title: The finite temperature QCD phase transition with domain wall fermions

abstract:
  The domain wall formulation of lattice fermions is expected to support
accurate chiral symmetry, even at finite lattice spacing. Here we attempt to
use this new fermion formulation to simulate two-flavor, finite temperature QCD
near the chiral phase transition. In this initial study, a variety of quark
masses, domain wall heights and domain wall separations are explored using an
8^3 x 4 lattice. Both the expectation value of the Wilson line and the chiral
condensate show the temperature dependence expected for the QCD phase
transition. Further, the desired chiral properties are seen for the chiral
condensate, suggesting that the domain wall fermion formulation may be an
effective approach for the numerical study of QCD at finite temperature.


title: Vortices in SU(2) lattice gauge theory

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


title:
Probing the QCD vacuum with flavour singlet objects: $\eta'$ on the
  lattice

abstract:
  We present a study on the direct determination of the $\eta '$ mass on the
full set of SESAM and T$\chi$L QCD vacuum configurations with 2 active flavours
of Wilson fermions, at $\beta = 5.6$. We observe a definite dependency of the
two-loop correlator on the topological charge sector.


title: A lattice path integral for supersymmetric quantum mechanics

abstract:
  We report on a study of the supersymmetric anharmonic oscillator computed
using a euclidean lattice path integral. Our numerical work utilizes a Fourier
accelerated hybrid Monte Carlo scheme to sample the path integral. Using this
we are able to measure massgaps and check Ward identities to a precision of
better than one percent. We work with a non-standard lattice action which we
show has an {\it exact} supersymmetry for arbitrary lattice spacing in the
limit of zero interaction coupling. For the interacting model we show that
supersymmetry is restored in the continuum limit without fine tuning. This is
contrasted with the situation in which a `standard' lattice action is employed.
In this case supersymmetry is not restored even in the limit of zero lattice
spacing. Finally, we show how a minor modification of our action leads to an
{\it exact}, local lattice supersymmetry even in the presence of interaction.


title:
Lattice regularization of chiral gauge theories to all orders of
  perturbation theory

abstract:
  In the framework of perturbation theory, it is possible to put chiral gauge
theories on the lattice without violating the gauge symmetry or other
fundamental principles, provided the fermion representation of the gauge group
is anomaly-free. The basic elements of this construction (which starts from the
Ginsparg-Wilson relation) are briefly recalled and the exact cancellation of
the gauge anomaly, at any fixed value of the lattice spacing and for any
compact gauge group, is then proved rigorously through a recursive procedure.


title:
Suppressing monopoles and vortices : A possibly smoother approach to
  scaling ?

abstract:
  Suppressing monopoles and vortices by introducing large chemical potentials
for them in the Wilson action for the SU(2) lattice gauge theory, we study the
nature of the deconfinement phase transition on N_\sigma^3 \times N_\tau
lattices for N_\tau = 4, 5, 6 and 8 and N_\sigma = 8--16. Using finite size
scaling theory, we obtain \omega = 1.93 \pm 0.03 for N_\tau = 4, in excellent
agreement with universality. Corresponding determinations for the N_\tau = 5
and 6 lattices are also found to be in very good agreement with this estimate.
The critical couplings for N_\tau= 4, 5, 6 and 8 lattices exhibit large shifts
towards the strong coupling region when compared with the usual Wilson action,
and suggest a lot smoother approach to scaling.


title: Deconfinement transition and string tensions in SU(4) Yang-Mills Theory

abstract:
  We present results from numerical lattice calculations of SU(4) Yang-Mills
theory. This work has two goals: to determine the order of the finite
temperature deconfinement transition on an $N_t = 6$ lattice and to study the
string tensions between static charges in the irreducible representations of
SU(4). Motivated by Pisarski and Tytgat's argument that a second-order
SU($\infty$) deconfinement transition would explain some features of the SU(3)
and QCD transitions, we confirm older results on a coarser, $N_t = 4$, lattice.
We see a clear two-phase coexistence signal, characteristic of a first-order
transition, at $8/g^2 = 10.79$ on a $6\times 20^3$ lattice, on which we also
compute a latent heat of $\Delta\epsilon\approx 0.6 \epsilon_{SB}$. Computing
Polyakov loop correlation functions we calculate the string tension at finite
temperature in the confined phase between fundamental charges, $\sigma_1$,
between diquark charges, $\sigma_2$, and between adjoint charges $\sigma_4$. We
find that $1 < \sigma_2/\sigma_1 < 2$, and our result for the adjoint string
tension $\sigma_4$ is consistent with string breaking.


title: Physical Results from Unphysical Simulations

abstract:
  We calculate various properties of pseudoscalar mesons in partially quenched
QCD using chiral perturbation theory through next-to-leading order. Our results
can be used to extrapolate to QCD from partially quenched simulations, as long
as the latter use three light dynamical quarks. In other words, one can use
unphysical simulations to extract physical quantities - in this case the quark
masses, meson decay constants, and the Gasser-Leutwyler parameters L_4-L_8. Our
proposal for determining L_7 makes explicit use of an unphysical (yet
measurable) effect of partially quenched theories, namely the double-pole that
appears in certain two-point correlation functions. Most of our calculations
are done for sea quarks having up to three different masses, except for our
result for L_7, which is derived for degenerate sea quarks.


title: Numerical Study of Dense Adjoint Matter in Two Color QCD

abstract:
  We identify the global symmetries of SU(2) lattice gauge theory with N
flavors of staggered fermion in the presence of a quark chemical potential mu,
for fermions in both fundamental and adjoint representations, and anticipate
likely patterns of symmetry breaking at both low and high densities. Results
from numerical simulations of the model with N=1 adjoint flavor on a 4^3x8
lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson
algorithms. It is shown that the sign of the fermion determinant starts to
fluctuate once the model enters a phase with non-zero baryon charge density.
HMC simulations are not ergodic in this regime, but TSMB simulations retain
ergodicity even in the dense phase, and in addition appear to show superior
decorrelation. The HMC results for the equation of state and the pion mass show
good quantitative agreement with the predictions of chiral perturbation theory,
which should hold only for N>=2. The TSMB results incorporating the sign of the
determinant support a delayed onset transition, consistent with the pattern of
symmetry breaking expected for N=1.


title: Heavy Quarks on Anisotropic Lattices: The Charmonium Spectrum

abstract:
  We present results for the mass spectrum of $c{\bar c}$ mesons simulated on
anisotropic lattices where the temporal spacing $a_t$ is only half of the
spatial spacing $a_s$. The lattice QCD action is the Wilson gauge action plus
the clover-improved Wilson fermion action. The two clover coefficients on an
anisotropic lattice are estimated using mean links in Landau gauge. The bare
velocity of light $\nu_t$ has been tuned to keep the anisotropic, heavy-quark
Wilson action relativistic. Local meson operators and three box sources are
used in obtaining clear statistics for the lowest lying and first excited
charmonium states of $^1S_0$, $^3S_1$, $^1P_1$, $^3P_0$ and $^3P_1$. The
continuum limit is discussed by extrapolating from quenched simulations at four
lattice spacings in the range 0.1 - 0.3 fm. Results are compared with the
observed values in nature and other lattice approaches. Finite volume effects
and dispersion relations are checked.


title: The eta and eta' mesons in QCD

abstract:
  We study the flavour singlet pseudoscalar mesons from first principles using
lattice QCD. We explore the quark content of the $\eta$ and $\eta'$ mesons and
we discuss their decay constants.


title: Unexpected results in asymptotically free quantum field theories

abstract:
  We study the behavior of asymptotically free (AF) spin and gauge models when
their continuous symmetry group is replaced by different discrete non-Abelian
subgroups. Precise numerical results with relative errors down to O(0.1%)
suggest that the models with large subgroups are in the universality class of
the underlying original models. We argue that such a scenario is consistent
with the known properties of AF theories. The small statistical errors allow a
detailed investigation of the cut-off effects also. At least up to correlation
lengths ~300 they follow effectively an O(a) rather than the expected O(a^2)
form both in the O(3) and in the dodecahedron model.


title: Casimir scaling of SU(3) static potentials

abstract:
  Potentials between static colour sources in eight different representations
are computed in four dimensional SU(3) gauge theory. The simulations have been
performed with the Wilson action on anisotropic lattices where the renormalised
anisotropies have been determined non-perturbatively. After an extrapolation to
the continuum limit we are able to exclude any violations of the Casimir
scaling hypothesis that exceed 5% for source separations of up to 1 fm.


title:
Equation of state and Goldstone-mode effects of the three-dimensional
  O(2) model

abstract:
  We investigate numerically the three-dimensional O(2) model on 8^3-160^3
lattices as a function of the magnetic field H. In the low-temperature phase we
verify the H-dependence of the magnetization M induced by Goldstone modes and
determine M in the thermodynamic limit both by extrapolation and by chiral
perturbation theory. This enables us to calculate the corresponding critical
amplitude. At T_c the critical scaling behaviour of the magnetization as a
function of H is used to determine another critical amplitude. In both cases we
find negative corrections-to-scaling. Our low-temperature results are well
described by the perturbative form of the model's magnetic equation of state,
with coefficients determined nonperturbatively from our data. The O(2) scaling
function for the magnetization is found to have a smaller slope than the one
for the O(4) model.


title: An illustration of chiral fermions on a 1+1 dimensional lattice

abstract:
  The vectorlike doubling of low-energy excitations is in fact a natural
consequence of the pair-production around the zero-energy (E=0) due to the
quantum field fluctuations of the lattice regularized vacuum. On the 1+1
dimensional lattice, we study an anomaly-free chiral model (11112) of four
left-movers and one right-mover with strong interactions. Exact computations of
relevant S-matrices illustrate that for high-momentum states, a negative
energy-gap (E<0) develops; the bound state and its constituents, which have the
same quantum numbers but opposite chiralities, fill the same energy-state so
that chiral symmetries are preserved; for low-momentum states, the negative
energy-gap vanishes and the bound state dissolves into its constituents near
zero energy. As a consequence of the gauge-anomaly cancellation and the index
theorem for flavor-singlet anomalies, the net number of zero-modes pushed down
into and pumped out from the zero-energy level by the gauge field is zero.


