title: Equation of state for pure SU(3) gauge theory with RG improved action

abstract:
  We present results for the equation of state for pure SU(3) gauge theory
obtained with a renormalization-group (RG) improved action. The energy density
and pressure are calculated on a $16^3\times 4$ and a $32^3\times 8$ lattice
employing the integral method. Extrapolating the results to the continuum
limit, we find the energy density and pressure to be in good agreement with
those obtained with the standard plaquette action within the error of 3-4%.


title: Reconstructing the conformal mode in simplicial gravity

abstract:
  We verify that summing 2D DT geometries correctly reproduces the Polyakov
action for the conformal mode, including all ghost contributions, at large
volumes. The Gaussian action is reproduced even for central charges greater
than one lending strong support to the hypothesis that the space of all
possible dyamical triangulations approximates well the space of physically
distinct metrics independent of the precise nature of the matter coupling.


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

abstract:
  We study finite-temperature phase transition and equation of state for
two-flavor QCD at $N_t=4$ using an RG-improved gauge action and a
meanfield-improved clover quark action. The pressure is computed using the
integral method. The O(4) scaling of chiral order parameter is also examined.


title: Semileptonic Decays of Heavy Mesons with the Fat Clover Action

abstract:
  We are studying a variety of semileptonic decays of heavy-light mesons in an
effort to improve the determination of the heavy-quark Standard-Model CKM
matrix elements. Our fermion action is a novel, improved ``fat'' clover action
that promises to reduce problems with exceptional configurations. Dynamical sea
quarks are included in a mixed approach, i.e. we use staggered sea quarks and
fat-clover valence quarks. Here we report preliminary results.


title: Pure SU(3) Potentials

abstract:
  The string tensions for fundamental and a variety of representations:
adjoint, 6, 10, 15-symmetric, 15-antisymmetric, and 27 have been measured in
pure gauge SU(3). The calculations have been done on anisotropic lattices,
using an $O(a^2)$ tadpole improved action. A range of lattice spacings and
lattice sizes has been used to control finite volume and finite lattice spacing
effects. Potentials between quarks in various representations have also been
calculated with the fat center vortices model. At intermediate distances, the
results show approximate Casimir scaling. From my lattice calculations, no
color screening has been observed so far, even for distances as large as about
2.5 fm.


title: First Signs for String Breaking in Two-Flavor QCD

abstract:
  We have been examining the phenomenon of string breaking in QCD with two
flavors of dynamical staggered quarks. We construct a transfer matrix from a
combination of ``string'' and ``two-meson'' channels. Preliminary results with
low statistics show the expected signs of string breaking.


title: Landau-Ginsberg Theory of Quark Confinement

abstract:
  We describe the SU(3) deconfinement transition using Landau-Ginsberg theory.
Drawing on perturbation theory and symmetry principles, we construct the free
energy as a function of temperature and the Polyakov loop. Once the two
adjustable parameters of the model are fixed, the pressure p, energy epsilon
and Polyakov loop expectation value P_F are calculable functions of
temperature. An excellent fit to the continuum extrapolation of lattice
thermodynamics data can be achieved. In an extended form of the model, the
glueball potential is responsible for breaking scale invariance at low
temperatures. Three parameters are required, but the glueball mass and the
gluon condensate are calculable functions of temperature, along with p, epsilon
and P_F.


title: Simulations of Protein Folding

abstract:
  We have developed a simple, phenomenological, Monte-Carlo code that predicts
the three-dimensional structure of globular proteins from the DNA sequences
that define them. We have applied this code to two small proteins, the villin
headpiece (1VII) and cole1 rop (1ROP). Our code folds both proteins to within 5
A rms of their native structures.

categories: hep-lat cond-mat.soft physics.bio-ph q-bio.BM


title: Global anomalies in Chiral Lattice Gauge Theory

abstract:
  As first realized by Witten an SU(2) gauge theory coupled to a single Weyl
fermion suffers from a global anomaly. This problem is addressed here in the
context of the recent developments on chiral gauge theories on the lattice. We
find Witten's anomaly manifests in the impossibility of defining globally a
fermion measure that reproduces the proper continuum limit. Moreover, following
Witten's original argument, we check numerically the crossing of the lowest
eigenvalues of Neuberger's operator along a path connecting two gauge fields
that differ by a topologically non-trivial gauge transformation.


title: Light Quark Masses from Lattice Quark Propagators at Large Momenta

abstract:
  We compute non-perturbatively the average up-down and strange quark masses
from the large momentum (short-distance) behaviour of the quark propagator in
the Landau gauge. This method, which has never been applied so far, does not
require the explicit calculation of the quark mass renormalization constant.
Calculations were performed in the quenched approximation, by using
O(a)-improved Wilson fermions. The main results of this study are
ml^RI(2GeV)=5.8(6)MeV and ms^RI(2GeV)=136(11)MeV. Using the relations between
different schemes, obtained from the available four-loop anomalous dimensions,
we also find ml^RGI=7.6(8)MeV and ms^RGI=177(14)MeV, and the MSbar-masses,
ml^MS(2GeV)=4.8(5)MeV and ms^MS(2GeV)=111(9)MeV.


title: Perturbation Theory for Fat-link Fermion Actions

abstract:
  We discuss weak coupling perturbation theory for lattice actions in which the
fermions couple to smeared gauge links. The normally large integrals that
appear in lattice perturbation theory are drastically reduced. Even without
detailed calculation, it is easy to determine to good accuracy the scale of the
logarithms that appear in cases where an anomalous dimension is present. We
describe several 1-loop examples for fat-link Wilson and clover fermions.
including the additive mass shift, the relation between the lattice and MSbar
quark masses, and the axial current renormalization factor ($Z_A$) for
light-light and static-light currents.


title: Scaling of magnetic monopoles in the pure compact QED

abstract:
  In the pure U(1) lattice gauge theory with the Villain action we find that
the monopole mass in the Coulomb phase and the monopole condensate in the
confinement phase scale according to simple power laws. This holds outside the
coupling region in which on finite toroidal lattices the metastability
phenomena occur. A natural explanation of the observed accuracy of the scaling
behaviour would be the second order of the phase transition between both phases
in the general space of couplings not far away from the Villain action.


title: Perturbative and Non-perturbative Corrections to $B\to D^{(*)}l\nu$

abstract:
  It is shown that certain double ratios introduced for computing semileptonic
form factors are accurate to order $1/m_Q^2$, even when the action and current
are accurate to order $1/m_Q$.


title: Pseudoscalar Vertex and Quark Masses

abstract:
  We analyse available data on the quark pseudoscalar vertex and extract the
contribution og the Goldstone boson pole. The strength of the pole is found to
be quite large at presently accessible scales. We draw the important
consequences of this finding for the various definitions of quark masses.


title: Improved flavor symmetry in Kogut-Susskind fermion actions

abstract:
  We study improved Kogut-Susskind fermion actions focusing on flavor symmetry
restoration. Several variants of fat actions suitable for dynamical simulations
are considered, including an action with no tree level order a-squared errors.
The spectrum of all the pions is computed and used as a measure of flavor
symmetry violation. Finally, the Naik term is introduced to restore rotational
symmetry.


title: Glueballs and Hybrids (Gluons as Constituents)

abstract:
  After a brief introduction to hybrid and glueball source operators, I
summarize recent lattice results for these particles.


title:
On a possibility of adjoint colored states condensation at finite
  temperatures in lattice gauge model

abstract:
  Cooled down and diluted quark-gluon matter is considered. A possibility of
condensation of multiquark clusters with zero N-alities is discussed.


title: Partially Quenched QCD with Non-Degenerate Dynamical Quarks

abstract:
  We discuss the importance of using partially quenched theories with three
degenerate quarks for extrapolating to QCD, and present some relevant results
from chiral perturbation theory.


