title: Some remarks on Abelian dominance

abstract:
  We use a renormalisation group based smoothing to address two questions
related to Abelian dominance. Smoothing enables us to extract the Abelian
heavy-quark potential from time-like Wilson loops on Polyakov gauge projected
configurations. We obtained a very small string tension which is inconsistent
with the string tension extracted from Polyakov loop correlators. This shows
that the Polyakov gauge projected Abelian configurations do not have a
consistent physical meaning. We also apply the smoothing on SU(2)
configurations to test how sensitive Abelian dominance in the maximal Abelian
gauge is to the short distance fluctuations. We find that on smoothed SU(2)
configurations the Abelian string tension was about 30% smaller than the SU(2)
string tension which was unaffected by smoothing. This suggests that the
approximate Abelian dominance found with the Wilson action is probably an
accident and it has no fundamental physical relevance.


title: Update on the hadron spectrum with two flavors of staggered quarks

abstract:
  We present an update on the MILC Collaboration's light hadron spectrum
calculation with two flavors of dynamical, staggered quarks. We present
extrapolations of the nucleon to rho mass ratio to the continuum limit for
fixed values of the pi to rho mass ratio including the physical one.


title: A Study of PCAC for the Nonperturbative Improvement of the Wilson Action

abstract:
  We present an exploratory study for the nonperturbative determination of the
coefficient of the ${\cal O}(a)$ improvement term to the Wilson action,
$c_{SW}$. Following the work by L\"{u}scher et al., we impose the PCAC relation
as a nonperturbative improvement condition on $c_{SW}$, without, however, using
the Schr\"{o}dinger functional in our calculation.


title: Towards N=1 Super-Yang-Mills on the Lattice

abstract:
  We consider the lattice regularization of N=1 supersymmetric Yang--Mills
theory with Wilson fermions. This formulation breaks supersymmetry at any
finite lattice spacing; we discuss how Ward identities can be used to define a
supersymmetric continuum limit, which coincides with the point where the gluino
becomes massless. As a first step towards the understanding of the zero
gluino-mass limit, we present results on the quenched low-lying spectrum of
SU(2) N=1 Super-Yang--Mills, at $\beta=2.6$ on a $V=16^3 \times 32$ lattice, in
the OZI approximation. Our results, in spite of the quenched and OZI
approximations, are in remarkable agreement with theoretical predictions in the
supersymmetric theory, for the states with masses which are not expected to get
a large contribution from fermion loops.


title:
Chiral Symmetry Breaking on the Lattice: a Study of the Strongly Coupled
  Lattice Schwinger Model

abstract:
  We revisit the strong coupling limit of the Schwinger model on the lattice
using staggered fermions and the hamiltonian approach to lattice gauge
theories. Although staggered fermions have no continuous chiral symmetry, they
posses a discrete axial invari ance which forbids fermion mass and which must
be broken in order for the lattice Schwinger model to exhibit the features of
the spectrum of the continuum theory. We show that this discrete symmetry is
indeed broken spontaneously in the strong coupling li mit. Expanding around a
gauge invariant ground state and carefully considering the normal ordering of
the charge operator, we derive an improved strong coupling expansion and
compute the masses of the low lying bosonic excitations as well as the chiral
co ndensate of the model. We find very good agreement between our lattice
calculations and known continuum values for these quantities already in the
fourth order of strong coupling perturbation theory. We also find the exact
ground state of the antiferromag netic Ising spin chain with long range Coulomb
interaction, which determines the nature of the ground state in the strong
coupling limit.


title: Monte Carlo Simulations with Complex-Valued Measure

abstract:
  A simulation method based on the RG blocking is shown to yield statistical
errors smaller than that of the crude MC using absolute values of the original
measures. The new method is particularly suitable to apply to the sign problem
of indefinite or complex-valued measures. We demonstrate the many advantages of
this method in the simulation of 2D Ising model with complex-valued
temperature.


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

abstract:
  The magnetic vortices which arise in SU(2) lattice gauge theory in center
projection are visualized for a given time slice. We establish that the number
of vortices piercing a given 2-dimensional sheet is a renormalization group
invariant and therefore physical quantity. We find that roughly 2 vortices
pierce an area of 1 fm^2.


title: A study of the quenched bc mass spectrum at beta=6.2

abstract:
  We present an analysis of the mass spectrum of heavy quarkonia with
non-degenerate quark masses. The heavier (bottom) valence quark is treated in a
non-relativistic fashion and the other (charm) is a relativistic Wilson-like
quark using the improved SW action. Such states provide and interesting probe
between the relativistic B meson states and the non-relativistic bottomonium
states.


title: Correlation functions and critical behaviour on fluctuating geometries

abstract:
  We study the two-point correlation function in the model of branched polymers
and its relation to the critical behaviour of the model. We show that the
correlation function has a universal scaling form in the generic phase with the
only scale given by the size of the polymer. We show that the origin of the
singularity of the free energy at the critical point is different from that in
the standard statistical models. The transition is related to the change of the
dimensionality of the system.


title:
Non-perturbative renormalization constants on the lattice from flavour
  non-singlet Ward identities

abstract:
  By imposing axial and vector Ward identities for flavour-non-singlet
currents, we estimate in the quenched approximation the non-perturbative values
of combinations of improvement coefficients, which appear in the expansion
around the massless case of the renormalization constants of axial,
pseudoscalar, vector, scalar non-singlet currents and of the renormalized mass.
  These coefficients are relevant for the completion of the improvement
programme to O(a) of such operators.
  The simulations are performed with a clover Wilson action non-perturbatively
improved.


title: Perturbative Matching of the NRQCD Heavy-Light Axial Current

abstract:
  A one-loop matching calculation between Lattice NRQCD and full QCD for the
heavy-light axial current is described and the effects on f_B are discussed.


title: Kaon B parameter from quenched Lattice QCD

abstract:
  We present results of a large-scale simulation for the Kaon B parameter $B_K$
in quenched lattice QCD with the Kogut-Susskind quark action. Calculating $B_K$
at 1% statistical accuracy for seven values of lattice spacing in the range
$a\approx 0.24-0.04$ fm on lattices up to $56^3\times 96$, we verify a
quadratic $a$ dependence of $B_K$ theoretically predicted. Strong indications
are found that, with our level of accuracy, $\alpha_{\bar{MS}}(1/a)^2$ terms
arising from our one-loop matching procedure have to be included in the
continuum extrapolation. We present $B_K$(NDR, 2 GeV)=0.628(42) as our final
value, as obtained by a fit including the $\alpha_{\bar{MS}}(1/a)^2$ term.


title:
High-precision computation of two-loop Feynman diagrams with Wilson
  fermions

abstract:
  We apply the coordinate-space method by Luescher and Weisz to the computation
of two-loop diagrams in full QCD with Wilson fermions on the lattice. The
essential ingredient is the high-precision determination of mixed
fermionic-bosonic propagators.


title: Dynamical Quark Effects in QCD

abstract:
  We discuss latest results of lattice QCD simulations with dynamical fermions.
Special emphasis is paid to the subjects of the static quark potential, the
light hadron spectrum, $\Upsilon$ spectrum, and the pion-nucleon-sigma term.


title:
Block Spin Effective Action for 4d SU(2) Finite Temperature Lattice
  Gauge Theory

abstract:
  The Svetitsky-Yaffe conjecture for finite temperature 4d SU(2) lattice gauge
theory is confirmed by observing matching of block spin effective actions of
the gauge model with those of the 3d Ising model. The effective action for the
gauge model is defined by blocking the signs of the Polyakov loops with the
majority rule. To compute it numerically, we apply a variant of the IMCRG
method of Gupta and Cordery.


title: 4d Simplicial Quantum Gravity Interacting with Gauge Matter Fields

abstract:
  The effect of coupling non-compact $U(1)$ gauge fields to four dimensional
simplicial quantum gravity is studied using strong coupling expansions and
Monte Carlo simulations. For one gauge field the back-reaction of the matter on
the geometry is weak. This changes, however, as more matter fields are
introduced. For more than two gauge fields the degeneracy of random manifolds
into branched polymers does not occur, and the branched polymer phase seems to
be replaced by a new phase with a negative string susceptibility exponent
$\gamma$ and fractal dimension $d_H \approx 4$.


title: Instanton Effects in Hadron Spectroscopy in SU(2) (Lattice) Gauge Theory

abstract:
  We describe quenched spectroscopy in SU(2) gauge theory using smoothed gauge
field configurations. We investigate the properties of quarks moving in
instanton background field configurations, where the sizes and locations of the
instantons are taken from simulations of the full gauge theory. By themselves,
these multi-instanton configurations do not confine quarks, but they induce
chiral symmetry breaking.


title: Surface width of the Solid-On-Solid models

abstract:
  The low-temperature series for the surface width of the Absolute value
Solid-On-Solid model and the Discrete Gaussian model both on the square lattice
and on the triangular lattice are generated to high orders using the improved
finite-lattice method. The series are analyzed to give the critical points of
the roughening phase transition for each model.


title: Lattice Calculations of Semileptonic Form Factors

abstract:
  We review the results of lattice QCD calculations of form factors for
semileptonic decays of D and B mesons. We also mention results for semileptonic
decays of b baryons and the rare radiative decay B to K* gamma.


title: Numerical Computations in the Worldsheet Formulation

abstract:
  The worldsheet formulation of lattice gauge theories has two appealing
features: the gauge non-redundancy and the geometrical transparency. Both
properties are profitable in order to perform numerical computations. In the
case of dynamical fermions this description offers additional advantages. For
instance, it does not suffer from the species doubling problem and it involves
fewer degrees of freedom.


title:
The Worldsheet Formulation as an Alternative Method for Simulating
  Dynamical Fermions

abstract:
  The recently proposed worldsheet formulation of lattice fermions is tested
for the first time carrying out a simulation for the simplest model: the
one-flavor, strictly massless lattice Schwinger model. A main advantage of this
alternative method for simulating dynamical fermions consists in its economy:
it involves many fewer degrees of freedom than the ordinary Kogut-Susskind
formulation. The known continuum limit is reproduced by the method for
relatively small lattices.


title: Heavy Hybrids from NRQCD

abstract:
  We present a quenched lattice calculation for the lowest lying $b \bar b
g$-hybrid states in the framework of NRQCD using the leading order Hamiltonian
up to ${\cal O}(mv^2)$. We demonstrate the existence of a nearly degenerate
rotational band of states with an excitation energy approximately 1.6 GeV above
the $\Upsilon$ ground state. This lies around the $B \bar B_J^*$-threshold but
well above the $B \bar B$-threshold. Therefore a heavy hybrid signal may well
be detected if the centre-of-mass energy in B-factories is raised a few hundred
MeV to coincide with other resonances above the 4S state. Our prediction is
consistent with most phenomenological models and lattice calculations carried
out in the static limit.