title:
An Almost Perfect Quantum Lattice Action for Low-energy SU(2)
  Gluodynamics

abstract:
  We study various representations of infrared effective theory of SU(2)
Gluodynamics as a (quantum) perfect lattice action. In particular we derive a
monopole action and a string model of hadrons from SU(2) Gluodynamics. These
are lattice actions which give almost cut-off independent physical quantities
even on coarse lattices. The monopole action is determined by numerical
simulations in the infrared region of SU(2) Gluodynamics. The string model of
hadrons is derived from the monopole action by using BKT transformation. We
illustrate the method and evaluate physical quantities such as the string
tension and the mass of the lowest state of the glueball analytically using the
string model of hadrons. It turns out that the classical results in the string
model is near to the one in quantum SU(2) Gluodynamics.


title: Effective Chiral Lagrangians and Lattice QCD

abstract:
  We propose a general method to obtain accurate estimates for some of the
"low-energy constants" in the one-loop effective chiral Lagrangian by means of
simulating lattice QCD. In particular, the method is sensitive to those
constants whose values are required to test the hypothesis of a massless
up-quark. Initial tests performed in the quenched approximation confirm that
good statistical precision can be achieved. As a byproduct we obtain an
accurate estimate for the ratio of pseudoscalar decay constants, F_K/F_pi, in
the quenched approximation, which lies 10% below the experimental result. The
quantities that serve to extract the low-energy constants also allow a test of
the scaling behaviour of different discretizations of QCD and a search for the
effects of dynamical quarks.


title: Strong Non-Ultralocality of Ginsparg-Wilson Fermionic Actions

abstract:
  It is shown that it is impossible to construct a free theory of fermions on
infinite hypercubic Euclidean lattice in even number of dimensions that: (a) is
ultralocal, (b) respects the symmetries of hypercubic lattice, (c) chirally
nonsymmetric part of its propagator is local, and (d) describes single species
of massless Dirac fermions in the continuum limit. This establishes
non-ultralocality for arbitrary doubler-free Ginsparg-Wilson fermionic action
with hypercubic symmetries ("strong non-ultralocality"), and complements the
earlier general result on non-ultralocality of infinitesimal
Ginsparg-Wilson-Luscher symmetry transformations ("weak non-ultralocality").


title: Vortices, monopoles and confinement

abstract:
  We construct the creation operator of a vortex using the methods developed
for monopoles. The vacuum expectation value of this operator is interpreted as
a disorder parameter describing vortex condensation and is studied numerically
on a lattice in SU(2) gauge theory. The result is that vortices behave in the
vacuum in a similar way to monopoles. The disorder parameter is different from
zero in the confined phase, and vanishes at the deconfining phase transition.
We discuss this behaviour in terms of symmetry. Correlation functions of the
vortex creation operator at zero temperature are also investigated. A
comparison is made with related results by other groups.


title:
On the Determination of Nonleptonic Kaon Decays from $K\to\pi$ Matrix
  Elements

abstract:
  The coupling constants of the order $p^2$ low-energy weak effective
lagrangian can be determined from the $K\to\pi$ and $K\to 0$ weak matrix
elements, choosing degenerate quark masses for the first of these. However, for
typical values of quark masses in Lattice QCD computations, next-to-leading
$O(p^4)$ corrections are too large to be ignored, and will need to be included
in future analyses. Here we provide the complete $O(p^4)$ expressions for these
matrix elements obtained from Chiral Perturbation Theory, valid for partially
quenched QCD with $N$ degenerate sea quarks. Quenched QCD corresponds to the
special case N=0. We also discuss the role of the $\eta'$ meson in some detail,
and we give numerical examples of the size of chiral logarithms.


title: Exact local fermionic zero modes

abstract:
  We introduce a simple method to find localized exact fermionic zero modes for
any local fermionic action. The zero modes are attached to specific local gauge
configurations. Examples are provided for staggered and Wilson fermion actions
in 2-6 dimensions, at finite and infinite lattice volumes, and for abelian and
non-abelian gauge groups. One of our concrete results is that a finite density
of almost zero modes must occur in quenched four dimensional lattice gauge
theory simulations that use traditional methods. This density is exponentially
suppressed in the gauge coupling constant.


title:
Numerical study of the Kugo-Ojima criterion and the Gribov problem in
  the Landau gauge

abstract:
  The Kugo-Ojima color confinement criterion, which is based on the BRST
symmetry of the continuum QCD is numerically tested by the lattice Landau gauge
simulation. We first discuss the Gribov copy problem and the BRST symmetry on
the lattice. The lattice Landau gauge can be formulated with options of the
gauge field definition, U(link)-linear type or log U type. The Kugo-Ojima
parameter u^a_b which is expected to be -1^a_b in the continuum theory is found
to be -0.7*1^a_b in the strong coupling region, and the magnitude is a little
less in the weak coupling region in log U type simulation. Those values are
weakened even further in U-linear type. The horizon function defined by
Zwanziger is evaluated in both types of gauge field and compared. The horizon
function in the log U version is larger than the other, but in the weak
coupling region, the expectation value of the horizon function is suggested to
be zero or negative.


title: Renormalization and O(a)-improvement of the static-light axial current

abstract:
  A systematic treatment of O(a)-improvement in lattice theories with static
quarks is presented. The Schr\"odinger functional is discussed and a
renormalization condition for the static axial current in the SF-scheme is
introduced. Its relation to other schemes is computed to 1-loop order and the
2-loop anomalous dimension is derived. In finite volume renormalization schemes
such as the SF-scheme, the renormalization scale dependence of the renormalized
quantities is described by the step scaling function which can be computed by
MC- simulations. We evaluate its lattice spacing effects in perturbation
theory.


title: Short-time critical dynamics

abstract:
  An introductory review to short-time critical dynamics is given. From the
scaling relation valid already in the early stage of the evolution of a system
at or near the critical point, one derives power law behaviour for various
quantities. By a numerical simulation of the system one can measure the
critical exponents and, by searching for the best power law behaviour, one can
determine the critical point. Critical slowing down as well as finite size
corrections are nearly absent, since the correlation length is still small for
times far before equilibrium is reached. By measuring the (pseudo) critical
points it is also possible to distinguish (weak) first-order from second-order
phase transitions.


title: Renormalisation and off-shell improvement in lattice perturbation theory

abstract:
  We discuss the improvement of flavour non-singlet point and one-link lattice
quark operators, which describe the quark currents and the first moment of the
DIS structure functions respectively. Suitable bases of improved operators are
given, and the corresponding renormalisation factors and improvement
coefficients are calculated in one-loop lattice perturbation theory, using the
Sheikholeslami-Wohlert (clover) action. To this order we achieve off-shell
improvement by eliminating the effect of contact terms. We use massive
fermions, and our calculations are done keeping all terms up to first order in
the lattice spacing, for arbitrary m^2/p^2, in a general covariant gauge. We
also compare clover fermions with fermions satisfying the Ginsparg-Wilson
relation, and show how to remove O(a) effects off-shell in this case too, and
how this is in many aspects simpler than for clover fermions. Finally, tadpole
improvement is also considered.


title: Percolation and Magnetization for Generalized Continuous Spin Models

abstract:
  For the Ising model, the spin magnetization transition is equivalent to the
percolation transition of Fortuin-Kasteleyn clusters; this result remains valid
also for the conventional continuous spin Ising model. The investigation of
more general continuous spin models may help to obtain a percolation
formulation for the critical behaviour in SU(2) gauge theory. We therefore
study a broad class of theories, introducing spin distribution functions,
longer range interactions and self-interaction terms. The thermal behaviour of
each model turns out to be in the Ising universality class. The corresponding
percolation formulations are then obtained by extending the Fortuin-Kasteleyn
cluster definition; in several cases they illustrate recent rigorous results.


title: Meron Pairs and Fermion Zero Modes

abstract:
  Merons, conjectured as a semiclassical mechanism for color confinement in
QCD, have been described analytically by either infinite action configurations
or an Ansatz with discontinuous action. We construct a smooth, finite action,
stationary lattice solution corresponding to a meron pair. We also derive an
analytical solution for the zero mode of the meron pair Ansatz, show that it
has the qualitative behavior of the exact zero mode of the lattice solution,
and propose the use of zero modes to identify meron gauge field configurations
in stochastic evaluations of the lattice QCD path integral.


title: Fixed Point Gauge Actions with Fat Links: Scaling and Glueballs

abstract:
  A new parametrization is introduced for the fixed point (FP) action in SU(3)
gauge theory using fat links. We investigate its scaling properties by means of
the static quark-antiquark potential and the dimensionless quantities $r_0 T_c,
T_c/\sqrt{\sigma}$ and $r_0 \sqrt{\sigma}$, where $T_c$ is the critical
temperature of the deconfining phase transition, $r_0$ is the hadronic scale
and $\sigma$ is the effective string tension. These quantities scale even on
lattices as coarse as $a \approx 0.3$ fm. We also measure the glueball spectrum
and obtain $m_{0^{++}}=1627(83)$ MeV and $m_{2^{++}}=2354(95)$ MeV for the
masses of the scalar and tensor glueballs, respectively.


title: Universality and Chaos in Quantum Field Theories

abstract:
  We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3)
gauge theory and in full QCD as well as in quenched U(1) theory on various
lattice sizes. As a measure of the fluctuation properties of the eigenvalues,
we consider the nearest-neighbor spacing distribution, $P(s)$. We further study
two-color QCD at nonzero chemical potential, $\mu$, by constructing the spacing
distribution of adjacent eigenvalues in the complex plane. We find that in all
regions of their phase diagrams, compact lattice gauge theories have bulk
spectral correlations given by random matrix theory, which is an indication for
quantum chaos. In the confinement phase, the low-lying Dirac spectrum of these
quantum field theories is well described by random matrix theory, exhibiting
universal behavior.


title: Spectrum of the U(1) staggered Dirac operator in four dimensions

abstract:
  We compare the low-lying spectrum of the staggered Dirac operator in the
confining phase of compact U(1) gauge theory on the lattice to predictions of
chiral random matrix theory. The small eigenvalues contribute to the chiral
condensate similar as for the SU(2) and SU(3) gauge groups. Agreement with the
chiral unitary ensemble is observed below the Thouless energy, which is
extracted from the data and found to scale with the lattice size according to
theoretical predictions.


title: Anomalous Chiral Behavior in Quenched Lattice QCD

abstract:
  A study of the chiral behavior of pseudoscalar masses and decay constants is
carried out in quenched lattice QCD with Wilson fermions. Using the modified
quenched approximation (MQA) to cure the exceptional configuration problem,
accurate results are obtained for pion masses as low as $\approx$ 200 MeV. The
anomalous chiral log effect associated with quenched $\eta'$ loops is studied
in both the relation between $m_{\pi}^2$ vs. $m_q$ and in the light-mass
behavior of the pseudoscalar and axial vector matrix elements. The size of
these effects agrees quantitatively with a direct measurement of the $\eta'$
hairpin graph, as well as with a measurement of the topological susceptibility,
thus providing several independent and quantitatively consistent determinations
of the quenched chiral log parameter $\delta$. For $\beta=5.7$ with
clover-improved fermions $(C_{sw} =1.57)$ all results are consistent with
$\delta=0.065\pm 0.013$ .


title:
Perturbative Renormalization of Weak-Hamiltonian Four-Fermion Operators
  with Overlap Fermions

abstract:
  The renormalization of the most general dimension-six four-fermion operators
without power subtractions is studied at one loop in lattice perturbation
theory using overlap fermions. As expected, operators with different chirality
do not mix among themselves and parity-conserving and parity-violating
multiplets renormalize in the same way. The renormalization constants of
unimproved and improved operators are also the same. These mixing factors are
necessary to determine physical matrix elements relevant to many
phenomenological applications of weak interactions. The most important are the
K0-K0bar and B0-B0bar mixings in the Standard Model and beyond, the Delta I
=1/2 rule and epsilon'/epsilon.