title: Testing m(up)=0 on the Lattice

abstract:
  A massless up quark is an intriguing solution to the strong CP problem. We
discuss how lattice computations can be used in conjunction with chiral
perturbation theory to address the consistency of $m_u=0$ with the observed
hadron spectrum and interactions. It is not necessary to simulate very light
quarks-three flavor partially quenched computations with comparable sea and
valence quark masses on the order of the strange quark mass could suffice.


title: Non-perturbative improvement of bilinears in unquenched QCD

abstract:
  We describe how the improvement of quark bilinears generalizes from quenched
to unquenched QCD, and discuss which of the additional improvement constants
can be determined using Ward Identities.


title:
The parity partner of the nucleon in quenched QCD with domain wall
  fermions

abstract:
  We present preliminary results for the mass spectrum of the nucleon and its
low-lying excited states from quenched lattice QCD using the domain wall
fermion method which preserves the chiral symmetry at finite lattice cutoff.
Definite mass splitting is observed between the nucleon and its parity partner.
This splitting grows with decreasing valence quark mass. We also present
preliminary data regarding the first positive-parity excited state.


title: Quantum Theory with Many Degrees of Freedom from Monte Carlo Hamiltonian

abstract:
  With our recently proposed effective Hamiltonian via Monte Carlo, we are able
to compute low energy physics of quantum systems. The advantage is that we can
obtain not only the spectrum of ground and excited states, but also wave
functions. The previous work has shown the success of this method in
(1+1)-dimensional quantum mechanical systems. In this work we apply it to
higher dimensional systems.


title: Mass Determination from Constraint Effective Potential

abstract:
  The Constraint Effective Potential (CEP) allows a determination of the mass
and other quantities directly, without relying upon asymptotic correlator
decays. We report and discuss the results of some mass calculations in
$(\lambda \Phi^4)_4$, obtained from CEP and our improved version of CEP (ICEP).


title:
Effective Mass Generation of Off-diagonal Gluons and Abelian Dominance
  in the Maximally Abelian Gauge in QCD

abstract:
  We study the properties of gluons in QCD in the maximally abelian (MA) gauge.
In the MA gauge, the off-diagonal gluon behaves as the massive vector boson
with the mass $\Meff \simeq 1.2 {\rm GeV}$, and therefore the off-diagonal
gluon cannot carry the long-range interaction for $r \gg \Meff^{-1} \simeq 0.2$
fm. The essence of the infrared abelian dominance in the MA gauge is physically
explained with the generation of the off-diagonal gluon mass $\Meff \simeq 1.2
{\rm GeV}$ induced by the MA gauge fixing, and the off-diagonal gluon mass
generation would predict general infrared abelian dominance in QCD in the MA
gauge. We report also the off-diagonal gluon propagator at finite temperature.


title: High temperature meson propagators with domain-wall quarks

abstract:
  We study the chiral properties of domain-wall quarks at high temperatures on
an ensemble of quenched configurations. Low lying eigenmodes of the Dirac
operator are calculated and used to check the extent to which the Atiyah-Singer
index theorem is obeyed on lattices with finite $N_5$. We calculate the
connected and disconnected screening propagators for the lowest mass scalar and
pseudoscalar mesons in the sectors of different topological charge and note
that they behave as expected. Separating out the would-be zero eigenmodes
enables us to accurately estimate the disconnected propagators with far less
effort than would be needed otherwise.


title: Low energy physics from the QCD Schr\"odinger functional

abstract:
  We review recent work by the ALPHA and UKQCD Collaborations where masses and
matrix elements were computed in lattice QCD using Schr\"odinger functional
boundary conditions and where the strange quark mass was determined in the
quenched approximation. We emphasize the general concepts and our strategy for
the computation of quark masses.


title: The lattice SU(2) confining string as an Abrikosov vortex

abstract:
  Numerical data for the SU(2) confining string in the maximal abelian
projection are analysed. The distribution of the electric flux and monopole
currents are perfectly described by the classical equations of motion for the
dual Abelian Higgs model. The mass of the vector boson is equal to the mass of
the monopole (Higgs particle) within numerical errors. The classical energy per
unit length of the Abrikosov vortex reproduces 94% of the full non-Abelian
string tension.


title: Determination of Vub from B->pi l nu on the lattice

abstract:
  We present results of a lattice study of the form factors in the decay B-> pi
l nu. We attempt to disentangle the the dependence of the form factors on the
light quark masses and the momentum transfer. Using models of the q^2
dependence we calculate the total decay rate, and compare to the experimental
measure to extract Vub. This study was performed in the quenched approximation
at beta=6.2 on a 24^3 X 48 lattice, with a non-perturbatively improved SW
fermion action.


title: Quark masses using domain wall fermions

abstract:
  Due to the attractive features that domain wall fermions possess with respect
to chiral symmetry, we continue our investigation of the light quark masses
with this discretization. Achieving reliable results, especially for $(m_u +
m_d)/2$, requires strict control of systematic uncertainties. Our present
results were obtained on a quenched $\beta =6.0$ lattice with spatial volume
$\approx (1.5~{\rm fm})^3$. Consequently we remark on effects of finite volume
as well as finite extent in the fictitious fifth dimension. We compute the
renormalization factors nonperturbatively and compare to the one--loop
perturbative result.


title: A perfect monopole action for SU(2) QCD

abstract:
  We found a quantum perfect lattice action in the 4-dimensional monopole
current theory which is known as an effective theory in the infrared region of
QCD. The perfect monopole action is transformed exactly into a lattice action
of a string model. When the monopole interactions are weak as in the case of
infrared SU(2) QCD, the string interactions are strong. The static potential
and the string tension in this region can be estimated analytically by the use
of the strong coupling expansion.


title:
String tension and glueball masses of SU(2) QCD from perfect action for
  monopoles and strings

abstract:
  We study the perfect monopole action as an infrared effective theory of SU(2)
QCD. It is transformed exactly into a lattice string model. Since the monopole
interactions are weak in the infrared SU(2) QCD, the string interactions become
strong. The strong coupling expansion of string model shows the quantum
fluctuation is small. The classical string tension is estimated analytically,
and we see it is very close to the quantum one in the SU(2) QCD. We also
discuss how to calculate the glueball mass in our model.


title: Recent topics of infrared effective lattice QCD

abstract:
  Three topics concerning infrared effective lattice QCD are discussed.
(1)Perfect lattice action of infrared SU(3) QCD and perfect operators for the
static potential are analytically given when we assume two-point monopole
interactions alone. The assumption seems to be justified from numerical
analyses of pure SU(3) QCD in maximally abelian gauge. (2)Gauge invariance of
monopole dominance can be proved theoretically if the gauge invariance of
abelian dominance is proved. The gauge invariance of monopole condensation
leads us to confinement of abelian neutral but color octet states after abelian
projection. (3)A stochastic gauge fixing method is developed to study the gauge
dependence of the Abelian projection, which interpolates between the maximally
abelian (MA) gauge and no gauge fixing. Abelian dominance for the heavy quark
potential holds even in the gauge which is far from Maximally Abelian one.


title:
Composite operators from the operator product expansion: what can go
  wrong?

abstract:
  The operator product expansion is used to compute the matrix elements of
composite renormalized operators on the lattice. We study the product of two
fundamental fields in the two-dimensional sigma-model and discuss the possible
sources of systematic errors. The key problem turns out to be the violation of
asymptotic scaling.


title: P-wave heavy-light mesons using NRQCD and D234

abstract:
  The masses of S- and P-wave heavy-light mesons are computed in quenched QCD
using a classically and tadpole-improved action on anisotropic lattices. Of
particular interest are the splittings among P-wave states, which have not yet
been resolved experimentally; even the ordering of these states continues to be
discussed in the literature. The present work leads to upper bounds for these
splittings, and is suggestive, but not conclusive, about the ordering.


