title:
Study of the order of the phase transition in pure U(1) gauge theory
  with Villain action

abstract:
  We address the question of the order of the deconfinement phase transition of
four dimensional U(1) lattice gauge theory. Simulations of the Z-gauge theory
dual to the Villain action on toroidal lattices up to lattice sizes of 28^4
give results consistent with both, a vanishing and a nonvanishing discontinuity
in the thermodynamic limit. A decision on the order of the phase transition
requires still larger lattice sizes.


title:
Neutral B Meson Mixing and Heavy-light Decay Constants from Quenched
  Lattice QCD

abstract:
  We present high-statistics results for neutral $B$-meson mixing and
heavy-light-meson leptonic decays in the quenched approximation from
tadpole-improved clover actions at $\beta = 6.0$ and $\beta = 6.2$. We consider
quantities such as $B_{B_{d(s)}}$, $f_{D_{d(s)}}$, $f_{B_{d(s)}}$ and the full
$\Delta B=2$ matrix elements as well as the corresponding SU(3)-breaking
ratios. These quantities are important for determining the CKM matrix element
$|V_{td}|$.


title: Abelian Links, Monopoles and Glueballs in SU(2) Lattice Gauge Theory

abstract:
  We investigate the masses of 0+ and 2+ glueballs in SU(2) lattice gauge
theory using abelian projection to the maximum abelian gauge. We calculate
glueball masses using both abelian links and monopole operators. Both methods
reproduce the known full SU(2) results quantitatively. Positivity problems
present in the abelian projection are discussed. We study the dependence of the
glueball masses on magnetic current loop size, and find that the 0+ state
requires a much greater range of sizes than does the 2+ state.