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

abstract:
  The deconfinement transition in SU(2) gauge theory and the magnetization
transition in the Ising model belong to the same universality class. The
critical behaviour of the Ising model can be characterized either as
spontaneous breaking of the $Z_2$ symmetry of spin states or as percolation of
appropriately defined spin clusters. We show that deconfinement in SU(2) gauge
theory can be specified as percolation of Polyakov loop clusters with
Fortuin-Kasteleyn bond weights, leading to the same critical exponents as the
conventional order-disorder description based on the Polykov loop expectation
value.


title: Large N limit of the IKKT matrix model

abstract:
  Using the dynamical triangulation approach we perform a numerical study of a
supersymmetric random surface model that corresponds to the large N limit of
the four-dimensional version of the IKKT matrix model. We show that the
addition of fermionic degrees of freedom suppresses the spiky world-sheet
configurations that are responsible for the pathological behaviour of the
purely bosonic model. We observe that the distribution of the gyration radius
has a power-like tail p(R) ~ R^{-2.4}. We check numerically that when the
number of fermionic degrees of freedom is not susy-balanced, p(R) grows with
$R$ and the model is not well-defined. Numerical sampling of the configurations
in the tail of the distribution shows that the bosonic degrees of freedom
collapse to a one-dimensional tube with small transverse fluctuations. Assuming
that the vertex positions can fluctuate independently within the tube, we give
a theoretical argument which essentially explains the behaviour of p(R) in the
different cases, in particular predicting p(R) ~ R^{-3} in the supersymmetric
case. Extending the argument to six and ten dimensions, we predict p(R) ~
R^{-7} and p(R) ~ R^{-15}, respectively.


title: Chiral properties of domain-wall quarks in quenched QCD

abstract:
  We investigate the chiral properties of quenched domain-wall QCD (DWQCD) at
the lattice spacings $a^{-1} \simeq 1$ and 2 GeV for both plaquette and
renormalization-group (RG) improved gauge actions. In the case of the plaquette
action we find that the quark mass defined through the axial Ward-Takahashi
identity remains non-vanishing in the DWQCD chiral limit that the bare quark
mass $m_f\to 0$ and the length of the fifth dimension $N_s\to\infty$,
indicating that chiral symmetry is not realized with quenched DWQCD up to
$a^{-1} \simeq 2$ GeV. The behavior is much improved for the RG-improved gauge
action: while a non-vanishing quark mass remains in the chiral limit at
$a^{-1}\simeq 1$ GeV, the result at $a^{-1}\simeq 2$ GeV is consistent with an
exponentially vanishing quark mass in the DWQCD chiral limit, indicating the
realization of exact chiral symmetry. An interpretation and implications are
briefly discussed.


title: A note on the practical feasibility of domain-wall fermions

abstract:
  Domain-wall fermions preserve chiral symmetry up to terms that decrease
exponentially when the lattice size in the fifth dimension is taken to
infinity. The associated rates of convergence are given by the low-lying
eigenvalues of a simple local operator in four dimensions. These can be
computed using the Ritz functional technique and it turns out that the
convergence tends to be extremely slow in the range of lattice spacings
relevant to large-volume numerical simulations of lattice QCD. Two methods to
improve on this situation are discussed.


title:
Scaling and Further Tests of Heavy Meson Decay Constant Determinations
  from Nonrelativistic QCD

abstract:
  We present results for the B_s meson decay constant f_{B_s} from simulations
at three lattice spacings in the range a^{-1}=1.1 to 2.6 GeV using NRQCD heavy
quarks and clover light quarks in the quenched approximation. We study scaling
of this quantity and check the consistency between mesons decaying from rest
and from a state with nonzero spatial momentum. The cancellation of power law
contributions that arise in the NRQCD formulation of heavy-light currents is
discussed. On the coarsest lattice the D_s meson decay constant f_{D_s} is
calculated. Our best values for the decay constants are given by f_{B_s} =
187(4)(4)(11)(2)(7)(6) MeV and f_{D_s} = 223(6)(31)(38)(23)(9)(^{+3}_{-1}) MeV.


title: Approximate Ginsparg-Wilson Fermions for QCD

abstract:
  Lattice fermions obeying the Ginsparg-Wilson relation do correctly represent
the physical properties related to chirality. This can be achieved by local
fermions, which involve an infinite number of couplings, however. For practical
purposes, it is useful to first construct approximate Ginsparg-Wilson fermions
within a short range. We report on a successful construction in QCD at \beta
=6. The good quality of the approximation is observed from the spectrum, which
is situated close to a Ginsparg-Wilson circle. These fermions also provide an
excellent approximation to rotational symmetry and they are promising for a
good scaling, since they arise from the perfect action framework. Their
insertion into the overlap formula renders the Ginsparg-Wilson relation exact.
It leads to an improved overlap fermion with a high level of locality. This
insertion is statistically on safe grounds at about \beta > 5.6.


title: Diquark condensation in two colour QCD

abstract:
  Unquenched lattice SU(2) is studied at nonzero chemical potential in the
strong coupling limit. The topic of diquark condensation is addressed analyzing
the probability distribution function of the diquark condensate. We present
results at zero external source without using any potentially dangerous
extrapolation procedure. We find strong evidences for a (high density) second
order phase transition where a diquark condensate appears, and show
quantitative agreement of lattice calculations with low-energy effective
Lagrangian calculations.


title: The three-dimensional, three-state Potts Model in an External Field

abstract:
  We analyze the critical behaviour of the three-dimensional, three-state Potts
model in the presence of an external ordering field. From a finite size scaling
analysis on lattices of size up to 70**3 we determine the critical endpoint of
the line of first order phase transitions as (b_c, h_c) =(0.54938(2),
0.000775(10)). We determine the relevant temperature like and symmetry breaking
directions at this second order critical point and explicitly verify that it is
in the universality class of the three-dimensional Ising model.


title:
Decay Constants of B and D Mesons from Non-perturbatively Improved
  Lattice QCD

abstract:
  The decay constants of B, D and K mesons are computed in quenched lattice QCD
at two different values of the coupling. The action and operators are O(a)
improved with non-perturbative coefficients. The results are
f_B=195(6)(+24/-23) MeV, f_D=206(4)(+17/-10) MeV, f_B_s=220(6)(+23/-28) MeV,
f_D_s=229(3)(+23/-12) MeV and f_K= 150(3)(+12/-8) MeV. Systematic errors are
discussed in detail. Results for vector decay constants, flavour symmetry
breaking ratios of decay constants, the pseudoscalar-vector mass splitting and
D meson masses are also presented.


title: Overlap-Dirac fermions with a small hopping parameter

abstract:
  We consider overlap-Dirac fermions at non-zero bare coupling and for a small
hopping parameter, or, equivalently, large $|M|$ with $M$ the domain-wall
height. We prove the existence of a phase at large positive $M$ where the
abelian axial group $U_A(1)$ is a symmetry, and the corresponding pseudo-scalar
is an exact Goldstone boson. We also provide a conjecture for the phase diagram
of asymptotically free gauge theories with overlap-Dirac fermions. In
particular, we suggest that, for large gauge coupling, the massive-fermion
phase at negative $M$ possibly extends to all $M<4$.


title: The Simple Center Projection of SU(2) Gauge Theory

abstract:
  We consider the SU(2) lattice gauge model. We propose a new gauge invariant
definition of center projection, which we call the Simple Center Projection. We
demonstrate the center dominance, i.e., the coincidence of the projected
potential with the full potential up to the mass renormalization term at low
energies. We also consider the center vortices and the center monopoles ({\em
nexuses}). It turns out that the behavior of such objects qualitatively
coincides with the behavior of the vortices and monopoles in the Maximal Center
gauge. The connection of the condensation of nexuses with the dual
superconductor theory is discussed. Numerically the procedure of extracting the
center vortices proposed in this paper is much simpler than the usual Maximal
Center Projection.


title: Chiral fermions on the lattice and index relations

abstract:
  Comparing recent lattice results on chiral fermions and old continuum results
for the index puzzling questions arise. To clarify this issue we start with a
critical reconsideration of the results on finite lattices. We then work out
various aspects of the continuum limit. After determining bounds and norm
convergences we obtain the limit of the anomaly term. Collecting our results
the index relation of the quantized theory gets established. We then compare in
detail with the Atiyah-Singer theorem. Finally we analyze conventional
continuum approaches.


title:
Perturbative renormalization factors of $\Delta S = 1$ four-quark
  operators for domain-wall QCD

abstract:
  Renormalization factors for $\Delta S =1$ four-quark operators in the
effective weak Hamiltonian are perturbatively evaluated in domain-wall QCD. The
one-loop corrections of $\Delta S=1$ four-quark operators consist of two types
of diagrams: one is gluon exchange between quark lines and the other is penguin
diagrams containing quark loops. Combining both contributions, our results
allow a lattice calculation of the amplitude for $K\to \pi\pi$ decays with
$O(g^2)$ corrections included.


title:
First order phase transition of the q-state Potts model in two
  dimensions

abstract:
  We have calculated the large-$q$ series of the energy cumulants, the
magnetization cumulants and the correlation length at the first order phase
transition point both in the ordered and disordered phases for the $q$-state
Potts model in two dimensions. The series enables us to estimate the numerical
values of the quantities more precisely by a factor of $10^2 - 10^4$ than the
Monte Carlo simulations. From the large-$q$ series of the eigenvalues of the
transfer matrix, we also find that the excited states form a continuum spectrum
and there is no particle state at the first order phase transition point.