title: Non-Perturbative Renormalisation using Domain Wall Fermions

abstract:
  The viability of the Non-Perturbative Renormalisation (NPR) method of the
Rome/Southampton group is studied, for the first time, in the context of domain
wall fermions. The procedure is used to extract the renormalisation
coefficients of the various quark bilinears, as well as the four-fermion
operators relevant to the $\Delta S=2$ effective Hamiltonian. The
renormalisation of the $\Delta S=1$ Hamiltonian is also discussed.


title: $K -> \pi \pi$ and $\epsilon^\prime/\epsilon$ using domain wall fermions

abstract: This paper has been withdrawn.


title: Baryon Mass Extrapolation

abstract:
  Consideration of the analytical properties of pion-induced baryon
self-energies leads to new functional forms for the extrapolation of light
baryon masses. These functional forms reproduce the leading non-analytic
behavior of chiral perturbation theory, the correct heavy-quark limit and have
the advantage of containing information on the extended structure of hadrons.
The forms involve only three unknown parameters which may be optimized by
fitting to present lattice data. Recent dynamical fermion results from CP-PACS
and UK-QCD are extrapolated using these new functional forms. We also use these
functions to probe the limit of the chiral perturbative regime and shed light
on the applicability of chiral perturbation theory to the extrapolation of
present lattice QCD results.


title: Improved Landau Gauge Fixing and Discretisation Errors

abstract:
  Lattice discretisation errors in the Landau gauge condition are examined. An
improved gauge fixing algorithm in which order a^2 errors are removed is
presented. Order a^2 improvement of the gauge fixing condition displays the
secondary benefit of reducing the size of higher-order errors. These results
emphasise the importance of implementing an improved gauge fixing condition.


title: Multicanonical hybrid Monte Carlo for compact QED

abstract:
  We demonstrate that substantial progress can be achieved in the study of the
phase structure of 4-dimensional compact QED by a joint use of hybrid Monte
Carlo and multicanonical algorithms, through an efficient parallel
implementation. This is borne out by the observation of considerable speedup of
tunnelling between the metastable states, close to the phase transition, on the
Wilson line. Our approach leads to a general parallelization scheme for the
efficient stochastic sampling of systems where (a part of) the Hamiltonian
involves the total action or energy in each update step.


title: Recent results on self-dual configurations on the torus

abstract:
  We review the recent progress on our understanding of self-dual SU(N)
Yang-Mills configurations on the torus.


title: N=1 Super Yang-Mills on the Lattice in the Strong Coupling Limit

abstract:
  We study the N=1 supersymmetric SU(N) Yang-Mills theory on the lattice at
strong coupling. We analyse and discuss the recent results obtained at strong
coupling and large N for the mesonic and fermionic propagators and spectrum.


title: New tests of the gauge-fixing approach to lattice chiral gauge theories

abstract:
  We report on recent progress with the gauge-fixing approach to lattice chiral
gauge theories. The bosonic sector of the gauge-fixing approach is studied with
fully dynamical U(1) gauge fields. We demonstrate that it is important to
formulate the Lorentz gauge-fixing action such that the dense set of lattice
Gribov copies is removed, and the gauge-fixing action has a unique absolute
minimum. We then show that the spectrum in the continuum limit contains only
the desired massless photon, as expected.


title: Order a improved renormalization constants

abstract:
  We impose the axial and vector Ward identities on local fermion bilinear
operators in the Sheikholesalami-Wohlert discretization of fermions. From this
we obtain all the coefficients needed to improve the theory at O(a), as well as
the scale and scheme independent renormalization constants, Z_A, Z_V and
Z_S/Z_P.


title:
The flavour and quark mass dependence of thermodynamic quantities in
  lattice QCD

abstract:
  The dependence of thermodynamic properties of QCD on the number of quark
flavours is investigated. Lattice results for the equation of state are
presented for 2, 2+1 and 3 quark flavours. The simulations have been performed
with the improved p4-staggered fermion and a Symanzik improved gluon action on
lattices of size 16^3 x 4


title: QCD hadron spectrum with domain wall fermions

abstract:
  We present the QCD hadron spectrum for the cases of both quenched and
two-flavor dynamical domain wall fermions. We compare the results obtained
using the Wilson gauge action and a renormalization group improved gauge
action. Finite volume effects and the dependence on the finite extent of the
fifth dimension are discussed.


title:
Scale Determination Using the Static Potential with Two Dynamical Quark
  Flavors

abstract:
  We study the static potential using gauge configurations that include the
effects of two flavors of dynamical Kogut-Susskind quarks. The configurations,
generated by the MILC collaboration, and used to study the spectrum and
heavy-light decay constants, cover a range $5.3 \le 6/g^2 \le 5.6$. There are
at least four quark masses for each coupling studied. Determination of $r_0$
from the potential can be used to set a scale. This alternative scale is useful
to study systematic errors on the spectrum and decay constants.


title: Meron-Cluster Solution of Fermion and Other Sign Problems

abstract:
  Numerical simulations of numerous quantum systems suffer from the notorious
sign problem. Important examples include QCD and other field theories at
non-zero chemical potential, at non-zero vacuum angle, or with an odd number of
flavors, as well as the Hubbard model for high-temperature superconductivity
and quantum antiferromagnets in an external magnetic field. In all these cases
standard simulation algorithms require an exponentially large statistics in
large space-time volumes and are thus impossible to use in practice.
Meron-cluster algorithms realize a general strategy to solve severe sign
problems but must be constructed for each individual case. They lead to a
complete solution of the sign problem in several of the above cases.


title: Strongly Coupled QCD at Finite Baryon Density

abstract:
  The analytical results obtained in the infinite mass and strong coupling
limits of QCD are difficult to reconcile with the predictions of the Monomer
Dimer Polymer algorithm. We have reconsidered in detail the results obtained
with this simulation scheme and evidences of severe convergence problems are
presented for the SU(3) and SU(2) gauge group.


title:
Heavy-Light Decay Constants with Dynamical Gauge Configurations and
  Wilson or Improved Valence Quark Action

abstract:
  We describe a calculation of heavy-light decay constants including virtual
quark loop effects. We have generated dynamical gauge configurations at three
$\beta$ values using two flavors of Kogut-Susskind quarks with a range of
masses. These are analyzed with a Wilson valence quark action. Preliminary
results based on a ``fat-link'' clover valence quark action are also reported.
Results from the two methods differ by 30 to 50 MeV, which is presumably due to
significant - but as yet unobserved - lattice spacing dependence in one or both
of the approaches.


title: New Numerical Methods for Quantum Field Theories on the Continuum

abstract:
  The Source Galerkin Method is a new numerical technique that is being
developed to solve Quantum Field Theories on the continuum. It is not based on
Monte Carlo techniques and has a measure to evaluate relative errors. It
promises to increase the accuracy and speed of calculations, and takes full
advantage of symmetries of the theory. The application of this method to the
non-linear sigma model is outlined.


title: Physical Effects of Infrared Quark Eigenmodes in LQCD

abstract:
  A truncated determinant algorithm is used to study the physical effects of
the quark eigenmodes associated with eigenvalues below 400 MeV. This initial
study focuses on coarse lattices (with O(a^2) improved gauge action), light
internal quark masses and large physical volumes. Four bellwether full QCD
processes are discussed: topological charge distributions, the eta prime
propagator, string breaking as observed in the static energy and the rho decay
into two pions.


title: Topology in QCD

abstract:
  I review recent (and some not so recent) results on the topological
susceptibility (with and without fermions), the eta-prime mass, topology and
chiral symmetry breaking, vacuum topological structure, and the possible role
of instantons in confinement.