title: Resolving Exceptional Configurations

abstract:
  In lattice QCD with Wilson fermions, exceptional configurations arise in the
quenched approximation at small quark mass. The origin of these large
previously uncontrolled lattice artifacts is identified. A simple well-defined
procedure (MQA) is presented which removes the artifacts while preserving the
correct continuum limit.


title:
Monte-carlo renormalization group study of gauged RP(2) spin models in
  two dimensions

abstract:
  The 2D RP(2) gauge model is studied using the Monte-Carlo Renormalization
Group. We confirm the first-order transition reported by Solomon et al. (PL
112B, (1982)) ending in a critical point associated with vorticity. We find
evidence for a new renormalized trajectory which is responsible for a
cross-over from the vortex dominated regime to the O(3) regime as the coupling
is reduced. Near to the cross-over region a good signal for scaling will be
observed in RP(2) but this is illusory and is due to the proximity of the new
renormalized trajectory. We suggest that this is the origin of the
`pseudo'-scaling observed Hasenbusch and Horgan (PR D53, (1996)). We find that
the continuum limit of RP(2) is controlled by the O(3) fixed point. It is
unclear whether the continuum limit of the new renormalized trajectory can be
taken at the observed critical point.


title: Applications of the Eigenmodes of the Staggered Dirac Operator

abstract:
  We have constructed the lowest few eigenvectors of the staggered Dirac
operator on SU(3) gauge configurations, both quenched and dynamical. We use
these modes to study the topological charge and to construct approximate
hadronic correlators.


title: f_B and the Heavy-light Spectrum from NRQCD

abstract:
  The present status of lattice calculations of the B spectrum and f_B, using
NRQCD for the b quark, is discussed.


title: Heavy quarks on the lattice: status and perspectives

abstract:
  The lattice method for the calculation of weak decay amplitudes of heavy
quark systems is introduced. Results for leptonic and semi-leptonic decays of
heavy mesons and $B-\bar{B}$ mixing are reviewed.


title: Vector like gauge theories with almost massless fermions on the lattice

abstract:
  A truncation of the overlap (domain wall fermions) is studied and a criterion
for reliability of the approximation is obtained by comparison to the exact
overlap formula describing massless quarks. We also present a truncated version
of regularized, pure gauge, supersymmetric models. The mechanism for generating
almost masslessness is shown to be a generalized see-saw which can also be
viewed as a version of Froggatt-Nielsen's method for obtaining natural large
mass hierarchies. Viewed in this way the mechanism preserving the mass
hierarchy naturally avoids preserving even approximately axial U(1). The new
insights into the source of the mass hierarchy suggest ways to increase the
efficiency of numerical simulations of QCD employing the truncated overlap.


title: B-parameters of 4-fermion operators from lattice QCD

abstract:
  This talk summarizes the status of the calculations of $B_K$, $B_7$, $B_8$,
and $B_s$, done in collaboration with T. Bhattacharya, G. Kilcup, and S.
Sharpe. Results for staggered, Wilson, and Clover fermions are presented.


title: SU(3) surface tension from the lattice with the fixed point action

abstract:
  The surface tension at the deconfinement transition of SU(3) is determined
with a parametrized version of the fixed point action of a renormalization
group transformation on lattices with temporal extent $N_\tau=3$ and 4 and
spatial extent $N_\sigma/N_\tau=3$ and 4. A considerable cut-off dependence can
be seen in comparison with earlier determinations from tree level Symanzik and
tadpole improved actions.


title:
Perturbative renormalization group, exact results and high temperature
  series to order 21 for the N-vector spin models on the square lattice

abstract:
  High temperature expansions for the susceptibility and the second correlation
moment of the classical N-vector model (also known as the O(N) symmetric
Heisenberg classical spin model or the as the lattice O(N) nonlinear sigma
model) on the square lattice are extended from order beta^{14} to beta^{21} for
arbitrary N. For the second field derivative of the susceptibility the series
expansion is extended from order beta^{14} to beta^{17}. For -2 < N < 2, a
numerical analysis of the series is performed in order to compare the critical
exponents gamma(N), nu(N) and Delta(N) to exact (though nonrigorous) formulas
and to compute the "dimensionless four point coupling constant" g_r(N). For N >
2, we present a study of the analiticity properties of chi, xi etc. in the
complex beta-plane and describe a method to estimate the parameters which
characterize their low-temperature behaviors. We compare our series estimates
to the predictions of the perturbative renormalization group theory, to exact
(but nonrigorous or conjectured) formulas and to the results of the 1/N
expansion, always finding a good agreement.


title: Nonlocal lattice fermion models on the 2d torus

abstract:
  Abelian fermion models described by the SLAC action are considered on a
finite 2d lattice. It is shown that modification of these models by introducing
additional Pauli - Villars regularization supresses nonlocal effects and
provides agreement with the continuum results in vectorial U(1) models. In the
case of chiral fermions the phase of the determinant differs from the continuum
one.


title: A Wilson-Yukawa model with a chiral spectrum in 2D

abstract:
  We summarize our recent study of the fermion spectrum in a fermion-scalar 2D
model with a chiral $U(1)_L \times U(1)_R$ global symmetry. This model is
obtained from a two-cutoff lattice formulation of a 2D U(1) chiral gauge
theory, in the limit of zero gauge coupling. The massless fermion spectrum
found deep in the vortex phase is undoubled and chiral.


title: Advances in the Determination of Quark Masses

abstract:
  Significant progress has been made in the determination of the light quark
masses, using both lattice QCD and sum rule methods, in the last year. We
discuss the different methods and review the status of current results.
Finally, we review the calculations of bottom and charm quark masses.


title: Improved actions for the two-dimensional sigma-model

abstract:
  For the O(N) sigma-model we studied the improvement program for actions with
two- and four-spin interactions. An interesting example is an action which is
reflection-positive, on-shell improved, and has all the coupling defined on an
elementary plaquette. We show the large N solution and preliminary Monte Carlo
results for N=3.


title: Heavy light mesons at a larger lattice spacing

abstract:
  We present results on the spectrum of B and D mesons including radial
excitations and discuss the pseudoscalar decay constant. The results are
obtained at beta=5.7 in the quenched approximation using NRQCD for the heavy
quark. To study scaling violations we also compare to results obtained at
beta=6.0.


title: Topology of Boundary Surfaces in 3D Simplicial Gravity

abstract:
  A model of simplicial quantum gravity in three dimensions(3D) was
investigated numerically based on the technique of dynamical triangulation
(DT). We are concerned with the genus of surfaces appearing on boundaries
(i.e., sections) of a 3D DT manifold with $S^{3}$ topology. Evidence of a
scaling behavior of the genus distributions of boundary surfaces has been
found.


title: Chaotic behavior of confining lattice gauge field configurations

abstract:
  We analyze the leading Lyapunov exponents of SU(2) Yang-Mills field
configurations on the lattice which are initialized by quantum Monte Carlo
simulations.
  We find that configurations in the strong coupling phase at finite
temperature are substantially more chaotic than in deconfinement.


title: Accurate Scale Determinations for the Wilson Gauge Action

abstract:
  Accurate determinations of the physical scale of a lattice action are
required to check scaling and take the continuum limit. We present a high
statistics study of the static potential for the SU(3) Wilson gauge action on
coarse lattices ($5.54 \leq \beta \leq 6.0$). Using an improved analysis
procedure we determine the string tension and the Sommer scale $r_0$ (and
related quantities) to 1% accuracy, including all systematic errors. Combining
our results with earlier ones on finer lattices, we present parameterizations
of these quantities that should be accurate to about 1% for $5.6 \leq \beta
\leq 6.5$. We estimate the $\La$-parameter of quenched QCD to be $\La_\MSb =
247(16)$ MeV.


title: One loop calculation in lattice QCD with domain-wall quarks

abstract:
  One loop corrections to the domain-wall quark propagator are calculated in
massless QCD. It is shown that no additative counter term to the current quark
mass is generated in this theory, and the wave function renormalization factor
of the massless quark is explicitly evaluated. We also show that an analysis
with a simple mean-field approximation can explain properties of the massless
quark in numerical simulations of QCD with domain-wall quarks.


title: Perturbative renormalization parameters for heavy quarks

abstract:
  We study the heavy quark mass dependence of the perturbative renormalization
factors for the heavy-light currents involving Wilson, Clover, and NRQCD heavy
quarks. We find that the one-loop Z-factor for the axial-vector current depends
significantly on the heavy quark mass commonly for all actions we study, while
that for the vector current has smaller dependence.


title: The Eta-prime Meson with Staggered Fermions

abstract:
  We have computed the eta-prime pseudoscalar octet mass splitting using
staggered fermions on both dynamical and quenched gauge configurations. We have
used Wuppertal smeared operators to reduce excited state contributions. We
compare our results with the theoretical forms predicted by partially quenched
chiral perturbation theory in the lowest order. Using lattice volumes of size
16^3 x 32 with a^{-1}=2GeV we obtain results consistent with the physical
eta-prime mass. We also demonstrate that the flavor singlet piece of the
eta-prime mass comes from zero modes of the Dirac operator.


title:
Local bilinear operators on the lattice and their perturbative
  renormalisation including O(a) effects

abstract:
  Some basic concepts are discussed to derive renormalisation factors of local
lattice operators relevant to deep inelastic structure functions and to other
measurable quantities. These $Z$ factors can be used to relate matrix elements
measured by lattice techniques to their continuum counterparts. We discuss the
$O(a)$ improvement of point and one-link lattice quark operators. Suitable
bases of improved operators are derived. Tadpole improvement is applied to get
more reliable perturbative results.


title:
Two-Dimensional Dynamical Triangulation using the Grand-canonical
  Ensemble

abstract:
  The string susceptibility exponents of dynamically triangulated two
dimensional surfaces with sphere and torus topology were calculated using the
grand-canonical Monte Carlo method. We also simulated the model coupled to
d-Ising spins (d=1,2,3,5).


title: Vortices and confinement at weak coupling

abstract:
  We discuss the physical picture of thick vortices as the mechanism
responsible for confinement at arbitrarily weak coupling in SU(2) gauge theory.
By introducing appropriate variables on the lattice we distinguish between
thin, thick and `hybrid' vortices, the latter involving Z(2) monopole loop
boundaries. We present numerical lattice simulation results that demonstrate
that the full SU(2) string tension at weak coupling arises from the presence of
vortices linked to the Wilson loop. Conversely, excluding linked vortices
eliminates the confining potential. The numerical results are stable under
alternate choice of lattice action as well as a smoothing procedure which
removes short distance fluctuations while preserving long distance physics.


title: A study of $O(1/m_{Q}^{2})$ corrections for $f_{B}$ with lattice NRQCD

abstract:
  We investigate higher order effects in the nonrelativistic expansion of
lattice QCD on the heavy-light meson decay constants and some other quantities
in order to understand the truncation error of NRQCD. While our numerical
results have large $O(a)$ and $O(\alpha_s)$ errors due to the use of Wilson
light quark action and the tree-level matching, we find that the truncation
error of higher order relativistic corrections are adequately small around the
mass of the $b$ quark. We also present a perturbatively matched results through
1-loop level without operator mixing effects.


title: Physics from the lattice: glueballs in QCD; topology; SU(N) for all N

abstract:
  Lectures given at the Isaac Newton Institute, NATO-ASI School on
"Confinement, Duality and Non-Perturbative Aspects of QCD", 23 June - 4 July,
1997.


title: $K^{+}\to\pi^{+}\pi^{0}$ Decay Amplitude in Quenched Lattice QCD

abstract:
  A new study is reported of a lattice QCD calculation of the $K^+\to\pi^+
\pi^0 $ decay amplitude with the Wilson quark action in the quenched
approximation at $\beta=6.1$. The amplitude is extracted from the $K\to\pi\pi$
Green function, and a conversion to the continuum value is made employing a
recent one-loop calculation of chiral perturbation theory. The result is
consistent with the experimental value if extrapolated to the chiral limit.


title: Light quark spectrum with improved gauge and fermion actions

abstract:
  We report on a study of the light quark spectrum using an improved gauge
action and both Kogut-Susskind and Naik quark actions. We have studied six
different lattice spacings, corresponding to plaquette couplings ranging from
6.8 to 7.9, with five to six quark masses per coupling. We compare the two
quark actions in terms of the spectrum and restoration of flavor symmetry. We
also compare these results with those from the conventional action.