title: Hadron Structure in Lattice QCD: Exploring the Gluon Wave Functional

abstract:
  The use of lattice QCD to understand hadron structure is described, with
particular emphasis on exploring the role of glue.


title: Instanton and Meron Physics in Lattice QCD

abstract:
  Lattice field theory provides a quantitative tool to study the role of
nonperturbative semiclassical configurations in QCD. This talk briefly reviews
our present understanding of the role of instantons in QCD and describes in
detail new developments in the study of merons on the lattice.


title: Quark propagator in the Landau gauge

abstract:
  The Landau gauge quark propagator in momentum space is investigated using the
O(a)-improved Sheikholeslami--Wohlert (SW) quark action with a tree-level
mean-field improved coefficient c_sw. We have studied the unimproved definition
of the quark propagator, as well as two different tree-level O(a)-improved
propagators. The ultraviolet behavior of the free lattice propagator is studied
for each of these in order to establish which of them provides the most
reliable description of the quark propagator up to the medium momentum regime.
A general method of tree-level correction is introduced. This exploits
asymptotic freedom and removes much of the trivial lattice artifacts at medium
to high momenta. We obtain results for the quark propagator which are
qualitatively similar to those typically used in quark models. A simple
extrapolation of the infrared quark mass M(p^2=0) to the chiral limit gives
(298+/-8+/-30) MeV, which is consistent with phenomenological expectations.


title: One-Flavour Hybrid Monte Carlo with Wilson Fermions

abstract:
  The Wilson fermion determinant can be written as product of the determinants
of two hermitian positive definite matrices. This formulation allows to
simulate non-degenerate quark flavors by means of the hybrid Monte Carlo
algorithm. A major numerical difficulty is the occurrence of nested inversions.
We construct a Uzawa iteration scheme which treats the nested system within one
iterative process.


title: Can Merons Describe Confinement?

abstract:
  Merons, conjectured as a semiclassical mechanism for color confinement in
QCD, are topological charge-1/2, singular solutions to the classical Yang-Mills
equations of motion. I will discuss how lattice techniques can extend the study
of merons to nonsingular stationary solutions without destroying properties
believed to be essential for confinement, and how zero modes can be used to
identify these gauge field configurations in stochastic evaluations of the
lattice QCD path integral.


title:
Green's Function Monte Carlo approach to SU(3) Yang-Mills theory in
  (3+1)D

abstract:
  A 'forward walking' Green's Function Monte Carlo algorithm is used to obtain
expectation values for SU(3) lattice Yang-Mills theory in (3+1) dimensions. The
ground state energy and Wilson loops are calculated, and the finite-size
scaling behaviour is explored. Crude estimates of the string tension are
derived, which agree with previous results at intermediate couplings; but more
accurate results for larger loops will be required to establish scaling
behaviour at weak coupling.


title: Aspects of Chiral Symmetry and the Lattice

abstract:
  I explore the non-perturbative issues entwining lattice gauge theory,
anomalies, and chiral symmetry. After briefly reviewing the importance of
chiral symmetry in particle physics, I discuss how anomalies complicate lattice
formulations. Considerable information can be deduced from effective chiral
Lagrangians, helping interpret the expectations for lattice models and
elucidating the role of the CP violating parameter $\Theta$. I then turn to a
particularly elegant scheme for exploring this physics on the lattice. This
uses an auxiliary extra space-time dimension, with the physical world being a
four dimensional interface.


title: Residual Chiral Symmetry Breaking in Domain-Wall Fermions

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


title: A study of the 't Hooft loop in SU(2) Yang-Mills theory

abstract:
  We study the behaviour of the spatial and temporal 't Hooft loop at zero and
finite temperature in the 4D SU(2) Yang-Mills theory, using a new numerical
method. In the deconfined phase $T>T_c$, the spatial 't Hooft loop exhibits a
dual string tension, which vanishes at $T_c$ with 3D Ising-like critical
exponent.


title: Cluster Percolation in O(n) Spin Models

abstract:
  The spontaneous symmetry breaking in the Ising model can be equivalently
described in terms of percolation of Wolff clusters. In O(n) spin models
similar clusters can be built in a general way, and they are currently used to
update these systems in Monte Carlo simulations. We show that for 3-dimensional
O(2), O(3) and O(4) such clusters are indeed the physical `islands' of the
systems, i.e., they percolate at the physical threshold and the percolation
exponents are in the universality class of the corresponding model. For O(2)
and O(3) the result is proven analytically, for O(4) we derived it by numerical
simulations.


title: An Almost Perfect Lattice Action for infrared QCD

abstract:
  A block-spin transformation on the dual lattice leads us to an almost perfect
lattice action for monopoles and strings in QCD. The perfect operator for a
static quark potential is fixed when we compare the above action with the
perfect action obtained analytically after infinite-step block-spin
transformations in a simple case. The continuum rotational invariance is
restored and the physical value of the string tension is reproduced fairly
well. Gauge independence of the abelian and the monopole scenario is discussed.


title: Examples of overlapping convergent expansions of scaling variables

abstract:
  We construct series expansions for the scaling variables (which transform
multiplicatively under a renormalization group (RG) transformation) in examples
where the RG flows, going from an unstable (Wilson's) fixed point to a stable
(high-temperature) fixed point, can be calculated numerically. The examples are
Dyson's hierarchical model and a simplified version of it. We provide numerical
evidence that the scaling variables about the two fixed points have overlapping
domain of convergence. We show how quantities such as the magnetic
susceptibility can be expressed in terms of these variables. This procedure
provide accurate analytical expressions both in the critical and
high-temperature region.


title: Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit

abstract:
  Quenched QCD simulations on three volumes, $8^3 \times$, $12^3 \times$ and
$16^3 \times 32$ and three couplings, $\beta=5.7$, 5.85 and 6.0 using domain
wall fermions provide a consistent picture of quenched QCD. We demonstrate that
the small induced effects of chiral symmetry breaking inherent in this
formulation can be described by a residual mass ($\mres$) whose size decreases
as the separation between the domain walls ($L_s$) is increased. However, at
stronger couplings much larger values of $L_s$ are required to achieve a given
physical value of $\mres$. For $\beta=6.0$ and $L_s=16$, we find
$\mres/m_s=0.033(3)$, while for $\beta=5.7$, and $L_s=48$,
$\mres/m_s=0.074(5)$, where $m_s$ is the strange quark mass. These values are
significantly smaller than those obtained from a more naive determination in
our earlier studies. Important effects of topological near zero modes which
should afflict an accurate quenched calculation are easily visible in both the
chiral condensate and the pion propagator. These effects can be controlled by
working at an appropriately large volume. A non-linear behavior of $m_\pi^2$ in
the limit of small quark mass suggests the presence of additional infrared
subtlety in the quenched approximation. Good scaling is seen both in masses and
in $f_\pi$ over our entire range, with inverse lattice spacing varying between
1 and 2 GeV.


title: Parallel tempering and decorrelation of topological charge in full QCD

abstract:
  The improvement of simulations of QCD with dynamical Wilson fermions by
combining the Hybrid Monte Carlo algorithm with parallel tempering is studied
on $10^4$ and $12^4$ lattices. As an indicator for decorrelation the
topological charge is used.


title: Gluons in the lattice SU(2) classical field

abstract:
  The SU(2) gluonic correlation functions, glueball effective masses in the
$J^{P}=0^{+}$, $2^{+}$ and $0^{-}$ channels were calculated from the lattice
classical gauge configurations which were obtained by smoothing the thermal
gauge configurations through the improved cooling method. The instanton-induced
attractive force in the $0^{+}$ channel and the repulsive force in the $0^-$
channel are confirmed in the Monte Carlo simulation. There is evidence that the
instanton vacuum contribution to the $0^+$ glueball mass is significant.


title: Eigenvalue Distributions of the QCD Dirac Operator

abstract:
  We compute by Monte Carlo methods the individual distributions of the $k$th
smallest Dirac operator eigenvalues in QCD, and compare them with recent
analytical predictions. We do this for both massless and massive quarks in an
SU(3) gauge theory with staggered fermions. Very precise agreement is found in
all cases. As a simple by-product we also extract the microscopic spectral
density of the Dirac operator in SU(3) gauge theory with dynamical massive
fermions for $N_f=1$ and 2, and obtain high-accuracy agreement with analytical
expressions.


title: Approximate Ginsparg-Wilson fermions: A first test

abstract:
  We construct a 4-d lattice Dirac operator D using a systematical expansion in
terms of simple operators on the lattice. The Ginsparg-Wilson equation turns
into a system of coupled equations for the expansion coefficients of D. We
solve these equations for a finite parametrization of D and find an approximate
solution of the Ginsparg-Wilson equation. We analyze the spectral properties of
our D for various ensembles of quenched SU(3) configurations. Improving the
gauge field action considerably improves the spectral properties of our D.


title: P-Vortices, Gauge Copies, and Lattice Size

abstract:
  We study the dependence of the center-projected string tension on both the
lattice size, and the number of gauge copies used for maximal center gauge
fixing. We show that a recent finding of Bornyakov, Komarov, Polikarpov, and
Veselov (hep-lat/0002017), indicating a substantial breakdown of center
dominance in maximal center gauge, is only obtained for rather small lattice
volumes, and is not found in numerical simulations on larger lattices. It is
shown that center-projected Creutz ratios approach the full asymptotic string
tension as lattice size increases, and that the P-vortex density is consistent,
at moderately weak couplings, with 2-loop scaling behavior.


title:
Operator Product Expansion on the Lattice: a Numerical Test in the
  Two-Dimensional Non-Linear Sigma-Model

abstract:
  We consider the short-distance behaviour of the product of the Noether O(N)
currents in the lattice nonlinear sigma-model. We compare the numerical results
with the predictions of the operator product expansion, using one-loop
perturbative renormalization-group improved Wilson coefficients. We find that,
even on quite small lattices (m a \approx 1/6), the perturbative operator
product expansion describes that data with an error of 5-10% in a large window
2a \ltapprox x \ltapprox m^{-1}. We present a detailed discussion of the
possible systematic errors.


title:
QCD with a theta-vacuum term: a complex system with a simple complex
  action

abstract:
  We reanalyze in the first part of this paper the old question of P and CT
realization in QCD. The second part is devoted to establish general results on
the phase structure of this model in the presence of a $\theta$-vacuum term.