title: SU(4) pure-gauge phase structure and string tensions

abstract:
  We present numerical evidence that the SU(4) pure-gauge dynamics has a
finite-temperature first-order phase transition. For a $6\times 20^3$ lattice,
this transition occurs at the inverse-square coupling of $8/g^2 \sim 10.79$.
Below this and above the known bulk phase transition at $8/g^2 \sim 10.2$ is a
confined phase in which we find two different string tensions, one between the
fundamental 4 and $4^*$ representations and the other between the self-dual
diquark 6 representations. The ratio of these two is about 1.5. The correlation
in the adjoint representation suggests no string forms between adjoint charges.


title: The Isgur Wise function from the Lattice

abstract:
  We derive the form factors relevant for decays of pseudo-scalar mesons
corresponding to the semi-leptonic decay B->D l nu. The simulations are
performed in the quenched approximation at beta=6.0 and beta=6.2 using a
non-perturbatively improved clover action. The slope of the Isgur Wise function
and |Vcb| are extracted from the form factors.


title: High-density QCD: the effects of strangeness

abstract:
  I discuss the zero temperature phase diagram of QCD, as a function of baryon
density and strange quark mass. The noteworthy points are that at sufficiently
high density chiral symmetry is always restored, and at low strange quark mass
there need be no phase transition between nuclear matter and quark matter. I
comment on the possibility that introducing a strange quark may make it easier
to see finite-density physics on the lattice.


title: Chiral Effects of Quenched Eta-Prime Loops

abstract:
  Preliminary results of a study of quenched chiral logarithms at beta=5.7 are
presented. Four independent determinations of the quenched chiral log parameter
delta are obtained. Two of these are from estimates of the eta-prime mass, one
from the residue of the hairpin diagram and the other from the topological
susceptibility combined with the Witten-Veneziano formula. The other two
determinations of delta are from measurement of virtual eta-prime loop effects
in mpi^2 vs. quark mass and in the chiral behavior of the pseudoscalar decay
constant. All results are consistent with delta=.080(15). The expected absence
of quenched chiral logs in the axial-vector decay constant is also observed.


title: Crossing the c=1 barrier in 2d Lorentzian quantum gravity

abstract:
  In an extension of earlier work we investigate the behaviour of
two-dimensional Lorentzian quantum gravity under coupling to a conformal field
theory with c>1. This is done by analyzing numerically a system of eight Ising
models (corresponding to c=4) coupled to dynamically triangulated Lorentzian
geometries. It is known that a single Ising model couples weakly to Lorentzian
quantum gravity, in the sense that the Hausdorff dimension of the ensemble of
two-geometries is two (as in pure Lorentzian quantum gravity) and the matter
behaviour is governed by the Onsager exponents. By increasing the amount of
matter to 8 Ising models, we find that the geometry of the combined system has
undergone a phase transition. The new phase is characterized by an anomalous
scaling of spatial length relative to proper time at large distances, and as a
consequence the Hausdorff dimension is now three. In spite of this qualitative
change in the geometric sector, and a very strong interaction between matter
and geometry, the critical exponents of the Ising model retain their Onsager
values. This provides evidence for the conjecture that the KPZ values of the
critical exponents in 2d Euclidean quantum gravity are entirely due to the
presence of baby universes. Lastly, we summarize the lessons learned so far
from 2d Lorentzian quantum gravity.


title: Distribution of fermionic and topological observables on the lattice

abstract:
  We analyze the topological and fermionic vacuum structure of four-dimensional
QCD on the lattice by means of correlators of fermionic observables and
topological densities. We show the existence of strong local correlations
between the topological charge and monopole density on the one side and the
quark condensate, charge and chiral density on the other side. Visualization of
individual gauge configurations demonstrates that instantons (antiinstantons)
carry positive (negative) chirality, whereas the quark charge density
fluctuates in sign within instantons.


title: Numerical Stability of Lanczos Methods

abstract:
  The Lanczos algorithm for matrix tridiagonalisation suffers from strong
numerical instability in finite precision arithmetic when applied to evaluate
matrix eigenvalues. The mechanism by which this instability arises is well
documented in the literature. A recent application of the Lanczos algorithm
proposed by Bai, Fahey and Golub allows quadrature evaluation of inner products
of the form $\psi^\dagger g(A) \psi$. We show that this quadrature evaluation
is numerically stable and explain how the numerical errors which are such a
fundamental element of the finite precision Lanczos tridiagonalisation
procedure are automatically and exactly compensated in the Bai, Fahey and Golub
algorithm. In the process, we shed new light on the mechanism by which roundoff
error corrupts the Lanczos procedure


title: Effects of Topology in the Dirac Spectrum of Staggered Fermions

abstract:
  We compare the lower edge spectral fluctuations of the staggered lattice
Dirac operator for the Schwinger model with the predictions of chiral Random
Matrix Theory (chRMT). We verify their range of applicability, checking in
particular the role of non-trivial topological sectors and the flavor symmetry
of the staggered fermions for finite lattice spacing. Approaching the continuum
limit we indeed find clear signals for topological modes in the eigenvalue
spectrum. These findings indicate problems in the verification of the chRMT
predictions.


title: Heavy Quarkonia from Anisotropic and Isotropic Lattices

abstract:
  We report on recent results for the spectrum of heavy quarkonia. Using coarse
and anisotropic lattices we achieved an unprecedented control over statistical
and systematic errors for higher excited states such as exotic hybrid states.
In a parallel study on isotropic lattices we also investigate the effect of two
dynamical flavours on the spin structure of charmonium and bottomonium for
several symmetric lattices.


title: Choice of Integrator in the Hybrid Monte Carlo Algorithm

abstract:
  We study efficiency of higher order integrator schemes for the hybrid Monte
Carlo (HMC) algorithm. Numerical tests are performed for Quantum Chromo
Dynamics (QCD) with two flavors of Wilson fermions. We compare 2nd, 4th and 6th
order integrators at various quark masses. The performance depends on both
volume and quark mass. On currently accessible large lattices ($V \sim 24^4$),
higher order integrators can be more efficient than the 2nd order one only in
heavy quark region, $m_q a > 0.3$. Thus we conclude that for most full QCD
simulations, except for heavy quark case, the usual 2nd order integrator is the
best choice.


title: On the eta-invariant in the four dimensional chiral U(1) theory

abstract:
  The imaginary part of the effective action is investigated in the 4D chiral
U(1) theory using the CFA.


title: B decays on the lattice

abstract:
  I review recent developments in lattice calculations of B decay matrix
elements and other related quantities.


title: Spectral Functions of Hadrons in Lattice QCD

abstract:
  Using the maximum entropy method, spectral functions of the pseudo-scalar and
vector mesons are extracted from lattice Monte Carlo data of the imaginary time
Green's functions. The resonance and continuum structures as well as the ground
state peaks are successfully obtained. Error analysis of the resultant spectral
functions is also given on the basis of the Bayes probability theory.


title: NNLO unquenched calculation of the b quark mass

abstract:
  By combining the first unquenched lattice computation of the B-meson binding
energy with the recently calculated two-loop contribution to the lattice HQET
mass, we determine the $\bar{MS}$ b-quark mass, $\bar{m}_{b}(\bar{m}_{b})$ at
the NNLO. We find $\bar{m}_{b}(\bar{m}_{b}) = (4.26\pm 0.03 \pm 0.04 \pm 0.05)
{\rm GeV}$. The inclusion of the two-loop effects is one of the steps necessary
to extract $\bar{m}_{b}(\bar{m}_{b})$ with a precision better than ${\cal
O}(\Lambda_{QCD})$, which is the uncertainty due to the presence of an IR
renormalon singularity in the perturbative series of the residual mass. Our
results have been obtained on a sample of 60 lattices of size $24^{3}\times 40$
at $\beta=5.6$, using the unquenched Wilson action with two degenerate sea
quarks. The quark propagators have been computed using the unquenched links
generated by the T$\chi$L Collaboration.