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

abstract:
  We present a detailed description of the method and results of our
calculation of the kaon B parameter using the Wilson quark action in quenched
QCD at $\beta=5.9-6.5$. The mixing problem of the $\Delta s=2$ four-quark
operators is solved non-perturbatively with full use of chiral Ward identities.
We find $B_K(NDR, 2 GeV)=0.562(64)$ in the continuum limit, which agrees with
the value obtained with the Kogut-Susskind quark action.


title:
Nucleon Spin Structures from Lattice QCD: Flavor Singlet Axial and
  Tensor Charges

abstract:
  The flavor singlet axial and tensor charges of the nucleon are calculated in
lattice QCD. We find $\Delta\Sigma=\Delta u+\Delta d+\Delta
s=+0.638(54)-0.347(46)-0.109(30) = +0.18(10)$ for the axial charge and
$\delta\Sigma=\delta u+\delta d+\delta s=+0.839(60)-0.231(55)-0.046(34) =
+0.562(88)$ for the tensor charge. The result for the axial charge shows
reasonable agreement with the experiment and that for the tensor charge is the
first prediction from lattice QCD before experimental measurements.


title:
The Light Quark Masses with the Wilson Quark Action using Chiral Ward
  Identities

abstract:
  We present results for the light quark masses for the Wilson quark action
obtained with the PCAC relation for the one-link extended axial vector current
in quenched QCD at $\beta=5.9-6.5$. This method leads to a remarkable
improvement of scaling behavior of the light quark masses compared to the
conventional method. We obtain ${\bar m}_l=3.87(37)$MeV for the averaged up and
down quark mass and ${\bar m}_s=97(9)$MeV for the strange quark mass in the
${\barMS}$ scheme at $\mu=2$GeV.


title: Light Hadron Spectroscopy

abstract:
  Recent developments in calculations of the light hadron spectrum are
reviewed. Particular emphasis is placed on discussion of to what extent the
quenched spectrum agrees with experiment. Recent progress, both for quenched
and full QCD, in reducing scaling violation with the use of improved actions is
presented.


title: The Geometry of the Elongated Phase in 4-D Simplicial Quantum Gravity

abstract:
  We discuss the elongated phase of 4D simplicial quantum gravity by exploiting
recent analytical results. In particular using Walkup's theorem we prove that
the dominating configurations in the elongated phase are tree-like structures
called "stacked spheres". Such configurations can be mapped into branched
polymers and baby universes arguments are used in order to analyse the critical
behaviour of theory in the weak coupling regime.


title: A New Approach of Fermion Field on Lattice

abstract:
  A new approach to formulate the fermion field on lattice is introduced by
proposing a new Dirac operator on lattice.This approach can eliminate the
Fermion doubling problem, preserve the chiral symmetry and get the same
dispersion relation for both Fermion and Boson fields.Then the Weinberg-Salam
model on lattice may be formulated in this approach.


title: The eta-prime propagator in quenched QCD

abstract:
  The calculation of the eta-prime hairpin diagram is carried out in the
modified quenched approximation (MQA) in which the lattice artifact which
causes exceptional configurations is removed by shifting observed poles at
kappa<kappa_c in the quark propagators to the critical value of hop ping
parameter. By this method, the eta-prime propagator can be accurately
calculated even for very light quark mass. A determination of the topological
susceptibility for quenched QCD is also obtained, using the fermionic method of
Smit and Vink to calculate winding numbers.


title: Heavy quark mass dependence of semileptonic form factors for B decays

abstract:
  We present our study of the dependence of the heavy-to-light semileptonic B
decay form factors on the heavy-light meson mass $M_{PS}$. Simulations are made
over a range of the heavy quark mass covering both the charm and bottom quarks
using the $O(a)$-improved clover action at $\beta=5.9$ on a $16^3\times 40$ and
$24^3\times 64$ lattice. We find that a weak dependence of form factors on
$M_{PS}$ observed in previous studies in the region of charm quark persists up
to the region of$b$ quark. The soft pion relation $f^0(q^2_{max})=f_B/f_\pi$ is
examined and found to be largely violated.


title: Gauge-invariant scalar and field strength correlators in 3d

abstract:
  Gauge-invariant non-local scalar and field strength operators have been
argued to have significance, e.g., as a way to determine the behaviour of the
screened static potential at large distances, as order parameters for
confinement, as input parameters in models of confinement, and as
gauge-invariant definitions of light constituent masses in bound state systems.
We measure such "correlators" in the 3d pure SU(2) and SU(2)+Higgs models on
the lattice. We extract the corresponding mass parameters and discuss their
scaling and physical interpretation. We find that the finite part of the MS-bar
scheme mass measured from the field strength correlator is large, more than
half the glueball mass. We also determine the non-perturbative contribution to
the Debye mass in the 4d finite T SU(2) gauge theory with a method due to
Arnold and Yaffe, finding $\delta m_D\approx 1.06(4)g^2T$.


title: Nonperturbatively Improved Hadron Spectroscopy Near the Continuum Limit

abstract:
  We report the results of our quenched lattice simulations of the Wilson
action with a nonperturbatively determined clover term at beta=6.2 and compare
them with those of the standard Wilson action at the same beta value.


title:
Numerical Study of the Fundamental Modular Region in the Minimal Landau
  Gauge

abstract:
  We study numerically the so-called fundamental modular region Lambda, a
region free of Gribov copies, in the minimal Landau gauge for pure SU(2)
lattice gauge theory. To this end we evaluate the influence of Gribov copies on
several quantities --- such as the smallest eigenvalue of the Faddeev-Popov
matrix, the third and the fourth derivatives of the minimizing function, and
the so-called horizon function --- which are used to characterize the region
Lambda. Simulations are done at four different values of the coupling: beta =
0, 0.8, 1.6, 2.7, and for volumes up to 16^4. We find that typical (thermalized
and gauge-fixed) configurations, including those belonging to the region
Lambda, lie very close to the Gribov horizon $\partial \Omega$, and are
characterized, in the limit of large lattice volume, by a negative-definite
horizon tensor.


title: Topology in QCD

abstract:
  Topology on the lattice is reviewed. In quenched QCD topological
susceptibility chi is fully understood. The Witten-Veneziano mechanism for the
eta' mass is confirmed. The topological susceptibility drops to zero at the
deconfining phase transition. Preliminary results are also presented for chi
and chi' in full QCD, and for the spin content of the proton. The only problem
there is the difficulty of the usual Hybrid Monte Carlo algorithm to bring
topology to equilibrium.


title:
A critical comparison of different definitions of topological charge on
  the lattice

abstract:
  A detailed comparison is made between the field-theoretic and geometric
definitions of topological charge density on the lattice. Their
renormalizations with respect to continuum are analysed. The definition of the
topological susceptibility, as used in chiral Ward identities, is reviewed.
After performing the subtractions required by it, the different lattice methods
yield results in agreement with each other. The methods based on cooling and on
counting fermionic zero modes are also discussed.


title: THE QCD ABACUS: A New Formulation for Lattice Gauge Theories

abstract:
  A quantum Hamiltonian is constructed for SU(3) lattice QCD entirely from
color triplet Fermions --- the standard quarks and a new Fermionic
``constituent'' of the gluon we call ``rishons''. The quarks are represented by
Dirac spinors on each site and the gauge fields by rishon-antirishon bilinears
on each link which together with the local gauge transforms are the generators
of an SU(6) algebra. The effective Lagrangian for the path integral lives in
$R^4 \times S^1$ Euclidean space with a compact ``fifth time'' of circumference
($\beta$) and non-Abelian charge ($e^2$) both of which carry dimensions of
length. For large $\beta$, it is conjectured that continuum QCD is reached and
that the dimensionless ratio $g^2 = e^2/\beta$ becomes the QCD gauge coupling.
The quarks are introduced as Kaplan chiral Fermions at either end of the finite
slab in fifth time. This talk will emphasize the gauge and algebraic structure
of the rishon or link Fermions and the special properties that may lead to fast
discrete dynamics for numerical simulations and new theoretical insight.


title: First study of $B \to \pi$ semileptonic decay form factors using NRQCD

abstract:
  We present a quenched calculation of the form factors of the semileptonic
weak decay $B \to \pi l \bar{\nu}$ with $O(1/m_Q)$ NRQCD heavy quark and Wilson
light quark on a $16^3 \times 32$ lattice at $\beta=5.8$. The form factors are
evaluated at six heavy quark masses, in the range of $m_Q \sim 1.5-8$ GeV.
$1/m_Q$ dependence of matrix elements are investigated and compared with HQET
predictions. We observe clear signal for the form factors near $q^2_{max}$,
even at the $b$-quark mass range. $f^0(q^2_{max})$ is compared with
$f_B/f_{\pi}$ based on the soft pion theorem and significant difference is
observed.


title:
Probing the Region of Massless Quarks in Quenched Lattice QCD using
  Wilson Fermions

abstract:
  We study the spectrum of $H(m)=\gamma_5 W(-m)$ with $W(m)$ being the
Wilson-Dirac operator on the lattice with bare mass equal to $m$. The
background gauge fields are generated using the SU(3) Wilson action at
$\beta=5.7$ on an $8^3\times 16$ lattice. We find evidence that the spectrum of
$H(m)$ is gapless for $1.02 < m < 2.0$, implying that the physical quark is
massless in this whole region.


title:
Instanton classical solutions of SU(3) fixed point actions on open
  lattices

abstract:
  We construct instanton-like classical solutions of the fixed point action of
a suitable renormalization group transformation for the SU(3) lattice gauge
theory. The problem of the non-existence of one-instantons on a lattice with
periodic boundary conditions is circumvented by working on open lattices. We
consider instanton solutions for values of the size (0.6-1.9 in lattice units)
which are relevant when studying the SU(3) topology on coarse lattices using
fixed point actions. We show how these instanton configurations on open
lattices can be taken into account when determining a few-couplings
parametrization of the fixed point action.