title: A variant approach to the overlap action

abstract:
  I describe an implementation of the overlap action, which is built from an
action which is itself an approximate overlap action. It appears to be about a
factor of 15-20 less expensive to use, than the usual overlap action with the
Wilson fermion action as its kernel. Ingredients include a fat link to suppress
coupling to dislocations and a free field action with a spectrum which
resembles an overlap; much of the gain comes from the use of eigenmodes of the
approximate action to begin the overlap calculation. As a physics example, I
compute the quark condensate in finite volume in the quenched approximation.


title: SU(2) gluon propagator on a coarse anisotropic lattice

abstract:
  We calculated the SU(2) gluon propagator in Landau gauge on an anisotropic
coarse lattice with the improved action. The standard and the improved scheme
are used to fix the gauge in this work. Even on the coarse lattice the lattice
gluon propagator can be well described by a function of the continuous
momentum. The effect of the improved gauge fixing scheme is found not to be
apparent. Based on the Marenzoni's model, the mass scale and the anomalous
dimension are extracted and can be reasonably extrapolated to the continuum
limit with the values $\alpha\sim 0.3$ and $M\sim 600MeV$. We also extract the
physical anisotropy $\xi$ from the gluon propagator due to the explicit $\xi$
dependence of the gluon propagator.


title: Lattice QCD with the Overlap Fermions at Strong Gauge Coupling (II)

abstract:
  In the previous paper we developed a strong-coupling expansion for the
lattice QCD with the overlap fermions and showed that L\"usher's "extended"
chiral symmetry is spontaneously broken in some parameter region of the overlap
fermions. In this paper, we derive a low-energy effective action of hadrons and
show that there exist quasi-Nambu-Goldstone bosons which are identified as the
pions. The pion field is a {\em nonlocal} composite field of quark and
anti-quark even at the strong-coupling limit because of the nonlocality of the
overlap fermion formalism and L\"usher's chiral symmetry. The pions become
massless in the limit of the vanishing bare-quark mass as it is desired. We
furthermore examine symmetries of the overlap fermions with the hopping
expansion and argue that there appear no other massless modes other than the
pions.


title: Topology and metastability in the lattice Skyrme model

abstract:
  We offer the Skyrme model on a lattice as an effective field theory - fully
quantized - of baryon-meson interactions at temperatures below the chiral phase
transition. We define a local topological density that involves the volumes of
tetrahedra in the target space S^3 and we make use of Coxeter's formula for the
Schlafli function to implement it. This permits us to calculate the mean-square
radius of a skyrmion in the three-dimensional lattice Skyrme model, which may
be viewed as a Ginzburg-Landau effective theory for the full quantum theory at
finite temperature. We find that, contrary to expectations, the skyrmion
shrinks as quantum and thermal fluctuations are enhanced. We ascribe this to a
large number of metastable states that become accessible as the temperature is
raised.


title: On the Non-Abelian Stokes Theorem

abstract:
  We present the non-Abelian Stokes theorem for the Wilson loop in various
forms and discuss its meaning. Its validity has been recently questioned by
Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their
criticism are based on mistakes in mathematics. Finally, we derive a variant of
our formula for the Wilson loop in lattice regularization.


title: Meson Correlators in Finite Temperature Lattice QCD

abstract:
  We analyze temporal and spatial meson correlators in quenched lattice QCD at
T>0. Below T_c we observe little change in the meson properties as compared
with T=0. Above T_c we observe new features: chiral symmetry restoration and
signals of plasma formation, but also indication of persisting mesonic
(metastable) states and different temporal and spatial masses in the mesonic
channels. This suggests a complex picture of QGP in the region 1 - 1.5 T_c.


title: Noisy Monte Carlo revisited

abstract:
  We present an exact Monte Carlo algorithm designed to sample theories where
the energy is a sum of many couplings of decreasing strength. Our algorithm,
simplified from that of L. Lin et al. hep-lat/9905033, avoids the computation
of almost all non-leading terms. We illustrate its use by simulating SU(2)
lattice gauge theory with a 5-loop action, and discuss further applications to
full QCD.


title:
Approximation of the determinant of large sparse symmetric positive
  definite matrices

abstract:
  This paper is concerned with the problem of approximating the determinant of
A for a large sparse symmetric positive definite matrix A. It is shown that an
efficient solution of this problem is obtained by using a sparse approximate
inverse of A. The method is explained and theoretical properties are discussed.
A posteriori error estimation techniques are presented. Furthermore, results of
numerical experiments are given which illustrate the performance of this new
method.


title: Testing MEM with Diquark and thermal Meson Correlation Functions

abstract:
  When applying the maximum entropy method (MEM) to the analysis of hadron
correlation functions in QCD a central issue is to understand to what extent
this method can distinguish bound states, resonances and continuum
contributions to spectral functions. We discuss these issues by analyzing meson
and diquark correlation functions at zero temperature as well as free quark
anti-quark correlators. The latter test the applicability of MEM to high
temperature QCD.


title: Super Yang-Mills on the lattice with domain wall fermions

abstract:
  The dynamical N=1, SU(2) Super Yang-Mills theory is studied on the lattice
using a new lattice fermion regulator, domain wall fermions. This formulation
even at non-zero lattice spacing does not require fine-tuning, has improved
chiral properties and can produce topological zero-mode phenomena. Numerical
simulations of the full theory on lattices with the topology of a torus
indicate the formation of a gluino condensate which is sustained at the chiral
limit. The condensate is non-zero even for small volume and small supersymmetry
breaking mass where zero mode effects due to gauge fields with fractional
topological charge appear to play a role.


title: Can nonlocal Dirac operators be topologically proper ?

abstract:
  By examining the analyticity of a sequence of topologically-proper lattice
Dirac operators, we show that they tend to a nonlocal Dirac operator. This
implies that a nonlocal lattice Dirac operator can have exact zero modes
satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero
topological charge.

categories: hep-lat cond-mat hep-ph hep-th math-ph math.MP


title:
Phase structure and critical temperature of two-flavor QCD with a
  renormalization group improved gauge action and clover improved Wilson quark
  action

abstract:
  We study the finite-temperature phase structure and the transition
temperature of QCD with two flavors of dynamical quarks on a lattice with the
temporal size $N_t=4$, using a renormalization group improved gauge action and
the Wilson quark action improved by the clover term. The region of a
parity-broken phase is identified, and the finite-temperature transition line
is located on a two-dimensional parameter space of the coupling ($\beta=6/g^2$)
and hopping parameter $K$. Near the chiral transition point, defined as the
crossing point of the critical line of the vanishing pion mass and the line of
finite-temperature transition, the system exhibits behavior well described by
the scaling exponents of the three-dimensional O(4) spin model. This indicates
a second-order chiral transition in the continuum limit. The transition
temperature in the chiral limit is estimated to be $T_c = 171(4)$ MeV.


title: The Gluon Propagator without lattice Gribov copies

abstract:
  We study the gluon propagator in quenched lattice QCD using the Laplacian
gauge which is free of lattice Gribov copies. We compare our results with those
obtained in the Landau gauge on the lattice, as well as with various
approximate solutions of the Dyson Schwinger equations. We find a finite value
$\sim (445 \rm{MeV})^{-2}$ for the renormalized zero-momentum propagator
(taking our renormalization point at 1.943 GeV), and a pole mass $\sim 640 \pm
140$ MeV.


title: Laplacian Center Vortices

abstract:
  I present a unified picture of center vortices and Abelian monopoles. Both
appear as local gauge ambiguities in the Laplacian Center Gauge. This gauge is
constructed for a general SU(N) theory. Numerical evidence is presented, for
SU(2) and SU(3), that the projected $Z_N$ theory confines with a string tension
similar to the non-Abelian one.


title: A study of center vortices in SU(2) and SU(3) gauge theories

abstract:
  We show how center vortices and Abelian monopoles both appear as local gauge
ambiguities in the Laplacian Center gauge. Numerical results, for SU(2) and
SU(3), support the view that the string tension obtained in the
center-projected theory matches the full string tension when the continuum
limit is taken.


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

abstract:
  We report on simulations of DT simplicial gravity for manifolds with the
topology of the 4-disk. We find evidence for four phases in a two-dimensional
parameter space. In two of these the boundary plays no dynamical role and the
geometries are equivalent to those observed earlier for the sphere $S^4$. In
another phase the boundary is maximal and the quantum geometry degenerates to a
one dimensional branched polymer. In contrast we provide evidence that the
fourth phase is effectively three-dimensional. We find discontinuous phase
transitions at all the phase boundaries.


title: Center Vortices and Monopoles without lattice Gribov copies

abstract:
  We construct a smooth gauge for the adjoint field which is free of
ambiguities on the lattice. In this Laplacian Center Gauge, center vortices and
monopoles appear together as local gauge defects. A numerical study of center
vortices in SU(2) and SU(3) supports equality of the $Z_N$ and SU(N) string
tensions in the continuum limit, and only then.


title:
Gauge invariant Z_2 vortex vacuum textures and the SU(2) gluon
  condensate

abstract:
  For SU(2) lattice gauge theory, a new SO(3) cooling procedure is proposed
which removes the SU(2)/Z(2) coset fields from the lattice configurations and
reveals a Z(2) vortex vacuum texture different from the P-vortex content
obtained in the maximal center gauge. Cooling can be restricted in a
renormalization group invariant way by a parameter controlling the remaining
SO(3) action density. A gauge invariant Z(2) vortex vacuum emerges
asymptotically if cooling is not restricted. This ``vortex texture'' does not
support the string tension or a finite part of it. The SU(2) action density
associated with the new Z(2) vortex texture has a smooth extrapolation to the
continuum limit. We propose an interpretation as a mass dimension four
condensate related to the gluon condensate featuring in the operator product
expansion.


title:
Incorporating Chiral Symmetry and Heavy Quark Theory in Extrapolations
  of Octet Baryon Charge Radii

abstract:
  We extrapolate lattice calculations of electric charge radii of the spin-1/2
baryon octet to the physical regime. The extrapolation procedure incorporates
chiral perturbation theory and heavy quark effective theory in the appropriate
limits. In particular, this procedure includes the non-analytic, logarithmic
terms from pion loops. The electric charge radii of the nucleons and $\Sigma^-$
obtained from the chiral extrapolations agree well with experimental data. We
make predictions for the charge radii of the remaining baryons in anticipation
of future experimental measurements.


title: The gluon condensate from gauge invariant vortex vacuum texture

abstract:
  In SU(2) lattice gauge theory, a new self-restricted cooling procedure is
developed to uncover the gauge invariant vortex vacuum texture. The emerging
vortex vacuum structure amounts to the full string tension and gives rise to a
mass dimension four condensate which is of pure vortex origin.