title:
Z2 Monopoles, Vortices, and the Deconfinement Transition in Mixed Action
  SU(2) Gauge Theory

abstract:
  Adding separate chemical potentials lambda and gamma for Z2 monopoles and
vortices respectively in the Villain form of the mixed fundamental-adjoint
action for the SU(2) lattice gauge theory, we investigate their role in the
interplay between the deconfinement and bulk phase transitions using Monte
Carlo techniques. Setting lambda to be nonzero, we find that the line of
deconfinement transitions is shifted in the coupling plane but it behaves
curiously also like the bulk transition line for large enough adjoint coupling,
as for lambda=0. In a narrow range of couplings, however, we find separate
deconfinement and bulk phase transitions on the same lattice for nonzero and
large lambda, suggesting the two to be indeed coincident in the region where a
first order deconfinement phase transition is seen. In the limit of large
lambda and gamma, we obtain only lines of second order deconfinement phase
transitions, as expected from universality.


title: How well do domain wall fermions realize chiral symmetry?

abstract:
  In the domain wall fermion formulation, chiral symmetry breaking in full QCD
is expected to fall exponentially with the length of the extra dimension. We
measure the chiral symmetry breaking due to a finite extra dimension in two
ways, which can be affected differently by finite volume and explicit fermion
mass. For quenched QCD the two methods generally agree, except for the largest
extent of the extra dimension, which makes the limit uncertain. We have less
data for full QCD, but see exponential suppression for the method where we have
data.


title:
Calculation Of Hadronic Matrix Elements Relevant For Delta I=1/2 Rule
  And Epsilon-prime In Lattice QCD With Staggered Fermions

abstract:
  This thesis presents the setup and results of numerical calculation of
hadronic matrix elements of Delta S=1 weak operators, with the aim of studying
the Delta I=1/2 rule and direct CP violation. Such study provides a useful
comparison of the Standard Model predictions with experiment. We work within
the framework of (partially quenched) Lattice QCD with the staggered
(Kogut-Susskind) version of fermions. We have achieved a reasonable statistical
accuracy in calculating all matrix elements in question. Based on these
results, we find that the Delta I=1/2 channel in K to 2 Pi decays is enhanced
compared to the Delta I=3/2 channel. This is consistent with experiment,
although the exact amount of enhancement is subject to considerable systematic
errors. I also discuss the difficulties encountered in attempting to calculate
the direct CP violation parameter epsilon-prime and our approximate solution
leading to a crude estimate. In a related study we nonperturbatively compute
bilinear renormalization factors Z_S and Z_P, which are needed for our estimate
of epsilon-prime and also allow to calculate the light quark masses. For the
strange quark mass in NDR MS-bar scheme at 2 GeV in the quenched approximation
we find: m_s = 102.9 +/- 5.1 MeV.


title: The quark propagator in momentum space

abstract:
  The quark propagator is calculated in the Landau gauge at beta=6.0. A method
for removing the dominant, tree-level lattice artefacts is presented, enabling
a calculation of the momentum-dependent dynamical quark mass.


title: Propagators of hot SU(2) gauge theory from 3d adjoint Higgs model

abstract:
  We study propagators of the lattice 3d adjoint Higgs model, considered as an
effective theory of 4d SU(2) gauge theory at high temperature. The propagators
are calculated in so-called lambda-gauges. From the long distance behaviour of
the propagators we extract the screening masses. It is shown that the pole
masses extracted from the propagators agree well with the screening masses
obtained recently in finite temperature SU(2) theory. The gauge dependence of
the screening masses is also discussed.


title:
Gauge invariant field strength correlators from RG smoothing and color
  correlations between topological charge clusters

abstract:
  Using the renormalization group based smoothing technique we have studied the
gauge invariant field strength correlator at T\ne0 and T=0 in pure SU(2) gauge
theory. In conjunction with a cluster analysis, the field strength correlator
is used to study correlations between the clusters in space and color
orientation.


title: Chirality tubes along monopole trajectories

abstract:
  We classify the lattice by elementary 3-cubes which are associated to dual
links occupied by, or free of monopoles. We then compute the quark condensate,
the quark charge and the chiral density on those cubes. By looking at
distributions we demonstrate that monopole trajectories carry considerably more
chirality with respect to the free vacuum.


title: QCD on \alpha-Clusters

abstract:
  It is shown that the 21264 Alpha processor can reach about 20% sustained
efficiency for the inversion of the Wilson-Dirac operator. Since fast ethernet
is not sufficient to get balancing between computation and communication on
reasonable lattice- and system-sizes, an interconnection using Myrinet is
discussed. We find a price/performance ratio comparable with state-of-the-art
SIMD-systems for lattice QCD.


title: The second moment of the pion's distribution amplitude

abstract:
  We present preliminary results for the second moment of the pion's
distribution amplitude. The lattice formulation and the phenomenological
implications are briefly reviewed, with special emphasis on some subtleties
that arise when the Lorentz group is replaced by the hypercubic group. Having
analysed more than half of the available configurations, the result obtained is
\xi^2_L = 0.06 \pm 0.02.


title: Lattice Determination of the $B^\ast B \pi$ Coupling

abstract:
  The coupling $g_{B^\ast B \pi}$ is related to the form factor at zero
momentum of the axial current between $B^\ast$ and $B$ states. Moreover it is
related to the effective coupling between heavy mesons and pions that appear
the heavy meson chiral Lagrangian. This coupling has been evaluated on the
lattice using static heavy quarks and light quark propagators determined by a
stochastic inversion of the fermionic bilinear. We found the value
$g=0.42(4)(8)$. Beside its theoretical interest, this quantity has
phenomenological implications in $B \to \pi + \bar l l$ decays.


title: 1-Loop improved lattice action for the nonlinear sigma-model

abstract:
  In this paper we show the Wilson effective action for the 2-dimensional
O(N+1)-symmetric lattice nonlinear sigma-model computed in the 1-loop
approximation for the nonlinear choice of blockspin $\Phi(x)$, $\Phi(x)=
\Cav\phi(x)/{|\Cav\phi(x)|}$,where $\Cav$ is averaging of the fundamental field
$\phi(z)$ over a square $x$ of side $\tilde a$.
  The result for $S_{eff}$ is composed of the classical perfect action with a
renormalized coupling constant $\beta_{eff}$, an augmented contribution from a
Jacobian, and further genuine 1-loop correction terms. Our result extends
Polyakov's calculation which had furnished those contributions to the effective
action which are of order $\ln \tilde a /a$, where $a$ is the lattice spacing
of the fundamental lattice. An analytic approximation for the background field
which enters the classical perfect action will be presented elsewhere.


title: Chiral gauge theories on the lattice with exact gauge invariance

abstract:
  A recently proposed formulation of chiral lattice gauge theories is reviewed,
in which the locality and gauge invariance of the theory can be preserved if
the fermion representation of the gauge group is anomaly-free.


title: Wavelet-induced renormalization group for the Landau-Ginzburg model

abstract:
  The scale hierarchy of wavelets provides a natural frame for renormalization.
Expanding the order parameter of the Landau-Ginzburg/$\Phi^4$ model in a basis
of compact orthonormal wavelets explicitly exhibits the coupling between scales
that leads to non-trivial behavior. The locality properties of Daubechies'
wavelets enable us to derive the qualitative renormalization flow of the
Landau-Ginzburg model from Gaussian fluctuations in wavelet space.


title: Review on String Breaking - the Query in Quest of the Evidence

abstract:
  Considerable progress has been achieved recently in the observation of string
breaking within non-Abelian Higgs models, by use of multi-channel methods
allowing for broken string states. Similarly, in pure gauge theory this
approach has been shown to reveal string breaking for color charges in the
adjoint represaentation. For QCD with dynmical fermions, one needs substantial
progress in noise reduction, however, to render such techniques viable.