title:
Lattice study of $B\to \pi$ semileptonic decay using nonrelativistic
  lattice QCD

abstract:
  We present an exploratory lattice study of $B\to\pi$ semileptonic decay form
factors using the nonrelativistic lattice QCD for heavy quark with Wilson light
quark on a $16^3 \times 32$ quenched lattice at $\beta=5.8$. The matrix
elements are calculated at eight values of heavy quark mass in a range of
$1.5-8$ GeV and with three values of light quark mass. The $1/m_B$ corrections
to the matrix elements are found to be fairly small except for the spatial
component proportional to the $B$ meson momentum. We find that the $q^2$
dependence of the form factor $f^+(q^2)$ near $q_{max}^2$ becomes much stronger
for larger heavy quark mass, which may suggest the increase of a pole
contribution. We perform a model independent fit of the form factors and study
whether the $q^2$ dependence is consistent with the pole contribution. Although
the soft pion theorem predicts $f^0(q_{max}^2)=f_B/f_{\pi}$ in the chiral
limit, we observe a significant violation of this relation.


title: Revealing Topological Structure in the SU(2) Vacuum

abstract:
  In this paper we derive a simple parametrization of the cycling method
developed by us in our earlier work. The new method, called renormalization
group (RG) mapping, consists of a series of carefully tuned APE-smearing steps.
We study the relation between cycling and RG mapping. We also investigate in
detail how smooth instantons and instanton-anti-instanton pairs behave under
the RG mapping transformation. We use the RG mapping technique to study the
topological susceptibility and instanton size distribution of SU(2) gauge
theory. We find scaling in both quantities in a wide range of coupling values.
Our result for the topological susceptibility, chi^1/4=220(6) MeV, agrees with
our earlier results.


title: Applications of Partially Quenched Chiral Perturbation Theory

abstract:
  Partially quenched theories are theories in which the valence- and sea-quark
masses are different. In this paper we calculate the nonanalytic one-loop
corrections of some physical quantities: the chiral condensate, weak decay
constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude,
using partially quenched chiral perturbation theory. Our results for weak decay
constants and masses agree with, and generalize, results of previous work by
Sharpe. We compare B_K and the K+ decay amplitude with their real-world values
in some examples. For the latter quantity, two other systematic effects that
plague lattice computations, namely, finite-volume effects and unphysical
values of the quark masses and pion external momenta are also considered. We
find that typical one-loop corrections can be substantial.


title: Topology in lattice QCD

abstract:
  The status of topology on the lattice is reviewed. Recent results show that
the topological susceptibility chi can be unambigously determined. Different
methods, if properly implemented, give results consistent with each other. For
SU(3) the Witten-Veneziano prediction is confirmed. Preliminary results for
full QCD are presented. The problem there is that the usual hybrid montecarlo
algorithm has severe difficulty to thermalize topology. Possible ways out are
under study.


title: Scaling in SU(3) theory with a MCRG improved lattice action

abstract:
  We test various improved gauge actions which are made of linear combinations
of Wilson loops. We observe the restoration of rotational symmetry in the
static interquark potential already on coarse lattices as small as 6^3x12.
Furthermore, we study scaling and asymptotic scaling of the string tension with
a MCRG-improved action on 12^3x24 lattices. Preliminary results show that
scaling sets in at a ~ 0.3 fm.


title: Simulating the vacuum properties of QCD with dynamical quarks

abstract:
  The vacuum properties of lattice QCD with staggered quarks are investigated
by an efficient simulation method. I present data for the quark condensate with
flavor number $N_f=0, ~ 1, ~ 2, ~ 3, ~ 4$ and many quark masses, including the
vacuum energy in the chiral limit. Obvious sea quark effects are observed in
some parameter space. I also describe a mechanism to understand this and a
formula relating the chiral condensate and zero modes.


title: Method for Extracting the Glueball Wave Function

abstract:
  We describe a nonperturbative method for calculating the QCD vacuum and
glueball wave functions, based on an eigenvalue equation approach to
Hamiltonian lattice gauge theory. Therefore, one can obtain more physical
information than the conventional simulation methods. For simplicity, we take
the 2+1 dimensional U(1) model as an example. The generalization of this method
to 3+1 dimensional QCD is straightforward.


title:
Strongly coupled U(1) lattice gauge theory as a microscopic model of
  Yukawa theory

abstract:
  Dynamical chiral symmetry breaking in a strongly coupled U(1) lattice gauge
model with charged fermions and scalar is investigated by numerical simulation.
Several composite neutral states are observed, in particular a massive fermion.
In the vicinity of the tricritical point of this model we study the effective
Yukawa coupling between this fermion and the Goldstone boson. The perturbative
triviality bound of Yukawa models is nearly saturated. The theory is quite
similar to strongly coupled Yukawa models for sufficiently large coupling
except the occurrence of an additional state -- a gauge ball of mass about half
the mass of the fermion.


title:
Dynamical fermion mass generation at a tricritical point in strongly
  coupled U(1) lattice gauge theory

abstract:
  Fermion mass generation in the strongly coupled U(1) lattice gauge theory
with fermion and scalar fields of equal charge is investigated by means of
numerical simulation with dynamical fermions. Chiral symmetry of this model is
broken by the gauge interaction and restored by the light scalar. We present
evidence for the existence of a particular, tricritical point of the
corresponding phase boundary where the continuum limit might possibly be
constructed. It is of interest as a model for dynamical symmetry breaking and
mass generation due to a strong gauge interaction. In addition to the massive
and unconfined fermion F and Goldstone boson $\pi$, a gauge ball of mass $m_S
\simeq 1/2 m_F$ and some other states are found. Tricritical exponents appear
to be non-classical.


title: Non-Perturbatively Improved Quenched Hadron Spectroscopy

abstract:
  We make a quenched lattice simulation of hadron spectroscopy at beta=6.2 with
the Wilson action non-perturbatively improved. With respect to the unimproved
case, the estimate of the lattice spacing is less influenced by the choice of
input hadron masses. We study also the effects of using an improved quark mass
in the fits to the dependence of hadron masses upon quark masses.


title: B meson decay constant from quenched Lattice QCD

abstract:
  A lattice QCD calculation of the B meson decay constant is presented. In
order to investigate the scaling violation associated with the heavy quark,
parallel simulations are carried out employing both Wilson and the
O(a)-improved clover actions for the heavy quark. The discretization errors due
to the large $b$ quark mass are estimated in a systematic way with the aid of
the non-relativistic interpretation approach of El-Khadra, Kronfeld and
Mackenzie. As our best value from the quenched simulations at $\beta$=5.9, 6.1
and 6.3 we obtain $f_B$=163$\pm$16 MeV and $f_{B_s}$=175$\pm$18 MeV in the
continuum limit where the error includes both statistical and systematic
uncertainties.


title: Improving the Lattice QCD Hamiltonian

abstract:
  Improvement of the Hamiltonian in lattice gauge theory is considered. We give
explicit expressions for classical improvement and discuss also quantum
corrections.


title: B meson decay constant with the Wilson and Clover heavy quark actions

abstract:
  We present results of our quenched study of the B meson decay constant
obtained with a parallel set of simulations with the Wilson and Clover actions
at \beta=5.9, 6.1 and 6.3. Systematic errors associated with the large b-quark
mass are analyzed within the Fermilab non-relativistic formalism. As our best
estimate in the continuum limit we obtain $f_B=163 \pm 16 MeV$ and $f_{B_s}=175
\pm 18 MeV$ with the Clover action.


title:
Light Hadron Spectroscopy on Coarse Lattices with O(a^2) Mean-Field
  Improved Actions

abstract:
  The masses and dispersions of light hadrons are calculated in lattice QCD
using an O(a^2) tadpole-improved gluon action and an O(a^2) tadpole-improved
next-nearest-neighbor fermion action originally proposed by Hamber and Wu. Two
lattices of constant volume with lattice spacings of approximately 0.40 fm and
0.24 fm are considered. The results reveal some scaling violations at the
coarser lattice spacing on the order of 5%. At the finer lattice spacing, the
calculated mass ratios reproduce state-of-the-art results using unimproved
actions. Good dispersion and rotational invariance up to momenta of pa ~ 1 are
also found. The relative merit of alternative choices for improvement operators
is assessed through close comparisons with other plaquette-based
tadpole-improved actions.


title:
First order signatures in 4D pure compact U(1) gauge theory with
  toroidal and spherical topologies

abstract:
  We study the pure compact U(1) gauge theory with the extended Wilson action
(\beta, \gamma couplings) by finite size scaling techniques, in lattices
ranging from L=6 to L=24 in the region of \gamma <= 0 with toroidal and
spherical topologies. The phase transition presents a double peak structure
which survives in the thermodynamical limit in the torus. In the sphere the
evidence support the idea of a weaker, but still first order, phase transition.
For negative values of gamma the transition becomes weaker and larger lattices
are needed to find its asymptotic behaviour. Along the transient region the
behaviour is the typical one of a weak first order transition for both
topologies, with a region where 1/d < nu < 0.5, which becomes nu compatible
with 1/d when larger lattices are used.


title:
$K^{+}\to\pi^{+}\pi^{0}$ Decay Amplitude with the Wilson Quark Action in
  Quenched Lattice QCD

abstract:
  We present a calculation for the $K^+\to\pi^+ \pi^0 $ decay amplitude using a
quenched simulation of lattice QCD with the Wilson quark action at
$\beta=6/g^2=6.1$. The decay amplitude is extracted from the ratio, the
$K\to\pi\pi$ three-point function divided by either $K$ and $\pi$ meson
two-point functions or $K$ meson two-point function and I=2 $\pi\pi$ four-point
function; the two different methods yield consistent results. Finite size
effects are examined with calculations made on $24^3\times 64$ and $32^3\times
64$ lattices, and are shown that they are explained by one-loop effects of
chiral perturbation theory. The lattice amplitude is converted to the continuum
value by employing a one-loop calculation of chiral perturbation theory,
yielding a value in agreement with experiment if extrapolated to the chiral
limit. We also report on the $K$ meson $B$ parameter $B_K$ obtained from the
$K^+\to\pi^+\pi^0$ amplitude using chiral perturbation theory.


title:
A multigrid implementation of the Fourier acceleration method for Landau
  gauge fixing

abstract:
  We present a new implementation of the Fourier acceleration method for Landau
gauge fixing. By means of a multigrid inversion we are able to avoid the use of
the fast Fourier transform. This makes the method more flexible, and well
suited for vector and parallel machines. We study the performance of this
algorithm on serial and on parallel (APE100) machines for the 4-dimensional
SU(2) case. We find that our method is equivalent to the standard
implementation of Fourier acceleration already on a serial machine, and that it
parallelizes very efficiently: its computational cost shows a linear speedup
with the number of processors. We have also implemented, on the parallel
machines, a version of the method using conjugate gradient instead of
multigrid. This leads to an algorithm that is efficient at intermediate lattice
volumes.