title:
Cost of the Generalised Hybrid Monte Carlo Algorithm for Free Field
  Theory

abstract:
  We study analytically the computational cost of the Generalised Hybrid Monte
Carlo (GHMC) algorithm for free field theory. We calculate the Metropolis
acceptance probability for leapfrog and higher-order discretisations of the
Molecular Dynamics (MD) equations of motion. We show how to calculate
autocorrelation functions of arbitrary polynomial operators, and use these to
optimise the GHMC momentum mixing angle, the trajectory length, and the
integration stepsize for the special cases of linear and quadratic operators.
We show that long trajectories are optimal for GHMC, and that standard HMC is
more efficient than algorithms based on Second Order Langevin Monte Carlo
(L2MC), sometimes known as Kramers Equation. We show that contrary to naive
expectations HMC and L2MC have the same volume dependence, but their dynamical
critical exponents are z = 1 and z = 3/2 respectively.


title:
Recent results in the center vortex model for the infrared sector of
  Yang-Mills theory

abstract:
  A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic
vortices represented by (closed) random surfaces, is presented. The model
quantitatively describes both confinement and the topological aspects of
Yang-Mills theory. Details (including an adequate list of references) can be
found in hep-lat/9912003 and hep-lat/0004013, both to appear in Nucl. Phys. B.


title:
QCD in a finite box: Numerical test studies in the three
  Leutwyler-Smilga regimes

abstract:
  The Leutwyler-Smilga prediction regarding the (ir)relevance of the global
topological charge for QCD in a finite box is subject to a test. To this end
the lattice version of a suitably chosen analogue (massive 2-flavour Schwinger
model) is analyzed in the small ($V\Sigma m \ll 1$), intermediate ($V\Sigma m
\simeq 1$) and large ($V\Sigma m \gg 1$) Leutwyler-Smilga regimes. The
predictions for the small and large regimes are confirmed and illustrated. New
results about the role of the functional determinant in all three regimes and
about the sensitivity of physical observables on the topological charge in the
intermediate regime are presented.


title:
Vortex dominance of the 0+ and 2+ glueball mass in SU(2) lattice gauge
  theory

abstract:
  The c-vortex ensembles are constructed by means of the recently proposed
cooling method which gradually removes the SU(2)/Z_2 coset fields from the
SU(2) lattice configurations and which thus reveals the Z_2 vortex vacuum
texture. Using Teper's blocking method, the screening masses of the 0+ and the
2+ glueball is calculated from these vortex ensembles and compared with the
masses obtained from full configurations. The masses of either case agree
within the achieved numerical accuracy of 10%. As a byproduct, we find that the
overlaps of the Teper operators with the glueball wavefunctions are
significantly larger in the case of the c-vortex ensembles.


title:
Discrete Symmetry Enhancement in Nonabelian Models and the Existence of
  Asymptotic Freedom

abstract:
  We study the universality between a discrete spin model with icosahedral
symmetry and the O(3) model in two dimensions. For this purpose we study
numerically the renormalized two-point functions of the spin field and the four
point coupling constant. We find that those quantities seem to have the same
continuum limits in the two models. This has far reaching consequences, because
the icosahedron model is not asymptotically free in the sense that the coupling
constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in
the short distance limit. By universality this then also applies to the O(3)
model, contrary to the predictions of perturbation theory.


title: Randomness on the Lattice

abstract:
  In this lecture we review recent lattice QCD studies of the statistical
properties of the eigenvalues of the QCD Dirac operator. We find that the
fluctuations of the smallest Dirac eigenvalues are described by chiral Random
Matrix Theories with the global symmetries of the QCD partition function.
Deviations from chiral Random Matrix Theory beyond the Thouless energy can be
understood analytically by means of partially quenched chiral perturbation
theory.


title:
Numerical Study of Gluon Propagator and Confinement Scenario in Minimal
  Coulomb Gauge

abstract:
  We present numerical results in SU(2) lattice gauge theory for the
space-space and time-time components of the gluon propagator at equal time in
the minimal Coulomb gauge. It is found that the equal-time would-be physical
3-dimensionally transverse gluon propagator $D^{tr}(\vec{k})$ vanishes at
$\vec{k} = 0$ when extrapolated to infinite lattice volume, whereas the
instantaneous color-Coulomb potential $D_{44}(\vec{k})$ is strongly enhanced at
$\vec{k} = 0$. This has a natural interpretation in a confinement scenario in
which the would-be physical gluons leave the physical spectrum while the
long-range Coulomb force confines color. Gribov's formula $D^{tr}(\vec{k}) =
(|\vec{k}|/2)[(\vec{k}^2)^2 + M^4]^{1/2}$ provides an excellent fit to our data
for the 3-dimensionally transverse equal-time gluon propagator
$D^{tr}(\vec{k})$ for relevant values of $\vec{k}$.


title: Critical Behaviour in the Dense Planar NJL Model

abstract:
  We present results of a Monte Carlo simulation of a 2+1 dimensional Nambu -
Jona-Lasinio model including diquark source terms. A diquark condensate <qq> is
measured as a function of source strength j. In the vacuum phase <qq> vanishes
linearly with j as expected, but simulations in a region with non-zero baryon
density suggest a power-law scaling and hence a critical system for all mu >
mu_c. There is no diquark condensation signalling superfluidity. Comparisons
are drawn with known results in two dimensional theories, and with the
pseudogap phase in cuprate superconductors. We also measure the dispersion
relation E(k) for fermionic excitations, and find results consistent with a
sharp Fermi surface. Any superfluid gap Delta is constrained to be much less
than the constituent quark mass scale Sigma_0.

categories: hep-lat cond-mat.supr-con hep-ph nucl-th


title:
From Monte Carlo Integration to Quantum Chromo Dynamics (an
  introduction)

abstract:
  In these lectures we provide a short introduction to the Monte Carlo
integration method and its applications. We show how the origin of ultraviolet
divergences if Field Theories is in the undefined formal product of
distributions and how one can define the Path Integral in terms of regularized
distributions in order to cancel these divergences. This technique provides the
only non perturbative regularization procedure of continuum Field Theories and,
at the same time, provides a practical method to compute correlation (Green)
functions (using Monte Carlo integration for the regularized path integrals).
We then apply these tools to formulate QCD on a lattice. Some of the examples
are accompanied by complete computer programs.


title: Quantum chaos and chiral symmetry at the QCD and QED phase transition

abstract:
  We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3)
gauge theory and in full QCD as well as in quenched U(1) theory. As a measure
of the fluctuation properties of the eigenvalues, we consider the
nearest-neighbor spacing distribution. We find that in all regions of their
phase diagrams, compact lattice gauge theories have bulk spectral correlations
given by random matrix theory, which is an indication for quantum chaos. In the
confinement phase, the low-lying Dirac spectrum of these quantum field theories
is well described by random matrix theory, exhibiting universal behavior.
Related results for gauge theories with minimal coupling are now discussed also
in the chirally symmetric phase.


title:
The Infrared behaviour of the gluon propagator in SU(2) and SU(3)
  without lattice Gribov copies

abstract:
  We present lattice results for the gluon propagator for SU(2) and SU(3) in
the Laplacian gauge which avoids lattice Gribov copies. In SU(3) we compare
with the most recent lattice calculation in Landau gauge and with various
approximate solutions of the Dyson Schwinger equations (DSE).


title:
Lattice QCD with the Overlap-Dirac Operator: Its $\Lambda$ Parameter,
  and One-Loop Renormalization of Fermionic Currents

abstract:
  We compute the ratio between the scale $\Lambda_L$ associated with a lattice
formulation of QCD using the overlap-Dirac operator, and $\Lambda_{MS-bar}$. To
this end, the one-loop relation between the lattice coupling $g_0$ and the
coupling renormalized in the MS-bar scheme is calculated, using the lattice
background field technique.
  We also compute the one-loop renormalization $Z_\Gamma$ of the two-quark
operators $\bar{\psi} \Gamma \psi$, where $\Gamma$ denotes a generic Dirac
matrix. Furthermore, we study the renormalization of quark bilinears which are
more extended and have better chiral properties.
  Finally, we present improved estimates of $Z_\Gamma$, coming from cactus
resummation and from mean field perturbation theory.


title: Lattice artefacts and the running of the coupling constant

abstract:
  We study the running of the L\"uscher-Weisz-Wolff (LWW) coupling constant in
the two dimensional O(3) nonlinear $\sigma$ model. To investigate the continuum
limit we refine the lattice spacing from the $1\over 16$ value used by LWW up
to $1\over 160$. We find that the lattice artefacts are much larger than
estimated by LWW and that most likely the coupling constant runs slower than
predicted by perturbation theory. A precise determination of the running in the
continuum limit would require a controlled ansatz of extrapolation, which, we
argue, is not presently available.


title:
Lattice hadron matrix elements with the Schroedinger functional: the
  case of the first moment of non-singlet quark density

abstract:
  We present the results of a non-perturbative determination of the pion matrix
element of the twist-2 operator corresponding to the average momentum of
non-singlet quark densities. The calculation is made within the Schroedinger
functional scheme. We report the results of simulations done with the standard
Wilson action and with the non-perturbatively improved clover action and we
show that their ratio correctly extrapolates, in the continuum limit, to a
value compatible with the residual correction factor expected from perturbation
theory.


title: Width difference in the Bs system from lattice HQET

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


title: The topological susceptibility and pion decay constant from lattice QCD

abstract:
  We study the topological susceptibility, chi, in two flavour lattice QCD. We
find clear evidence for the expected suppression of chi at small quark mass.
The estimate of the pion decay constant, f_pi = 105 +/-5 +18/-10 MeV, is
consistent with the experimental value of approximately 93 MeV. We compare chi
to the large-N_c prediction and find consistency over a large range of quark
masses.


title:
Simulation of SU(2) Dynamical Fermion at Finite Chemical Potential and
  at Finite Temperature

abstract:
  SU(2) lattice gauge theory with dynamical fermion at non-zero chemical
potential and at finite temperature is studied. We focus on the influence of
chemical potential for quark condensate and mass of pseudoscalar meson at
finite temperature.
  Hybrid Monte Carlo simulations with $N_f=8$ staggered fermions are carried
out on $12 \times 12\times 24 \times 4$ lattice. At $\beta=1.1$ and
$m_{q}=$0.05,0.07,0.1, we calculate the quark condensate and masses of
pseudoscalar meson consisting of light and heavier quarks for chemical
potential $\mu=$ 0.0,0.02,0.05,0.1,0.2.