title: Lattice Gross-Neveu model with domain-wall fermions

abstract:
  We investigate the two-dimensional lattice Gross-Neveu model, using the
domain-wall fermion formulation, as a toy model of lattice QCD. We study
features of the phase diagram related to the mechanism of chiral symmetry
restoration, and find that the parity-broken phase (Aoki phase) exists for
finite extent in the extra dimension ($N_s$). We also find that O(a) scaling
violation terms vanishes in the limit of $N_s\to\infty$.


title: Lattice QCD with Domain-Wall Fermions

abstract:
  We study the quenched lattice QCD using domain-wall fermions at $\beta=6.0$.
Behaviors of both pion mass and the explicit breaking term in the axial
Ward-Takahashi identity support the existence of the chiral zero modes. We
observe a good agreement between the pion decay constants $f_\pi$ from both the
conserved axial current and the local current perturbatively renormalized at
1-loop. Finally the possible existence of the parity broken phase is also
examined in this model.


title:
Deriving exact results for Ising-like models from the cluster variation
  method

abstract:
  The cluster variation method (CVM) is an approximation technique which
generalizes the mean field approximation and has been widely applied in the
last decades, mainly for finding accurate phase diagrams of Ising-like lattice
models. Here we discuss in which cases the CVM can yield exact results,
considering: (i) one-dimensional systems and strips (in which case the method
reduces to the transfer matrix method), (ii) tree-like lattices and (iii) the
so-called disorder points of euclidean lattice models with competitive
interactions in more than one dimension.


title: Finite Volume Effects in Self Coupled Geometries

abstract:
  By integrating the pressure equation at the surface of a self coupled
curvilinear boundary, one may obtain asymptotic estimates of energy shifts,
which is especially useful in lattice QCD studies of nonrelativistic bound
states. Energy shift expressions are found for periodic (antiperiodic) boundary
conditions on antipodal points, which require Neumann (Dirichlet) boundary
conditions for even parity states and Dirichlet (Neumann) boundary conditions
for odd parity states. It is found that averaging over periodic and
antiperiodic boundary conditions is an effective way of removing the asymptotic
energy shifts from the boundary. Asymptotic energy shifts from boxes with self
coupled walls are also considered and shown to be effectively antipodal. The
energy shift equations are illustrated by the solution of the bounded harmonic
oscillator and hydrogen atoms.


title: Factorization of Fermion Doubles on the Lattice

abstract:
  We address the problem of the fermion species doubling on the Lattice. Our
strategy is to factorize the fermion doubles from the action. The mass term of
the Dirac-Wilson action is changed. In this case the extra roots which appear
in the action of free fermions in the moment representation are independent of
the mass and can be factorized from the fermion propagator. However the gauge
couplings suffer from the pathological ghost poles which are common to
non-local actions. This action can be used to find a solution of the Ginsparg
Wilson relation, which is cured from the non-local pathology. Finally we
compare this factorized action with solutions of The Ginsparg Wilson relation.
We find that the present is equivalent to the Zenkin action, and that is not
quite as local as the Neuberger action.


title: Lambda-parameter of lattice QCD with the overlap-Dirac operator

abstract:
  We compute the ratio $\Lambda_L/\Lambda_{\bar{MS}}$ between the scale
parameter $\Lambda_L$, associated with a lattice formulation of QCD using the
overlap-Dirac operator, and $\Lambda_{\bar{MS}}$ of the $\bar{\rm MS}$
renormalization scheme. To this end, the necessary one-loop relation between
the lattice coupling $g_0$ and the coupling renormalized in the $\bar{{\rm
MS}}$ scheme is calculated, using the lattice background field technique.


title:
$O(\alpha_{s}a)$ matching coefficients for axial vector current and
  $\Delta B$$=$2 operator

abstract:
  We present a calculation of the perturbative matching coefficients including
mixing with higher dimensional operators for the temporal component of the
heavy-light axial current, $A_{4}$, and the $\Delta B=2$ operator, $O_S$. For
$A_{4}^{\scriptsize static, NRQCD}$, calculations with various RG-improved
gauge actions are peformed. Matching coefficients with NRQCD and heavy-clover
actions are also compared.


title: Hadron masses and decay constants in quenched QCD

abstract:
  We present results for the mass spectrum and decay constants using
non-perturbatively O(a) improved Wilson fermions. Three values of $\beta$ and
30 different quark masses are used to obtain the chiral and continuum limits.
Special emphasis will be given to the question of taking the chiral limit and
the existence of non-analytic behavior predicted by quenched chiral
perturbation theory.


title:
The Phase Diagrams of the Schwinger and Gross-Neveu Models with Wilson
  Fermions

abstract:
  A new method to analytically determine the partition function zeroes of
weakly coupled theories on finite-size lattices is developed. Applied to the
lattice Schwinger model, this reveals the possible absence of a phase
transition at fixed weak coupling. We show how finite-size scaling techniques
on small or moderate lattice sizes may mimic the presence of a spurious phase
transition. Application of our method to the Gross-Neveu model yields a phase
diagram consistent with that coming from a saddle point analysis.


title: Electroweak Phase Transitions

abstract:
  Recent developments on the four dimensional (4d) lattice studies of the
finite temperature electroweak phase transition (EWPT) are summarized. The
phase diagram is given in the continuum limit. The finite temperature
SU(2)-Higgs phase transition is of first order for Higgs-boson masses m_H<66.5
+/- 1.4 GeV. Above this endpoint only a rapid cross-over can be seen. The full
4d result agrees completely with that of the dimensional reduction
approximation. The Higgs-boson endpoint mass in the Standard Model (SM) would
be 72.1 +/- 1.4 GeV. Taking into account the LEP Higgs-boson mass lower bound
excludes any EWPT in the SM. A one-loop calculation of the static potential in
the SU(2)-Higgs model enables a precise comparison between lattice simulations
and perturbative results. The most popular extension of the SM, the Minimal
Supersymmetric SM (MSSM) is also studied on 4d lattices.


title:
Renormalization constants of local operators within the Schr\"odinger
  functional scheme

abstract:
  We define, within the Schr\"odinger functional (SF) scheme, the matrix
elements of the twist-2 operators corresponding to the first two moments of
non-singlet parton density, and the first moment of singlet parton densities.
We perform a lattice one-loop calculation that fixes the relation between the
SF scheme and other common schemes and shows the main source of lattice
artefacts. Few remarks on the improvement case are added.


title: String breaking and lines of constant physics in the SU(2) Higgs model

abstract:
  We present results for the ground state and first excited state static
potentials in the confinement "phase" of the SU(2) Higgs model. String breaking
and the crossing of the energy levels are clearly visible. We address the
question of the cut-off effects in our results and observe a remarkable scaling
of the static potentials.


title:
The Heavy Hybrid Spectrum from NRQCD and the Born-Oppenheimer
  Approximation

abstract:
  The spectrum of heavy-quark hybrids is studied in the leading
Born-Oppenheimer (LBO) approximation and using leading-order NRQCD simulations
with an improved gluon action on anisotropic lattices. The masses of four
hybrid states are obtained from our simulations for lattice spacings 0.1 fm and
0.2 fm and are compared to the LBO predictions obtained using
previously-determined glue-excited static potentials. The consistency of
results from the two approaches reveals a compelling physical picture for
heavy-quark hybrid states.