title:
Three-dimensional U(1) gauge+Higgs theory as an effective theory for
  finite temperature phase transitions

abstract:
  We study the three-dimensional U(1)+Higgs theory (Ginzburg-Landau model) as
an effective theory for finite temperature phase transitions from the 1 K scale
of superconductivity to the relativistic scales of scalar electrodynamics. The
relations between the parameters of the physical theory and the parameters of
the 3d effective theory are given. The 3d theory as such is studied with
lattice Monte Carlo techniques. The phase diagram, the characteristics of the
transition in the first order regime, and scalar and vector correlation lengths
are determined. We find that even rather deep in the first order regime, the
transition is weaker than indicated by 2-loop perturbation theory. Topological
effects caused by the compact formulation are studied, and it is demonstrated
that they vanish in the continuum limit. In particular, the photon mass
(inverse correlation length) is observed to be zero within statistical errors
in the symmetric phase, thus constituting an effective order parameter.


title:
Finite Lattice Hamiltonian Computations in the P-Representation: the
  Schwinger Model

abstract:
  The Schwinger model is studied in a finite lattice by means of the
P-representation. The vacuum energy, mass gap and chiral condensate are
evaluated showing good agreement with the expected values in the continuum
limit.


title: Spectroscopy of B_s and D_s Mesons

abstract:
  We study Bs and Ds spectroscopy in quenched lattice QCD using the Fermilab
approach to heavy quarks. We obtain results at four lattice spacings, $a$,
using $O(a)$-improved Wilson quarks. We compare and contrast the various
methods for heavy quarks on the lattice, discussing discussing which methods
work best for different physical systems and the ease with which calculations
may be performed.


title: Monte Carlo results for three-dimensional self-avoiding walks

abstract:
  We discuss possible sources of systematic errors in the computation of
critical exponents by renormalization-group methods, extrapolations from exact
enumerations and Monte Carlo simulations. A careful Monte Carlo determination
of the susceptibility exponent gamma for three-dimensional self-avoiding walks
has been used to test the claimed accuracy of the various methods.


title: The Effectiveness of Non-Perturbative O(a) Improvement in Lattice QCD

abstract:
  The ALPHA collaboration has determined the O(a) improved Wilson quark action
for lattice spacings $a\leq 0.1$ fm, in the quenched approximation. We extend
this result to coarser lattices, $a\leq 0.17$ fm, and calculate the hadron
spectrum on them. The large range of lattice spacings obtained by combining our
results with earlier ones on finer lattices, allow us to present a convincing
demonstration of the efficiency of non-perturbative O(a) improvement. We find
that scaling violations of the hadron masses studied drop from 30-40% for the
unimproved Wilson action on the coarsest lattice to only 2-3%.


title: Lattice B-parameters for $\Delta S = 2$ and $\Delta I = 3/2$ Operators

abstract:
  We compute several matrix elements of dimension-six four-fermion operators
and extract their B-parameters. The calculations have been performed with the
tree-level Clover action at $\beta = 6.0$. The renormalization constants and
mixing coefficients of the lattice operators have been obtained
non-perturbatively. In the $\MSbar$ renormalization scheme, at a
renormalization scale $\mu \simeq 2$ GeV, we find $B_K (B_9^{3/2}) = 0.66(11),
B_7^{3/2} = 0.72(5)$ and $B_8^{3/2} = 1.03(3)$. The result for $B_8^{3/2}$ has
important implications for the calculation of $\epsilon^\prime / \epsilon$.


title:
Perfect Lattice Perturbation Theory: A Study of the Anharmonic
  Oscillator

abstract:
  As an application of perfect lattice perturbation theory, we construct an
O(\lambda) perfect lattice action for the anharmonic oscillator analytically in
momentum space. In coordinate space we obtain a set of 2-spin and 4-spin
couplings \propto \lambda, which we evaluate for various masses. These
couplings never involve variables separated by more than two lattice spacings.
The O(\lambda) perfect action is simulated and compared to the standard action.
We discuss the improvement for the first two energy gaps \Delta E_1, \Delta E_2
and for the scaling quantity \Delta E_2 / \Delta E1 in different regimes of the
interaction parameter, and of the correlation length.


title: The domain-wall model in an asymptotic-free dynamics

abstract:
  We investigate a possibility that the rough gauge problem, which have
appeared to be a main reason for failures of lattice chiral gauge theories, is
cured by an asymptotic-free dynamics. Taking the domain-wall model in 2(+1)
dimensions with SU(2) gauge group, we carry out the quenched simulation of
gauge fields in the extra dimension. By studying fermion spectra in several
volumes, we show that the chiral zero modes exist on the wall without having
the spontaneous symmetry breaking thanks to the asymptotic-free dynamics. This
result suggests that the rough gauge problem is solved in some class of lattice
chiral fermions as well as in 4 dimensions if an asymptotic-free dynamics is
incorporated.


title: Low temperature expansion of the gonihedric Ising model

abstract:
  We investigate a model of closed $(d-1)$-dimensional soft-self-avoiding
random surfaces on a $d$-dimensional cubic lattice. The energy of a surface
configuration is given by $E=J(n_{2}+4k n_{4})$, where $n_{2}$ is the number of
edges, where two plaquettes meet at a right angle and $n_{4}$ is the number of
edges, where 4 plaquettes meet. This model can be represented as a
$\Z_{2}$-spin system with ferromagnetic nearest-neighbour-, antiferromagnetic
next-nearest-neighbour- and plaquette-interaction. It corresponds to a special
case of a general class of spin systems introduced by Wegner and Savvidy. Since
there is no term proportional to the surface area, the bare surface tension of
the model vanishes, in contrast to the ordinary Ising model. By a suitable
adaption of Peierls argument, we prove the existence of infinitely many ordered
low temperature phases for the case $k=0$. A low temperature expansion of the
free energy in 3 dimensions up to order $x^{38}$ ($x={e}^{-\beta J}$) shows,
that for $k>0$ only the ferromagnetic low temperature phases remain stable. An
analysis of low temperature expansions up to order $x^{44}$ for the
magnetization, susceptibility and specific heat in 3 dimensions yields critical
exponents, which are in agreement with previous results.


title: Monopole clusters in Abelian projected gauge theories

abstract:
  We show that the monopole currents which one obtains in the maximally Abelian
gauge of SU(2) fall into two quite distinct classes (when the volume is large
enough). In each field configuration there is precisely one cluster that
permeates the whole lattice volume. It has a current density and a magnetic
screening mass that scale and it produces the whole of the string tension. The
remaining clusters have a number density that follows an approximate power law
proportional to the inverse cube of l where l is the length of the monopole
world line in lattice units. These clusters are localised in space-time with
radii which vary as the square root of l. In terms of the radius r these
`lumps' have a scale-invariant distribution proportional to (dr/r . 1/{r^4}).
Moreover they appear not to contribute at all to the string tension. The fact
that they are scale-invariant at small distances would seem to rule out an
instanton origin.


title: Update on lattice QCD with domain wall quarks

abstract:
  Using domain wall fermions, we estimate B_K(mu approx 2 GeV)=0.602(38) in
quenched QCD which is consistent with previous calculations. We also find
ratios of decay constants that are consistent with experiment, within our
statistical errors. Our initial results indicate good scaling behavior and
support expectations that O(a) errors are exponentially suppressed in low
energy (E<< a^{-1}) observables. It is also shown that the axial current
numerically satisfies the lattice analog of the usual continuum axial Ward
identity and that the matrix element of the four quark operator needed for B_K
exhibits excellent chiral behavior.


title: A quark action for very coarse lattices

abstract:
  We investigate a tree-level O(a^3)-accurate action, D234c, on coarse
lattices. For the improvement terms we use tadpole-improved coefficients, with
the tadpole contribution measured by the mean link in Landau gauge.
  We measure the hadron spectrum for quark masses near that of the strange
quark. We find that D234c shows much better rotational invariance than the
Sheikholeslami-Wohlert action, and that mean-link tadpole improvement leads to
smaller finite-lattice-spacing errors than plaquette tadpole improvement. We
obtain accurate ratios of lattice spacings using a convenient ``Galilean
quarkonium'' method.
  We explore the effects of possible O(alpha_s) changes to the improvement
coefficients, and find that the two leading coefficients can be independently
tuned: hadron masses are most sensitive to the clover coefficient, while hadron
dispersion relations are most sensitive to the third derivative coefficient
C_3. Preliminary non-perturbative tuning of these coefficients yields values
that are consistent with the expected size of perturbative corrections.


title:
Study of Lattice Correlation Functions at Small Times using the QCD Sum
  Rules Continuum Model

abstract:
  In this paper we study the work of Leinweber by applying the Continuum Model
of QCD Sum Rules (QCDSR) to the analysis of (quenched) lattice correlation
functions. We expand upon his work in several areas: we study meson states as
well as baryons; we analyse data from several lattice spacings; and we include
data from the Sheikholeslami-Wohlert (clover) improved action. We find that the
QCDSR Continuum Model Ansatz can reproduce the data, but only for non-physical
values of its parameters. This leads us to reject it as a model for hadronic
correlation functions.
  We study the non-relativistic quark model and conclude that it predicts
essentially the same form for the correlation function as the QCDSR Continuum
Model approach. Furthermore, because it doesn't have the Continuum Model's
restrictions on the parameters, the non-relativistic quark model can be viewed
as a successful Ansatz.
  As well as studying the validity or otherwise of the QCDSR Continuum Model
approach, this paper defines 4-parameter fitting functions that can be used to
fit lattice data even for a time window close to the source. These functions
are shown to be an improvement over 2-exponential fits especially in the case
of mesons. We encourage the application of this approach to situations where
the conventional fitting procedures are problematic due to poor ground state
dominance.


title: Lattice Models of Random Geometries

abstract:
  We review models of random geometries based on the dynamical lattice
approach. We discuss one dimensional model of simplicial complexes (branched
polymers), two dimensional model of dynamical triangulations and four
dimensional model of simplicial gravity.


title:
Monte Carlo Simulation Calculation of Critical Coupling Constant for
  Continuum \phi^4_2

abstract:
  We perform a Monte Carlo simulation calculation of the critical coupling
constant for the continuum {\lambda \over 4} \phi^4_2 theory. The critical
coupling constant we obtain is [{\lambda \over \mu^2}]_crit=10.24(3).


title: Single massless Majorana fermion in the domain-wall formalism

abstract:
  We study the domain-wall formalism with additional Majorana mass term for the
unwanted zero mode, which has recently been proposed for lattice construction
of 4D N=1 super Yang-Mills theory without fine-tuning. Switching off the gauge
field, we study the dispersion relation of the energy eigenstates numerically,
and find that the method works for reasonable values of Majorana mass. We point
out, however, that a problem arises for too large Majorana mass, which can be
understood in terms of the seesaw mechanism.