title: Vortex configurations in SO(3) \times Z(2)

abstract:
  We study the configuration space of the Tomboulis $SO(3) \times Z(2)$
formulation with periodic boundary conditions. The dynamical variables are
constrained by the required coincidence of Z(2) and SO(3) monopoles.
Furthermore, there is an additional constraint coming from the boundary
conditions. We propose an update algorithm that satisfies the constraints and
is straightforward to implement.


title: Simulations in SO(3) \times Z(2) lattice gauge theory

abstract:
  We explore simulations on periodic lattices in the Tomboulis $SO(3) \times
Z(2)$ formulation. We measure gauge invariant vortex counters for "thin",
"thick" and "hybrid" vortex sheets in order to tag Wilson loops by the
occurance of gauge invariant vortices linking them. We also measure projection
vortex counters defined in the maximal center gauge for comparison.


title: Vortices in $SO(3)\times Z(2)$ simulations

abstract:
  We explore simulations on periodic lattices in the Tomboulis $SO(3)\times
Z(2)$ formulation. The dynamical variables are constrained. We propose an
update algorithm that satisfies the constraints and is straightforward to
implement. We show how boundary conditions put constraints on the configuration
space.


title:
Vortices and monopole distributions in $Z(2) \times SO(3)$ lattice gauge
  theory

abstract:
  We examine the occurance of Z(2) and SO(3) vorticies and monopole
distributions in the neighborhood of Wilson loops. We use the Tomboulis
formulation, equivalent to the Wilson action, in which the links are invariant
under Z(2) transformations and new plaquette variables carry the Z(2) degrees
of freedom. This gives new gauge invariant observables to help gain insight
into the area law and structure of the flux tube.


title: Exact topological density in the lattice Skyrme model

abstract:
  We propose using the Skyrme model on a lattice as an effective field theory
of meson-baryon interactions. To this end we construct a local topological
density that involves the volumes of tetrahedra in the target space S^3 and we
make use of Coxeter's formula for the Schlafli function to implement it. We
calculate the mean-square radius of a skyrmion in the three-dimensional Skyrme
model, and find some surprises.


title: The radial wavefunctions of a heavy-light meson calculated on a lattice

abstract:
  A brief review is given of attempts to understand the energies of four-quark
systems calculated on a lattice in terms of nuclear-physics-inspired many-body
techniques involving interquark potentials. Results are given for the next
stage of this study where the wavefunctions of heavy-light mesons are also
calculated on a lattice.


title: High Temperature QCD and Dimensional Reduction

abstract:
  In this talk I will first give a short discussion of some lattice results for
QCD at finite temperature. I will then describe in some detail the technique of
dimensional reduction, which in principle is a powerful technique to obtain
results on the long distance properties of the quark-gluon plasma. Finally I
will describe some new results, which test the technique in a simpler model,
namely three dimensional gauge theory.


title: Center vortices and colour confinement in lattice QCD

abstract:
  We review lattice evidence showing that center-vortex condensation is a
serious candidate for the mechanism of colour confinement in quantum
chromodynamics.


title:
Perturbative renormalization of moments of quark momentum, helicity and
  transversity distributions with overlap and Wilson fermions

abstract:
  Using overlap as well as Wilson fermions, we have computed the one-loop
renormalization factors of ten non-singlet operators which measure the third
moment of quark momentum and helicity distributions (the lowest two having been
computed in a previous paper), as well as the lowest three moments of the $g_2$
structure function and the lowest two non-trivial moments of the $h_1$
transversity structure function (plus the tensor charge). These factors are
needed to extract physical observables from Monte Carlo simulations of the
corresponding matrix elements.
  An exact chiral symmetry is maintained in our calculations with overlap
fermions, and its most important consequence here is that the operators
measuring $g_2$ do not show any of the power-divergent mixings with operators
of lower dimension which are present in the Wilson case. Many of our results
for Wilson fermions are also new; for the remaining ones, we agree with the
literature except in one case. The computations have been carried out using the
symbolic language FORM, in a general covariant gauge, which turns out also to
be useful in checking the gauge-invariance of the final results.


title:
Numerical study of the scaling properties of SU(2) lattice gauge theory
  in Palumbo non-compact regularization

abstract:
  In the framework of a non-compact lattice regularization of nonabelian gauge
theories we look, in the SU(2) case, for the scaling window through the
analysis of the ratio of two masses of hadronic states. In the two-dimensional
parameter space of the theory we find the region where the ratio is constant,
and equal to the one in the Wilson regularization. In the scaling region we
calculate the lattice spacing, finding it at least 20% larger than in the
Wilson case; therefore the simulated physical volume is larger.


title:
Renormalons on the Lattice and the OPE for the plaquette: a status
  report

abstract:
  The first ten coefficients in the perturbative expansion of the plaquette in
Lattice SU(3) are computed both on a 8^4 and on a 24^4 lattice. They are shown
to be fully consistent with the growth dictated by the first IR Renormalon and
with the expected finite size effects on top of that. As already pointed out a
few years ago, this leads to a puzzling result on the smaller lattice: when the
contribution associated with the Renormalon is subtracted from Monte Carlo
measurements of the plaquette, what is left over does not scale (as expected)
as a^4, but as a^2. While the analysis is not yet complete on the larger
lattice, the implications of such a finding is discussed.


title:
Non-perturbative results for the coefficients b_m and b_a-b_p in O(a)
  improved lattice QCD

abstract:
  We determine the improvement coefficients b_m and b_a-bp in quenched lattice
QCD for a range of beta-values, which is relevant for current large scale
simulations. At fixed beta, the results are rather sensitive to the precise
choices of parameters. We therefore impose improvement conditions at constant
renormalized parameters, and the coefficients are then obtained as smooth
functions of g_0^2. Other improvement conditions yield a different functional
dependence, but the difference between the coefficients vanishes with a rate
proportional to the lattice spacing. We verify this theoretical expectation in
a few examples and are therefore confident that O(a) improvement is achieved
for physical quantities. As a byproduct of our analysis we also obtain the
finite renormalization constant which relates the subtracted bare quark mass to
the bare PCAC mass.


title:
Light quark masses from quenched lattice QCD simulations with domain
  wall quarks

abstract:
  Values for the strange quark mass and average up/down mass have been obtained
from quenched lattice QCD simulations using the domain wall fermion action.
This discretization preserves the properties of flavor and chiral symmetry at
nonzero lattice spacing. Results are shown for two values of the lattice
spacing. The mass renormalization constant is computed nonperturbatively.


title:
Light hadronic physics using domain wall fermions in quenched lattice
  QCD

abstract:
  In the past year domain wall fermion simulations have moved from exploratory
stages to the point where systematic effects can be studied with different
gauge couplings, volumes, and lengths in the fifth dimension. Results are
presented here for the chiral condensate, the light hadron spectrum, and the
strange quark mass. We focus especially on the pseudoscalar meson mass and show
that, in small volume, the correlators used to compute it can be contaminated
to different degrees by topological zero modes. In large volume a nonlinear
extrapolation to the chiral limit, e.g. as expected from quenched chiral
perturbation theory, is needed in order to have a consistent picture of low
energy chiral symmetry breaking effects.


title: Odd-flavor Simulations by the Hybrid Monte Carlo

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


title:
Two Higgs doublet dynamics at the electroweak phase transition: a
  non-perturbative study

abstract:
  Using a three-dimensional (3d) effective field theory and non-perturbative
lattice simulations, we study the MSSM electroweak phase transition with two
dynamical Higgs doublets. We first carry out a general analysis of spontaneous
CP violation in 3d two Higgs doublet models, finding that this part of the
parameter space is well separated from that corresponding to the physical MSSM.
We then choose physical parameter values with explicit CP violation and a light
right-handed stop, and determine the strength of the phase transition. We find
a transition somewhat stronger than in 2-loop perturbation theory, leading to
the conclusion that from the point of view of the non-equilibrium constraint,
MSSM electroweak baryogenesis can be allowed even for a Higgs mass mH \approx
115 GeV. We also find that small values of the mass parameter mA (\lsim 120
GeV), which would relax the experimental constraint on mH, do not weaken the
transition noticeably for a light enough stop. Finally we determine the
properties of the phase boundary.


title:
On the continuum limit of fermionic topological charge in lattice gauge
  theory

abstract:
  It is proved that the fermionic topological charge of SU(N) lattice gauge
fields on the 4-torus, given in terms of a spectral flow of the Hermitian
Wilson--Dirac operator, or equivalently, as the index of the Overlap Dirac
operator, reduces to the continuum topological charge in the classical
continuum limit when the parameter $m_0$ is in the physical region $0<m_0<2$.


title: Comparative Benchmarks of full QCD Algorithms

abstract:
  We report performance benchmarks for several algorithms that we have used to
simulate the Schr"odinger functional with two flavors of dynamical quarks. They
include hybrid and polynomial hybrid Monte Carlo with preconditioning. An
appendix describes a method to deal with autocorrelations for nonlinear
functions of primary observables as they are met here due to reweighting.


title:
Microcanonical Simulation of Complex Actions: The Wess Zumino Witten
  Case

abstract:
  We present the main results of our microcanonical simulation of the Wess
Zumino Witten action functional. This action, being highly non-trivial and
capable of exhibiting many different phase transitions, is chosen to be
representative of general complex actions. We verify the applicability of
microcanonical simulation by successfully obtaining two of the many critical
points of the Wess Zumino Witten action. The microcanonical algorithm has the
additional advantage of exhibiting critical behaviour for a small $8\times 8$
lattice. We also briefly discuss the subtleties that, in general, arise in
simulating a complex action. Our algorithm for complex actions can be extended
to the study of
  D-branes in the Wess Zumino Witten action.


title: On the Triviality of Textbook Quantum Electrodynamics

abstract:
  By adding a small, irrelevant four fermi interaction to the action of lattice
Quantum Electrodynamics (QED), the theory can be simulated with massless quarks
in a vacuum free of lattice monopoles. This allows an ab initio high precision,
controlled study of the existence of "textbook" Quantum Electrodynamics with
several species of fermions. The lattice theory possesses a second order chiral
phase transition which we show is logarithmically trivial. The logarithms of
triviality, which modify mean field scaling laws, are pinpointed in several
observables. The result supports Landau's contention that perturbative QED
suffers from complete screening and would have a vanishing fine structure
constant in the absence of a cutoff.