title:
Large-q expansion of the correlation length in the two-dimensional
  q-state Potts model

abstract:
  The large-q expansions of the exponential correlation length and the second
moment correlation length for the q-state Potts model in two dimensions are
calculated at the first order phase transition point both in the ordered and
disordered phases. The expansion coefficients in the ordered and disordered
phases coincide in lower orders for both of the two types of the correlation
lengths, but they differ a little from each other in higher orders for the
second moment correlation length. The second largest eigenvalues of the
transfer matrix have the continuum spectrum both in the ordered and disordered
phases in the large-q region, which is suggested to be maintained even in the
limit of $q\to 4$ from the analysis of the expansion series.


title: On-shell and off-shell improvement for Ginsparg-Wilson fermions

abstract:
  We discuss the improvement of bilinear fermionic operators for
Ginsparg-Wilson fermions. We present explicit formulae for improved Green's
functions, which apply both on-shell and off-shell.


title:
Numerical Stochastic Perturbation Theory. Convergence and features of
  the stochastic process. Computations at fixed (Landau) Gauge

abstract:
  Concerning Numerical Stochastic Perturbation Theory, we discuss the
convergence of the stochastic process (idea of the proof, features of the limit
distribution, rate of convergence to equilibrium). Then we also discuss the
expected fluctuations in the observables and give some idea to reduce them. In
the end we show that also computation of quantities at fixed (Landau) Gauge is
now possible.


title:
Beta-function, Renormalons and the Mass Term from Perturbative Wilson
  Loops

abstract:
  Several Wilson loops on several lattice sizes are computed in Perturbation
Theory via a stochastic method. Applications include: Renormalons, the Mass
Term in Heavy Quark Effective Theory and (possibly) the beta-function.


title: Flavor Singlet Axial Coupling of the Proton - An Updated Analysis

abstract:
  We present a combined analysis of SESAM and TxL data for the flavor singlet
axial coupling G_A^1 of the proton, which is very helpful to stabilize the
disconnected signals at small quark masses.
  From connected and disconnected contributions we use the tadpole improved
renormalization constant Z_A and obtain G_A^1=0.21(12).


title: Connected Correlators in Random Geometries

abstract:
  We analyze correlation functions in a toy model of a random geometry
interacting with matter. We show that in general the connected correlator will
contain a long-range scaling part which is in some sense a remnant of the
disconnected part. This result supports the previously conjectured general form
of correlation functions. We discuss the interplay between matter and geometry
and the role of the symmetry in the matter sector.


title: The Weak-Coupling Limit of 3D Simplicial Quantum Gravity

abstract:
  We investigate the weak-coupling limit, kappa going to infinity, of 3D
simplicial gravity using Monte Carlo simulations and a Strong Coupling
Expansion. With a suitable modification of the measure we observe a transition
from a branched polymer to a crinkled phase. However, the intrinsic geometry of
the latter appears similar to that of non-generic branched polymer, probable
excluding the existence of a sensible continuum limit in this phase.


title: First results from the asymmetric O(a) improved Fermilab action

abstract:
  We present first results from calculations using O(a) improved (FNAL)
space-time asymmetric action on a 12^3 x 24 quenched lattice at \beta = 5.7 and
c_SW = 1.57. The asymmetry parameter is determined non-perturbatively from the
energy-momentum dispersion relation. This improvement scheme is mass dependent,
and the calculations have been done in the charm and bottom quark mass sectors
since it is at these heavier masses that the asymmetry is expected to be
relevant.


title: Quarks, Gluons and Frustrated Antiferromagnets

abstract:
  The Contractor Renormalization Group method (CORE) is used to establish the
equivalence of various Hamiltonian free fermion theories and a class of
generalized frustrated antiferromagnets. In particular, after a detailed
discussion of a simple example, it is argued that a generalized frustrated
SU(3) antiferromagnet whose single-site states have the quantum numbers of
mesons and baryons is equivalent to a theory of free massless quarks.
Furthermore, it is argued that for slight modification of the couplings which
define the frustrated antiferromagnet Hamiltonian, the theory becomes a theory
of quarks interacting with color gauge-fields.


title:
A lattice NRQCD computation of the bag parameters for $\Delta B$ = 2
  operators

abstract:
  We present an update of our NRQCD calculation of $B_B$ at $\beta$=5.9 with
increased statistics. We also discuss a calculation of $B_S$, which is relevant
to the width difference in the $B_s-\bar{B}_s$ mixing.


title: Glueball Mass Predictions of the Valence Approximation to Lattice QCD

abstract:
  We evaluate the infinite volume, continuum limit of glueball masses in the
valence (quenched) approximation to lattice QCD. For the lightest scalar and
tensor states we obtain masses of $1648 \pm 58$ MeV and $2267 \pm 104$ MeV,
respectively.


title: Scalar Quarkonium Masses and Mixing with the Lightest Scalar Glueball

abstract:
  We evaluate the continuum limit of the valence (quenched) approximation to
the mass of the lightest scalar quarkonium state for a range of different quark
masses and to the mixing energy between these states and the lightest scalar
glueball. Our results support the interpretation of $f_0(1710)$ as composed
mainly of the lightest scalar glueball.


title: Nucleon decay matrix elements with the Wilson quark action: an update

abstract:
  We present preliminary results of a new lattice computation of hadronic
matrix elements of baryon number violating operators which appear in the
low-energy effective Lagrangian of (SUSY-)Grand Unified Theories. The
contribution of irrelevant form factor which has caused an underestimate of the
matrix elements in previous studies is subtracted in this calculation. Our
results are 2$\sim$4 times larger than the most conservative values often
employed in phenomenological analyses of nucleon decay with specific GUT
models.


title: B and D semileptonic decays to light mesons

abstract:
  We present an update of our calculation of the form factors and partial
widths of semileptonic heavy-to-light meson decays, in the quenched
approximation. Our complete data set has now been analysed and our results
include chiral extrapolations and a study of the lattice spacing dependence.


title:
Monte Carlo Renormalization Group analysis of QCD in two dimensional
  coupling space

abstract:
  We report our results of the Monte Carlo Renormalization Group analysis in
two dimensional coupling space. The qualitative features of the RG flow are
described with a phenomenological RG equation. The dependence on the lattice
spacing for various actions provides the conditions to determine the parameters
entering the RG equation.


title:
How To Fix Non-Perturbatively A Parameter Dependent Covariant Gauge On
  The Lattice

abstract:
  We describe how to overcome some problems that usually prevent from obtaining
an efficient algorithm to fix a generic covariant gauge on the lattice. This
gauge is the lattice equivalent of the generic gauge usually adopted in
perturbative calculations. It depends on a parameter whose value can be varied
in order to check the gauge dependence of measured matrix elements.


title:
A further study of the possible scaling region of lattice chiral
  fermions

abstract:
  In the possible scaling region for an SU(2) lattice chiral fermion advocated
in {\it Nucl. Phys.} B486 (1997) 282, no hard spontaneous symmetry breaking
occurs and doublers are gauge-invariantly decoupled via mixing with composite
three-fermion-states that are formed by local multifermion interactions.
However the strong coupling expansion breaks down due to no ``static limit''
for the low-energy limit ($pa\sim 0$). In both neutral and charged channels, we
further analyze relevant truncated Green functions of three-fermion-operators
by the strong coupling expansion and analytical continuation of these Green
functions in the momentum space. It is shown that in the low-energy limit,
these relevant truncated Green functions of three-fermion-states with the
``wrong'' chiralities positively vanish due to the generalized form factors
(the wave-function renormalizations) of these composite three-fermion-states
vanishing as O((pa)^4) for $pa\sim 0$. This strongly implies that the composite
three-fermion-states with ``wrong'' chirality are ``decoupled'' in this limit
and the low-energy spectrum is chiral, as a consequence, chiral gauge
symmetries can be exactly preserved.