title: Quenched hadron spectroscopy with improved staggered quark action

abstract:
  We investigate light hadron spectroscopy with an improved quenched staggered
quark action. We compare the results obtained with an improved gauge plus an
improved quark action, an improved gauge plus standard quark action, and the
standard gauge plus standard quark action. Most of the improvement in the
spectroscopy results is due to the improved gauge sector. However, the improved
quark action substantially reduces violations of Lorentz invariance, as
evidenced by the meson dispersion relations.


title: Phase Structure of Dynamical Triangulation Models in Three Dimensions

abstract:
  The dynamical triangulation model of three-dimensional quantum gravity is
shown to have a line of transitions in an expanded phase diagram which includes
a coupling mu to the order of the vertices. Monte Carlo renormalization group
and finite size scaling techniques are used to locate and characterize this
line. Our results indicate that for mu < mu1 ~ -1.0 the model is always in a
crumpled phase independent of the value of the curvature coupling. For mu < 0
the results are in agreement with an approximate mean field treatment. We find
evidence that this line corresponds to first order transitions extending to
positive mu. However, the behavior appears to change for mu > mu2 ~ 2-4. The
simplest scenario that is consistent with the data is the existence of a
critical end point.


title: Tempered Fermions in the Hybrid Monte Carlo Algorithm

abstract:
  Parallel tempering simulates at many quark masses simultaneously, by changing
the mass during the simulation while remaining in equilibrium. The algorithm is
faster than pure HMC if more than one mass is needed, and works better the
smaller the smallest mass is.


title: Singular Behaviour of the Potts Model in the Thermodynamic Limit

abstract:
  The self-duality transformation is applied to the Fisher zeroes near the
critical point in the thermodynamic limit in the q>4 state Potts model in two
dimensions. A requirement that the locus of the duals of the zeroes be
identical to the dual of the locus of zeroes (i) recovers the ratio of specific
heat to internal energy discontinuity at criticality and the relationships
between the discontinuities of higher cumulants and (ii) identifies duality
with complex conjugation. Conjecturing that all zeroes governing ferromagnetic
critical behaviour satisfy the latter requirement, the full locus of Fisher
zeroes is shown to be a circle. This locus, together with the density of zeroes
is shown to be sufficient to recover the singular form of all thermodynamic
functions in the thermodynamic limit.


title:
Quenched staggered light hadron spectroscopy from $48^3\times64$ at
  $\beta = 6.5$

abstract:
  We report our light hadron mass calculation based on an increased statistics
of 250 quenched gauge configurations on a (48^3 \times 64) lattice at (\beta =
6.5). Quark propagators are calculated for each of these configurations with
staggered wall source and point sink at quark mass values of (m_q = 0.01,
0.005, 0.0025) and (0.00125). We also did additional calculations to improve
our understanding of systematic biases arising from autocorrelation, source
size, and propagator calculations. Our earlier conclusions that the flavor
symmetry breaking is reduced and the ratio (m_N/m_\rho (\sim 1.25(4))) is small
remains robust.


title:
On the spectrum of the Wilson-Dirac lattice operator in topologically
  non-trivial background configurations

abstract:
  We study characteristic features of the eigenvalues of the Wilson-Dirac
operator in topologically non-trivial gauge field configurations by examining
complete spectra of the fermion matrix. In particular we discuss the role of
eigenvectors with real eigenvalues as the lattice equivalents of the continuum
zero-modes. We demonstrate, that those properties of the spectrum which
correspond to non-trivial topology are stable under adding fluctuations to the
gauge fields. The behavior of the spectrum in a fully quantized theory is
discussed using QED_2 as an example.


title:
One-loop matching of lattice and continuum heavy-light axial vector
  currents using NRQCD

abstract:
  The temporal component of the heavy-light axial vector current is constructed
to one-loop order in perturbation theory and to order 1/M, where M is the heavy
quark mass, in terms of operators suitable for use in lattice simulations of B
and D mesons. The O(a)-improved clover action is used for the massless light
quark, where a is the lattice spacing, and propagation of the heavy quark is
described by a nonrelativistic lattice action.


title: The Gross-Neveu model and QCDs chiral phase transition

abstract:
  Quantum chromodynamics has a rather complicated phase structure. The finite
temperature, chiral phase structure depends on the number of flavours and to a
large extent on the particular values of the fermion masses. For two massless
flavours there is a true second order transition. It has been argued that this
transition belongs to the universality class of the three-dimensional O(4) spin
model. The arguments have been questioned recently, and the transition was
claimed to be mean field behaved. In this lecture we discuss this issue at the
example of the three-dimensional, parity symmetric Gross-Neveu model at finite
temperature, with a large number N of fermions. At zero temperature there is a
phase where parity is spontaneously broken. At finite temperature, this model
has a parity restoring second order transition. It reveals considerable
similarity to the QCD chiral phase transition. There are related questions here
concerning the universality class. We solve this problem essentially by means
of the following methods: Large N expansion, dimensional reduction in the
framework of quantum field theory, and high order convergent series expansions
about disordered lattice systems.


title: Vortex Dynamics in Classical Non--Abelian Spin Models

abstract:
  We discuss the abelian vortex dynamics in the abelian projection approach to
non-abelian spin models. We show numerically that in the three-dimensional
SU(2) spin model in the Maximal Abelian projection the abelian off-diagonal
vortices are not responsible for the phase transition contrary to the diagonal
vortices. A generalization of the abelian projection approach to SU(N) spin
models is briefly discussed.


title: The Hybrid Monte Carlo Algorithm for Quantum Chromodynamics

abstract:
  The Hybrid Monte Carlo (HMC) algorithm currently is the favorite scheme to
simulate quantum chromodynamics including dynamical fermions. In this
talk-which is intended for a non-expert audience--I want to bring together
methodical and practical aspects of the HMC for full QCD simulations. I will
comment on its merits and shortcomings, touch recent improvements and try to
forecast its efficiency and r\^ole in future full QCD simulations.


title: Critical Dynamics of the Hybrid Monte Carlo Algorithm

abstract:
  We investigate the critical dynamics of the Hybrid Monte Carlo algorithm
approaching the chiral limit of standard Wilson fermions. Our observations are
based on time series of lengths O(5000) for a variety of observables. The
lattice sizes are 16^3 x 32 and 24^3 x 40. We work at beta=5.6, and
kappa=0.156, 0.157, 0.1575, 0.158, with 0.83 > m_pi/m_rho > 0.55. We find
surprisingly small integrated autocorrelation times for local and extended
observables. The dynamical critical exponent $z$ of the exponential
autocorrelation time is compatible with 2. We estimate the total computational
effort to scale between V^2 and V^2.25 towards the chiral limit.


title:
A Coupled-Cluster Formulation of Hamiltonian Lattice Field Theory: The
  Non-Linear Sigma Model

abstract:
  We apply the coupled cluster method (CCM) to the Hamiltonian version of the
latticised O(4) non-linear sigma model. The method, which was initially
developed for the accurate description of quantum many-body systems, gives rise
to two distinct approximation schemes. These approaches are compared with each
other as well as with some other Hamiltonian approaches. Our study of both the
ground state and collective excitations leads to indications of a possible
chiral phase transition as the lattice spacing is varied.


title:
Exponential suppression of radiatively induced mass in the truncated
  overlap

abstract:
  A certain truncation of the overlap (domain wall fermions) contains $k$
flavors of Wilson-Dirac fermions. We show that for sufficiently weak lattice
gauge fields the effective mass of the lightest Dirac particle is exponentially
suppressed in $k$. This suppression is seen to disappear when lattice topology
is non-trivial. We check explicitly that the suppression holds to one loop in
perturbation theory. We also provide a new expression for the free fermion
propagator with an arbitrary additional mass term.


title: Temperature dependence of instantons in QCD

abstract:
  We investigate the temperature dependence of the instanton contents of gluon
fields, using unquenched lattice QCD and the cooling method. The instanton size
parameter deduced from the correlation function decreases from 0.44fm below the
phase-transition temperature $T_c$ ($\approx 150$MeV) to 0.33fm at 1.3 $T_c$.
The instanton charge distribution is Poissonian above $T_c$, but it deviates
from the convoluted Poisson at low temperature. The topological susceptibility
decreases rapidly below $T_c$, showing the apparent restoration of the $U(1)_A$
symmetry already at $T \approx T_c$.


title: The Self-Energy of Massive Lattice Fermions

abstract:
  We address the perturbative renormalization of massive lattice fermions. We
derive expressions-valid to all orders in perturbation theory and for all
values of the bare fermion mass-for the rest mass, the kinetic mass, and the
wave-function renormalization factor. We obtain the fermion's self energy at
the one-loop level with a mass-dependent, $O(a)$ improved action. Numerical
results for two interesting special cases, the Wilson and
Sheikholeslami-Wohlert actions, are given. The mass dependence of these results
smoothly connects the massless and infinite-mass limits, as expected. Combined
with Monte Carlo calculations our results can be employed to determine the
quark masses in common renormalization schemes.


title:
Monopole-antimonopole condensation in the interpolating Georgi-Glashow
  model

abstract:
  We study the three dimensional Georgi-Glashow model (which interpolates
smoothly between pure U(1) and SU(2) limits) using a constrained cooling which
preserves 't Hooft-Polyakov monopoles. We find that the monopole-antimonopole
condensation gives an area law for the Wilson loops. The monopole contribution
to the string tension is close to the Monte Carlo value in the intermediate
region.


title: Statistical properties at the spectrum edge of the QCD Dirac operator

abstract:
  The statistical properties of the spectrum of the staggered Dirac operator in
an SU(2) lattice gauge theory are analyzed both in the bulk of the spectrum and
at the spectrum edge. Two commonly used statistics, the number variance and the
spectral rigidity, are investigated. While the spectral fluctuations at the
edge are suppressed to the same extent as in the bulk, the spectra are more
rigid at the edge. To study this effect, we introduce a microscopic unfolding
procedure to separate the variation of the microscopic spectral density from
the fluctuations. For the unfolded data, the number variance shows oscillations
of the same kind as before unfolding, and the average spectral rigidity becomes
larger than the one in the bulk. In addition, the short-range statistics at the
origin is studied. The lattice data are compared to predictions of chiral
random-matrix theory, and agreement with the chiral Gaussian Symplectic
Ensemble is found.


title: Dual Wilson Loop and Inter-Monopole Potential in Lattice QCD

abstract:
  We study the dual Wilson loop and the inter-monopole potential(the static
potential between the color magnetic monopoles) in the maximally abelian gauge
to clarify the dual Higgs mechanism induced by monopole condensation. There is
no (color-)electric current in the monopole part, which includes the essence of
the nonperturbative QCD, and hence the system can be described by the dual
gauge field $B_\mu$ without the singularity like the Dirac string. We find that
the dual Wilson loop seems to obey the perimeter law, and the inter-monopole
potential becomes Yukawa-type in the infrared region. From the inter-monopole
potential, we estimate the dual gluon mass $m_B$ and the effective size $R$ of
the monopole: $m_B \simeq 0.5$GeV, $R \simeq 0.35$fm.