title: Simulating Simplified Versions of the IKKT Matrix Model

abstract:
  We simulate a supersymmetric matrix model obtained from dimensional reduction
of 4d SU(N) super Yang-Mills theory (a 4d counter part of the IKKT model or IIB
matrix model). The eigenvalue distribution determines the space structure. The
measurement of Wilson loop correlators reveals a universal large N scaling.
Eguchi-Kawai equivalence may hold in a finite range of scale, which is also
true for the bosonic case. We finally report on simulations of a low energy
approximation of the 10d IKKT model, where we omit the phase of the Pfaffian
and look for evidence for a spontaneous Lorentz symmetry breaking.


title:
Towards the application of the Maximum Entropy Method to finite
  temperature Upsilon Spectroscopy

abstract:
  According to the Narnhofer Thirring Theorem interacting systems at finite
temperature cannot be described by particles with a sharp dispersion law. It is
therefore mandatory to develop new methods to extract particle masses at finite
temperature. The Maximum Entropy method offers a path to obtain the spectral
function of a particle correlation function directly. We have implemented the
method and tested it with zero temperature Upsilon correlation functions
obtained from an NRQCD simulation. Results for different smearing functions are
discussed.


title: Exact Chiral Symmetry with a non-perturbative cutoff

abstract:
  The main ideas behind the new ways to preserve chiral symmetries for lattice
fermions are presented. The discussion is focused on vector-like fermions, the
case relevant for lattice QCD.


title: Regulated chiral gauge theories

abstract:
  Noncompact chiral abelian gauge theories are defined on the lattice using the
overlap formalism. The main definitions are presented, the role of anomaly
cancelation is discussed, and the triviality issue in four dimensions is
explained.


title: Fermion Condensates in Two Colours Finite Density QCD at Strong Coupling

abstract:
  We study unquenched lattice SU(2) at nonzero chemical potential at strong
coupling and with eight flavours of Kogut-Susskind fermions. Introducing a
diquark source term we analyze the behaviour of different types of fermion
condensates. Using a non standard approach we can obtain results at zero
external source without extrapolations. We find strong evidences for a (high
density) second order phase transition where a diquark condensate appears. The
corresponding critical chemical potential is in good agreement with half the
pion mass.


title: P-vortices and Drama of Gribov Copies

abstract:
  We present results of the careful study of the Gribov copies problem in SU(2)
lattice gauge theory for the direct maximal center projection widely used in
confinement studies. Applying simulated annealing algorithm we demonstrate that
this problem is more severe than it was thought before. The projected (gauge
noninvariant) string tension is not in the agreement with the physical string
tension. We do not find any indications that P-vortices reproduce the full
SU(2) string tension neither in the infinite volume limit nor in the continuum
limit.


title: Real Representation in Chiral Gauge Theories on the Lattice

abstract:
  The Weyl fermion belonging to the real representation of the gauge group
provides a simple illustrative example for L\"uscher's gauge-invariant lattice
formulation of chiral gauge theories. We can explicitly construct the fermion
integration measure globally over the gauge-field configuration space in the
arbitrary topological sector; there is no global obstruction corresponding to
the Witten anomaly. It is shown that this Weyl formulation is equivalent to a
lattice formulation based on the Majorana (left--right-symmetric) fermion, in
which the fermion partition function is given by the Pfaffian with a definite
sign, up to physically irrelevant contact terms. This observation suggests a
natural relative normalization of the fermion measure in different topological
sectors for the Weyl fermion belonging to the complex representation.


title: Topological defects in lattice gauge theories

abstract:
  We present a non-perturbative formalism for measuring defect free energies
(monopole mass or vortex tension) in three-dimensional SU(2)+adjoint Higgs
models. Starting from twisted, translation invariant boundary conditions, we
perform a change of variables that allows us to express the defect free
energies in terms of 't Hooft loops. We propose that the defect free energies
can be used to distinguish between phases in this model, and also more
generally in other gauge field theories where no local order parameters exist.
In the case of monopoles, our construction can also be used in four-dimensional
pure-gauge SU(2) theory, where it gives the monopole mass in the maximally
Abelian gauge without the need of actually fixing the gauge in the simulation.
Moreover, the expression is manifestly independent of the choice of the Abelian
projection as long as it is compatible with the classical 't Hooft-Polyakov
solution.


title: Order a improved renormalization constants

abstract:
  We present non-perturbative results for the constants needed for on-shell
$O(a)$ improvement of bilinear operators composed of Wilson fermions. We work
at $\beta=6.0$ and 6.2 in the quenched approximation. The calculation is done
by imposing axial and vector Ward identities on correlators similar to those
used in standard hadron mass calculations. A crucial feature of the calculation
is the use of non-degenerate quarks. We also obtain results for the constants
needed for off-shell $O(a)$ improvement of bilinears, and for the scale and
scheme independent renormalization constants, (Z_A), (Z_V) and (Z_S/Z_P).
Several of the constants are determined using a variety of different Ward
identities, and we compare their relative efficacies. In this way, we find a
method for calculating $c_V$ that gives smaller errors than that used
previously. Wherever possible, we compare our results with those of the ALPHA
collaboration (who use the Schr\"odinger functional) and with 1-loop
tadpole-improved perturbation theory.


title: Numerical evidence for monopoles in 3-dimensional Yang-Mills theory

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


title: The Mass of the b Quark from Lattice NRQCD

abstract:
  We present results for the mass of the $b$ quark in the $\bar{MS}$ scheme
obtained by calculating the binding energy of the $B$ meson in the static
limit. The self energy of a static quark, $E_0^\infty$ needed for this purpose,
is now known to $O(\alpha^3)$ in the quenched approximation. We find a {\it
preliminary} value of $\bar{m_b}(\bar{m_b})=4.34(7)$ GeV at $n_f=0$. The error
is dominated by the remaining uncertainty in $E_0^\infty$. In addition, using
$E_0^\infty$ at $O(\alpha^2)$, we estimate that the quark mass is reduced by
approximately 70 MeV when two flavours of dynamical quarks are introduced.


title: Heavy-light meson spectrum with and without NRQCD

abstract:
  Results for the spectrum of S and P-wave charmed mesons are obtained in the
quenched approximation from a tadpole-improved anisotropic gauge field action
and a D234 quark action. This is compared to the spectrum obtained from an
NRQCD charm quark and a D234 light antiquark. NRQCD results for bottom mesons
are also discussed.


title: Wigner Functions on a Lattice

abstract:
  The Wigner functions on the one dimensional lattice are studied. Contrary to
the previous claim in literature, Wigner functions exist on the lattice with
any number of sites, whether it is even or odd. There are infinitely many
solutions satisfying the conditions which reasonable Wigner functions should
respect. After presenting a heuristic method to obtain Wigner functions, we
give the general form of the solutions. Quantum mechanical expectation values
in terms of Wigner functions are also discussed.


title: Theories with global gauge anomalies on the lattice

abstract:
  A global anomaly in a chiral gauge theory manifests itself in different ways
in the continuum and on the lattice. In the continuum case, functional
integration of the fermion determinant over the whole space of gauge fields
yields zero. In the case of the lattice, it is not even possible to define a
fermion measure over the whole space of gauge configurations. However, this is
not necessary, and as in the continuum, a reduced functional integral is
sufficient for the existence of the theory.


title:
A numerical study of Goldstone-mode effects and scaling functions of the
  three-dimensional O(2) model

abstract:
  We investigate numerically the three-dimensional O(2) model on 8^3-160^3
lattices as a function of the magnetic field H. In the low-temperature phase we
verify the H-dependence of the magnetization M induced by the Goldstone modes
and determine M in the thermodynamic limit on the coexistence line both by
extrapolation and by chiral perturbation theory. We compute two critical
amplitudes from the scaling behaviours on the coexistence line and on the
critical line. In both cases we find negative corrections to scaling. With
additional high temperature data we calculate the scaling function and show
that it has a smaller slope than that of the O(4) model. For future tests of
QCD lattice data we study as well finite-size-scaling functions.


title: Flavour singlet pseudoscalar masses in N_f = 2 QCD

abstract:
  We perform a lattice mass analysis in the flavour singlet pseudoscalar
channel on the SESAM and TXL full QCD vacuum configurations, with 2 active
flavours of dynamical Wilson fermions at beta = 5.6. At our inverse lattice
spacing, a^-1 = 2.3 GeV, we retrieve by a chiral extrapolation to the physical
light quark masses the value m_eta' = 3.7(+8)(-4) m_pi. A crude extrapolation
from (N_f = 3) phenomenology would suggest m_eta' \approx 5.1 m_pi for N_f = 2
QCD. we verify that the mass gap between the singlet state eta' and the pi
flavour triplt state is due to gauge configurations with non-trivial topology.


title: Noisy Monte Carlo Algorithm

abstract:
  We present an exact Monte Carlo algorithm designed to sample theories where
the energy is a sum of many couplings of decreasing strength. The algorithm
avoids the computation of almost all non-leading terms. Its use is illustrated
by simulating SU(2) lattice gauge theory with a 5-loop improved action. A new
approach for dynamical fermion simulations is proposed.


title: Scalar and Tensor Glueballs on Asymmetric Coarse Lattices

abstract:
  Scalar and tensor glueball spectrum is studied using an improved gluonic
action on asymmetric lattices in the pure SU(3) gauge theory. The smallest
spatial lattice spacing is about 0.08fm which makes the extrapolation to the
continuum limit more reliable. In particular, attention is paid to the scalar
glueball mass which is known to have problems in the extrapolation. Converting
our lattice results to physical units using the scale set by the static quark
potential, we obtain the following results for the glueball masses:
$M_G(0^{++})=1730(90)MeV$ for the scalar glueball mass and
$M_G(2^{++})=2400(95)MeV$ for the tensor glueball.


title: Testing imaginary vs. real chemical potential in finite-temperature QCD

abstract:
  One suggestion for determining the properties of QCD at finite temperatures
and densities is to carry out lattice simulations with an imaginary chemical
potential whereby no sign problem arises, and to convert the results to real
physical observables only afterwards. We test the practical feasibility of such
an approach for a particular class of physical observables, spatial correlation
lengths in the quark-gluon plasma phase. Simulations with imaginary chemical
potential followed by analytic continuation are compared with simulations with
real chemical potential, which are possible by using a dimensionally reduced
effective action for hot QCD. We find that for imaginary chemical potential the
system undergoes a phase transition at |mu/T| \approx pi/3, and thus
observables are analytic only in a limited range. However, utilising this
range, relevant information can be obtained for the real chemical potential
case.