title:
Gluon Propagator in Maximally Abelian Gauge and Abelian Dominance for
  Long-Range Interaction

abstract:
  We study the gluon propagator in the MA gauge with the lattice QCD Monte
Carlo simulation. The simulation is performed using the heat-bath algorithm on
the SU(2) lattice with $12^3 \times 24$ and $\beta = 2.3, 2.35$. The propagator
of the off-diagonal charged gluon behaves as the massive gauge boson and
provides the short-range interaction, while the diagonal gluon propagates long
distance. This is the origin of the abelian dominance in the long-range
physics.


title: Kramers Equation Algorithm with Kogut-Susskind Fermions on Lattice

abstract:
  We compare the performance of the Kramers Equation Monte Carlo (KMC)
Algorithm with that of the Hybrid Monte Carlo (HMC) algorithm for numerical
simulations with dynamical Kogut-Susskind fermions. Using the lattice
Gross-Neveu model in 2 space-time dimensions, we calculate the integrated
autocorrelation time of different observables at a number of couplings in the
scaling region on 16^2 and 32^2 lattices while varying the parameters of the
algorithms for optimal performance. In our investigation the performance of KMC
is always significantly below than that of HMC for the observables used. We
also stress the importance of having a large number of configurations for the
accurate estimation of the integrated autocorrelation time.


title: Lattice Fermions and the Chiral Anomaly

abstract:
  We show in the Wilson model that the contribution of the regular mass term to
the four-divergence of the axial vector current in weak coupling perturbation
theory is not zero in the chiral limit and is precisely the axial anomaly.
Explicit breaking of chiral symmetry in the Wilson term is not relevant for the
result. The ABJ anomaly is generated by the fermion mass term also with a
chirally symmetric irrelevant term.


title:
Asymptotic scaling corrections in QCD with Wilson fermions from the
  3-loop average plaquette

abstract:
  We calculate the 3-loop perturbative expansion of the average plaquette in
lattice QCD with N_f massive Wilson fermions and gauge group SU(N). The
corrections to asymptotic scaling in the corresponding energy scheme are also
evaluated. We have also improved the accuracy of the already known pure gluonic
results at 2 and 3 loops.


title: Resolution of the Landau pole problem in QED

abstract:
  We present new numerical results for the renormalized mass and coupling in
non-compact lattice QED with staggered fermions. Implications for the continuum
limit and the role of the Landau pole are discussed.


title: Proposal for Topologically Unquenched QCD

abstract:
  A proposal is presented for simulating an improvement on quenched QCD with
dynamical fermions which interact with the gluon configuration only via the
topological index of the latter. Strengths and shortcomings of the method are
discussed and it is argued that the approximation - though being crude - shares
some qualitative aspects of full QCD which relate to the issue of chiral
symmetry breaking.


title: Critical Equalities for Potts Models

abstract:
  We apply a simple analytical criterion for locating critical temperatures to
Potts models on square and triangular lattices. In the self-dual case, i.e. on
the square lattice we reproduce known exact values of the critical temperature
and derive the internal energy of the model at the critical point. For the
Potts model on the triangular lattice we obtain very good numerical estimate of
the critical temperature and also of the internal energy at the critical point.


title:
The three-loop beta function of SU(N) lattice gauge theories with Wilson
  fermions

abstract:
  We calculate the third coefficient of the lattice beta function associated
with the Wilson formulation for both gauge fields and fermions. This allows us
to evaluate the three-loop correction (linear in $g_0^2$) to the relation
between the lattice Lambda-parameter and the bare coupling $g_0$, which is
important in order to verify asymptotic scaling predictions. Our calculation
also leads to the two-loop relation between the coupling renormalized in the
MSbar scheme and $g_0$.
  The original version of this paper contained a numerical error in one of the
diagrams, which has now been corrected. The calculations, as well as the layout
of the paper have remained identical, but there are some important changes in
the numerical results.


title: Topological Structure of the SU(3) Vacuum

abstract:
  We investigate the topological structure of the vacuum in SU(3) lattice gauge
theory. We use under-relaxed cooling to remove the high-frequency fluctuations
and a variety of "filters" to identify the topological charges in the resulting
smoothened field configurations. We find a densely packed vacuum with an
average instanton size, in the continuum limit, of about 0.5 fm. The density at
large sizes decreases as a large inverse power of the size. At small sizes we
see some sign of a trend towards the asymptotic perturbative behaviour. We find
that an interesting polarisation phenomenon occurs: the large topological
charges tend to have, on the average, the same sign and are over-screened by
the smaller charges which tend to have, again on the average, the opposite sign
to the larger instantons. We also calculate the topological susceptibility for
which we obtain a continuum value of about 187 MeV. We perform the calculations
for various volumes, lattice spacings and numbers of cooling sweeps, so as to
obtain some control over the associated systematic errors. The coupling range
is from beta=6.0 to beta=6.4 and the lattice volumes range from 16x16x16x48 to
32x32x32x64.


title:
Confinement Artifacts in the U(1) and SU(2) Compact Lattice Gauge
  Theories

abstract:
  We identify the artifact that causes confinement at strong coupling in
compact U(1) lattice gauge theory and show that most of the string tension in
compact SU(2) lattice gauge theory is due to plaquettes of negative trace.


title: Abelian Dyons in the Maximal Abelian Projection of SU(2) Gluodynamics

abstract:
  Correlations of the topological charge Q, the electric current J^e and the
magnetic current J^m in SU(2) lattice gauge theory in the Maximal Abelian
projection are investigated. It occurs that the correlator <<QJ^e J^m>> is
nonzero for a wide range of values of the bare charge. It is shown that: (i)
the abelian monopoles in the Maximal Abelian projection are dyons which carry
fluctuating electric charge; (ii) the sign of the electric charge e(x)
coincides with that of the product of the monopole charge m(x) and the
topological charge density Q(x).


title: Properties of Abelian Monopoles in SU(2) Lattice Gluodynamics

abstract:
  We discuss some properties of abelian monopoles in the Maximal Abelian
projection of the SU(2) lattice gluodynamics. We show that in the maximal
abelian projection abelian monopoles carry fluctuating electric charge and that
the monopole currents are correlated with the magnetic and the electric parts
of the SU(2) action density.


title: Hot Electroweak Matter Near to the Critical Higgs Mass

abstract:
  We discuss the end of the first order phase transition and the bound state
spectrum, both at weak transition and at the crossover.


title: The Scalar Quarkonium Spectrum and Quarkonium-Glueball Mixing

abstract:
  We evaluate the valence approximation to the mass of scalar quarkonium and to
the mixing energy between scalar quarkonium and the lightest scalar glueball
for a range of different lattice sizes and quark masses. Our results support
the identification of $f_0(1710)$ as the lightest scalar glueball.


title:
The role of the Polyakov loop in the Dirac operator of QCD at finite
  temperature

abstract:
  We show how all the contributions to the determinant of the
Dirac-Kogut-Susskind operator of QCD at finite temperature containing a net
number of Polyakov loops become irrelevant in the infinite volume limit. We
discuss also on two of the most interesting physical implications of this
result: i) the restoration of the Polyakov symmetry in the full theory with
dynamical fermions and ii) the total suppression of baryonic thermal
fluctuations in QCD at finite temperature.


title:
The hermitian Wilson-Dirac operator in smooth SU(2) instanton
  backgrounds

abstract:
  We study the spectral flow of the hermitian Wilson-Dirac operator $\ham(m)$
as a function of $m$ in smooth SU(2) instanton backgrounds on the lattice. For
a single instanton background with Dirichlet boundary conditions on $\ham(m)$,
we find a level crossing in the spectral flow of $\ham(m)$, and we find the
shape of the crossing mode at the crossing point to be in good agreement with
the zero mode associated with the single instanton background. With
anti-periodic boundary conditions on $\ham(m)$, we find that the instanton
background in the singular gauge has the correct spectral flow but the one in
regular gauge does not. We also investigate the spectral flows of two instanton
and instanton-anti-instanton backgrounds.


title:
Monopole Loop Suppression and Loss of Confinement in Restricted Action
  SU(2) Lattice Gauge Theory

abstract:
  The effect of restricting the plaquette ($1\times 1$ Wilson loop) to be
greater than a certain cutoff is studied. The action considered is the standard
Wilson action with the addition of the plaquette restriction, which does not
affect the continuum limit. A deconfining phase transition occurs as the cutoff
is raised, even in the strong coupling limit. Abelian-projected monopoles in
the maximal abelian gauge are strongly suppressed by the action restriction.
Analysis of the steeply declining monopole loop distribution function indicates
that for cutoffs $c > 0.5$, large monopole loops which are any finite fraction
of the lattice size do not exist in the infinite lattice limit. This would seem
to imply the theory lacks confinement, which is consistent with a fixed point
behavior seen in the normalized fourth cumulant of the Polyakov loop.


title: Renormalization of strongly coupled U(1) lattice gauge theories

abstract:
  Recent numerical studies of the 4D pure compact U(1) lattice gauge theory, I
have participated in, are reviewed. We look for a possibility to construct an
interesting nonperturbatively renormalizable continuum theory at the phase
transition between the confinement and Coulomb phases. First I describe the
numerical evidence, obtained from calculation of bulk observables on spherical
lattices, that the theory has a non-Gaussian fixed point. Further the
gauge-ball spectrum in the confinement phase is presented and its universality
confirmed. The unexpected result is that, in addition to massive states, the
theory contains a very light, possibly massless scalar gauge ball. I also
summarize results of studies of the compact U(1) lattice theory with fermion
and scalar matter fields and point out that at strong coupling it represents a
model of dynamical fermion mass generation.


title:
Chiral Fermions on the Lattice through Gauge Fixing -- Perturbation
  Theory

abstract:
  We study the gauge-fixing approach to the construction of lattice chiral
gauge theories in one-loop weak-coupling perturbation theory. We show how
infrared properties of the gauge degrees of freedom determine the nature of the
continuous phase transition at which we take the continuum limit. The fermion
self-energy and the vacuum polarization are calculated, and confirm that, in
the abelian case, this approach can be used to put chiral gauge theories on the
lattice in four dimensions. We comment on the generalization to the nonabelian
case.


title: Thermodynamics of Lattice QCD with Chiral 4-Fermion Interactions

abstract:
  We have studied lattice QCD with an additional, irrelevant 4-fermion
interaction having a U(1)xU(1) chiral symmetry, at finite temperatures. Adding
this 4-fermion term allowed us to work at zero quark mass, which would have
otherwise been impossible. The theory with 2 massless staggered quark flavours
appears to have a first order finite temperature phase transition at N_t=4 for
the value of 4-fermion coupling we have chosen, in contrast to what is expected
for 2-flavour QCD. The pion screening mass is seen to vanish below this
transition, only to become massive and degenerate with the sigma (f_0) above
this transition where the chiral symmetry is restored, as is seen by the
vanishing of the chiral condensate.


title:
Topology, fermionic zero modes and flavor singlet correlators in finite
  temperature QCD

abstract:
  We compute the screening correlators in the sigma and eta' flavor singlet
channels in finite temperature QCD with 2 light quark flavors. Together with
the correlators in the pi and delta channels, these are used to discuss several
issues related to symmetry restoration and the nature of the QCD phase
transition. Our calculations span a range of temperature extending from
approximately 125 MeV to 170 MeV and are carried out in the context of a
staggered fermion formulation on a 16^3x8 lattice. In addition to the
computation at a fixed quark mass (am_q=0.00625), we discuss the issue of the
chiral limit. After careful consideration of the zero-mode shift lattice
artefact, we present rather strong (topological) arguments in favor of the
non-restoration of U_A(1) at T_c.


title: The index theorem in QCD with a finite cut-off

abstract:
  The fixed point Dirac operator on the lattice has exact chiral zero modes on
topologically non-trivial gauge field configurations independently whether
these configurations are smooth, or coarse. The relation $n_L-n_R = Q^{FP}$,
where $n_L$ $(n_R)$ is the number of left (right)-handed zero modes and
$Q^{FP}$ is the fixed point topological charge holds not only in the continuum
limit, but also at finite cut-off values. The fixed point action, which is
determined by classical equations, is local, has no doublers and complies with
the no-go theorems by being chirally non-symmetric. The index theorem is
reproduced exactly, nevertheless. In addition, the fixed point Dirac operator
has no small real eigenvalues except those at zero, i.e. there are no
'exceptional configurations'.


title: Perfect Actions with Chemical Potential

abstract:
  We show how to include a chemical potential \mu in perfect lattice actions.
It turns out that the standard procedure of multiplying the quark fields \Psi,
\bar\Psi at Euclidean time t by \exp(\pm \mu t), respectively, is perfect. As
an example, the case of free fermions with chemical potential is worked out
explicitly. Even after truncation, cut-off effects in the pressure and the
baryon density are small. Using a (quasi-)perfect action, numerical QCD
simulations for non-zero chemical potential become more powerful, because
coarse lattices are sufficient for extracting continuum physics.


title: SYM on the lattice

abstract:
  Non-perturbative predictions and numerical simulations in supersymmetric
Yang-Mills (SYM) theories are reviewed.


title: Contents of LAT97 Proceedings

abstract:
  We give here the contents pages for the Proceedings of the Lattice '97
conference (15th International Symposium on Lattice Field Theory) that took
place in July 1997 in Edinburgh, Scotland. The contents are in html form with
clickable links to the papers that exist on the hep-lat archive. We hope that
this will make it easier to access the output of the conference in a systematic
way. Comments on how useful this is/ how it could be improved should be sent to
c.davies@physics.gla.ac.uk.


title: Low-lying Eigenvalues of the improved Wilson-Dirac Operator in QCD

abstract:
  The spectral flow of the low-lying eigenvalues of the improved and unimproved
Wilson-Dirac operator is studied on instanton-like configurations and on
thermalized quenched configurations at various $\beta$-values and lattice
sizes. We also investigate the space-time localisation and chirality of the
corresponding eigenvectors.


title: The Yang Lee Edge Singularity on Feynman Diagrams

abstract:
  We investigate the Yang-Lee edge singularity on non-planar random graphs,
which we consider as the Feynman Diagrams of various d=0 field theories, in
order to determine the value of the edge exponent.
  We consider the hard dimer model on phi3 and phi4 random graphs to test the
universality of the exponent with respect to coordination number, and the Ising
model in an external field to test its temperature independence. The results
here for generic (``thin'') random graphs provide an interesting counterpoint
to the discussion by Staudacher of these models on planar random graphs.


title: Detection of Center Vortices in the Lattice Yang-Mills Vacuum

abstract:
  We discuss the implementation of the ``direct'' maximal center gauge (a gauge
which maximizes the lattice average of the squared-modulus of the trace of link
variables), and its use in identifying Z(2) center vortices in Yang-Mills
vacuum configurations generated by lattice Monte Carlo. We find that center
vortices identified in the vacuum state account for the full asymptotic string
tension. Scaling of vortex densities with lattice coupling, change in vortex
size with cooling, and sensitivity to Gribov copies is discussed. Preliminary
evidence is presented, on small lattices, for center dominance in SU(3) lattice
gauge theory.


title: Lattice quark masses: a non-perturbative measurement

abstract:
  We discuss the renormalization of different definitions of quark masses in
the Wilson and the tree-level improved SW-Clover fermionic action. For the
improved case we give the correct relationship between the quark mass and the
hopping parameter. Using perturbative and non-perturbative renormalization
constants, we extract quark masses in the $\MSbar$ scheme from Lattice QCD in
the quenched approximation at $\beta=6.0$, $\beta=6.2$ and $\beta=6.4$ for both
actions. We find: $\bar{m}^{\MSbar}(2 GeV)=5.7 \pm 0.1 \pm 0.8$ MeV,
$m_s^{\MSbar}(2GeV)= 130 \pm 2 \pm 18 $ MeV and $m_c^{\MSbar}(2 GeV) = 1662\pm
30\pm 230$ MeV.


title: Remark on lattice BRST invariance

abstract:
  A recently claimed resolution to the lattice Gribov problem in the context of
chiral lattice gauge theories is examined. Unfortunately, I find that the old
problem remains.


title: Interaction of confining vortices in SU(2) lattice gauge theory

abstract:
  Center projection of SU(2) lattice gauge theory allows to isolate magnetic
vortices as confining configurations. The vortex density scales according to
the renormalization group, implying that the vortices are physical objects
rather than lattice artifacts. Here, the binary correlations between points at
which vortices pierce a given plane are investigated. We find an attractive
interaction between the vortices. The correlations show the correct scaling
behavior and are therefore physical. The range of the interaction is found to
be (0.4 +/- 0.2) fm, which should be compared with the average planar vortex
density of approximately 2 vortices/fm^2. We comment on the implications of
these results for recent discussions of the Casimir scaling behavior of higher
dimensional representation Wilson loops in the vortex confinement picture.


title: More about exactly massless quarks on the lattice

abstract:
  In a previous publication [hep-lat/9707022] I showed that the fermion
determinant for strictly massless quarks can be written on the lattice as $\det
D$, where $D$ is a certain finite square matrix explicitly constructed from the
lattice gauge fields. Here I show that $D$ obeys the Ginsparg-Wilson relation
$D\gamma_5 D = D\gamma_5 +\gamma_5 D$.


title: The nature of the continuum limit in the 2D $RP^2$ gauge model

abstract:
  The RP(2) gauge model is studied in 2D. We use Monte-Carlo renormalization
techniques for blocking the mean spin-spin interaction, <A>, and the mean gauge
field plaquette, <P>. The presence of the O(3) renormalized trajectory is
verified and is consistent with the known three-loop beta-function. The
first-order `vorticity' transition observed by Solomon et al. is confirmed, and
the location of the terminating critical point is established. New scaling
flows in (<A>,<P>) are observed associated with a large exponent kappa in the
range 4~5. The scaling flows give rise to a strong cross-over effect between
regions of high and low vorticity and are likely to induce an apparent signal
for scaling in the cross-over region which we propose explains the scaling
observed for RP(2), RP(3) and SO(4)-matrix models. The signal for this `pseudo'
scaling will occur for the RP(2) spin model in the cross-over region which is
the region in which computer simulations are done. We find that the RP(2) spin
model is in the same universality class as the O(3) spin model but that it is
likely to require a very large correlation length before the true scaling of
this class sets in. We conjecture that the scaling flows are due either to the
influence of a nearby new renormalized trajectory or to the ghost of the
Kosterlitz-Thouless trajectory in the associated XY model.


title: Quark Confinement in the Deconfined Phase

abstract:
  In cylindrical volumes with C-periodic boundary conditions in the long
direction, static quarks are confined even in the gluon plasma phase due to the
presence of interfaces separating the three distinct high-temperature phases.
An effective "string tension" is computed analytically using a dilute gas of
interfaces. At T_c, the deconfined-deconfined interfaces are completely wet by
the confined phase and the high-temperature "string tension" turns into the
usual string tension below T_c. Finite size formulae are derived, which allow
to extract interface and string tensions from the expectation value of a single
Polyakov loop. A cluster algorithm is built for the 3-d three-state Potts model
and an improved estimator for the Polyakov loop is constructed, based on the
number of clusters wrapping around the C-periodic direction of the cluster.


title: $O(a)$ Improvement for Quenched Wilson Fermions

abstract:
  We briefly describe some of our recent results for the mass spectrum and
matrix elements using $O(a)$ improved fermions for quenched QCD. Where possible
a comparison is made between improved and Wilson fermions.


title: On the index theorem for Wilson fermions

abstract:
  We consider a Wilson-Dirac operator with improved chiral properties. We show
that, for arbitrarily rough gauge fields, it satisfies the index theorem if we
identify the zero modes with the small real eigenvalues of the fermion operator
and use the geometrical definition of topological charge. This is also
confirmed in a numerical study of the quenched Schwinger model. These results
suggest that integer definitions of the topological charge based on counting
real modes of the Wilson operator are equivalent to the geometrical definition.
The problem of exceptional configurations and the sign problem in simulations
with an odd number of dynamical Wilson fermions are briefly discussed.


title:
High-statistics finite size scaling analysis of U(1) lattice gauge
  theory with Wilson action

abstract:
  We describe the results of a systematic high-statistics Monte-Carlo study of
finite-size effects at the phase transition of compact U(1) lattice gauge
theory with Wilson action on a hypercubic lattice with periodic boundary
conditions. We find unambiguously that the critical exponent nu is lattice-size
dependent for volumes ranging from 4^4 to 12^4. Asymptotic scaling formulas
yield values decreasing from nu(L >= 4) = 0.33 to nu(L >= 9) = 0.29. Our
statistics are sufficient to allow the study of different phenomenological
scenarios for the corrections to asymptotic scaling. We find evidence that
corrections to a first-order transition with nu=0.25 provide the most accurate
description of the data. However the corrections do not follow always the
expected first-order pattern of a series expansion in the inverse lattice
volume V^{-1}. Reaching the asymptotic regime will require lattice sizes
greater than L=12. Our conclusions are supported by the study of many cumulants
which all yield consistent results after proper interpretation.


title: Structure of the QCD Vacuum As Seen By Lattice Simulations

abstract:
  This talk is a review of our studies of instantons and their properties as
seen in our lattice simulations of SU(2) gauge theory. We have measured the
topological susceptibility and the size distribution of instantons in the QCD
vacuum.
  We have also investigated the properties of quarks moving in instanton
background field configurations, where the sizes and locations of the
instantons are taken from simulations of the full gauge theory. By themselves,
these multi-instanton configurations do not confine quarks, but they induce
chiral symmetry breaking.