title: No-go theorem on spontaneous parity breaking revisited

abstract:
  An essential assumption in the Vafa and Witten's theorem on P and CT
realization in vector-like theories concerns the existence of a free energy
density in Euclidean space in the presence of any external hermitian symmetry
breaking source. We show how this requires the previous assumption that the
symmetry is realized in the vacuum. Even if Vafa and Witten's conjecture is
plausible, actually a theorem is still lacking.


title: Three and Two Colours Finite Density QCD at Strong Coupling: A New Look

abstract:
  Simulations in finite density, beta=0 lattice QCD by means of the
Monomer-Dimer-Polymer algorithm show a signal of first order transition at
finite temporal size. This behaviour agrees with predictions of the mean field
approximation, but is difficult to reconcile with infinite mass analytical
solution. The MDP simulations are considered in detail and severe convergence
problems are found for the SU(3) gauge group, in a wide region of chemical
potential. Simulations of SU(2) model show discrepancies with MDP results as
well.


title: End-to-end distribution function for dilute polymers

abstract:
  We study the end-to-end distribution function for dilute polymers. We present
a computation to order $O(\epsilon^2)$, $\epsilon = 4 - d$, and discuss in
detail its asymptotic behaviour for small and large distances. The theoretical
predictions are compared with Monte Carlo results, finding good agreement.


title:
Renormalization Group Invariant Matrix Elements of DS = 2 and DI = 3/2
  Four-Fermion Operators without Quark Masses

abstract:
  We introduce a new parameterization of four-fermion operator matrix elements
which does not involve quark masses and thus allows a reduction of systematic
uncertainties. In order to simplify the matching between lattice and continuum
renormalization schemes, we express our results in terms of renormalization
group invariant B-parameters which are renormalization-scheme and scale
independent. As an application of our proposal, matrix elements of DI=3/2 and
SUSY DS =2 operators have been computed. The calculations have been performed
using the tree-level improved Clover lattice action at two different values of
the strong coupling constant (beta=6/g^2=6.0 and 6.2), in the quenched
approximation. Renormalization constants and mixing coefficients of lattice
operators have been obtained non-perturbatively. Using lowest order ChiPT, we
also obtain <Pi Pi| O_7|K >^{NDR}_{I=2} = (0.11\pm 0.02) GeV^4 and <Pi Pi|
O_8|K >^{NDR}_{I=2} = (0.51\pm 0.05) GeV^4 at mu=2 GeV.


title:
Perturbative two- and three-loop coefficients from large beta Monte
  Carlo

abstract:
  Perturbative coefficients for Wilson loops and the static quark self-energy
are extracted from Monte Carlo simulations at large beta on finite volumes,
where all the lattice momenta are large. The Monte Carlo results are in
excellent agreement with perturbation theory through second order. New results
for third order coefficients are reported. Twisted boundary conditions are used
to eliminate zero modes and to suppress Z_3 tunneling.


title: Results and Perspectives in HEP, vis-a-vis Lattice QCD

abstract:
  I review in this presentation some aspects of phenomenology in High Energy
Physics which are related to recent and possibly future progress in lattice
QCD. In particular, I cover (i) the extraction of CKM matrix elements from B
physics, (ii) the determination of epsilon'/epsilon, as well as (iii) some
issues emerged in the physics of high energy jets produced in hadronic
collisions, where input from non-perturbative calculations would benefit our
capability to perform better theoretical predictions.


title: An Investigation of the Soft Pion Relation in Quenched Lattice QCD

abstract:
  A lattice determination of the form factor and decay constants for the
semileptonic decay of heavy pseudoscalar (PS) mesons at zero recoil is
presented from which the soft pion relation is satisfied. Chiral extrapolation
of the form factor is performed at constant $q^2$. Pole dominance is used to
extrapolate the form factor in heavy quark mass. At the B mass, the form factor
at zero recoil lies somewhat below the ratio of decay constants; the relation
remains satisfied within error.


title: Decays of Heavy Mesons

abstract:
  We present preliminary results for heavy to light transitions of pseudoscalar
mesons, induced by the vector and tensor operators. This lattice study is
performed in quenched approximation, by using the nonperturbatively improved
Wilson action and operators. We also update the values of the heavy-light meson
decay constants.


title: Quenched QCD with O(a) improvement: I. The spectrum of light hadrons

abstract:
  We present a comprehensive study of the masses of pseudoscalar and vector
mesons, as well as octet and decuplet baryons computed in O(a) improved
quenched lattice QCD. Results have been obtained using the non-perturbative
definition of the improvement coefficient c_sw, and also its estimate in
tadpole improved perturbation theory. We investigate effects of improvement on
the incidence of exceptional configurations, mass splittings and the parameter
J. By combining the results obtained using non-perturbative and tadpole
improvement in a simultaneous continuum extrapolation we can compare our
spectral data to experiment. We confirm earlier findings by the CP-PACS
Collaboration that the quenched light hadron spectrum agrees with experiment at
the 10% level.


title: Scaling and Eigenmode Tests of the Improved Fat Clover Action

abstract:
  We test a recently proposed improved lattice-fermion action, the fat link
clover action, examining indicators of pathological small-quark-mass lattice
artifacts ("exceptional configurations") on quenched lattices of spacing 0.12
fm and studying scaling properties of the light hadron spectrum for lattice
spacing a=0.09 and 0.16 fm. We show that the action apparently has fewer
problems with pathological lattice artifacts than the conventional
nonperturbatively improved clover action and its spectrum scales just as well.


title: SSOR preconditioning in simulations of the QCD Schr\"odinger functional

abstract:
  We report on a parallelized implementation of SSOR preconditioning for O(a)
improved lattice QCD with Schr\"odinger functional boundary conditions.
Numerical simulations in the quenched approximation at parameters in the light
quark mass region demonstrate that a performance gain of a factor $\sim$ 1.5
over even-odd preconditioning can be achieved.


title: Pushing NRQCD to the limit

abstract:
  Lattice NRQCD has proven successful in describing the physics of the upsilon
system and B-mesons, though some concerns arise when it is used in simulations
of charm quarks. It is certainly possible that the NRQCD expansion is not
converging fast enough at this scale. We present some preliminary results on
the low-mass breakdown of NRQCD, in particular the behaviour of heavy
quarkonium and heavy-light meson spectra as the bare heavy quark mass is
decreased well below 1, with the aim of understanding more about the
manifestation of this breakdown.


title: The B -> D* l nu Form Factor at Zero Recoil

abstract:
  We describe a model independent lattice QCD method for determining the
deviation from unity for h_{A1}(1), the B -> D* l nu form factor at zero
recoil. We extend the double ratio method previously used to determine the B ->
D l nu form factor. The bulk of statistical and systematic errors cancel in the
double ratios we consider, yielding form factors which promise to reduce
present theoretical uncertainties in the determination of V_{cb}. We present
results from a prototype calculation at a single lattice spacing corresponding
to beta=5.7.


title: Symmetry Breaking, Duality and Fine-Tuning in Hierarchical Spin Models

abstract:
  We discuss three questions related to the critical behavior of hierarchical
spin models: 1) the hyperscaling relations in the broken symmetry phase; 2) the
combined use of dual expansions to calculate the non-universal quantities; 3)
the fine-tuning issue in approximately supersymmetric models.


title: Potts Flux Tube Model at Nonzero Chemical Potential

abstract:
  We model the deconfinement phase transition in quantum chromodynamics at
nonzero baryon number density and large quark mass by extending the flux tube
model (three-state, three-dimensional Potts model) to nonzero chemical
potential. In a direct numerical simulation we confirm mean-field-theory
predictions that the deconfinement transition does not occur in a baryon-rich
environment.


title: A note on the solutions of the Ginsparg-Wilson relation

abstract: The role of R in the solutions of the Ginsparg-Wilson relation is discussed.


title:
Application of Noncommutative Differential Geometry on Lattice to
  Anomaly

abstract:
  The chiral anomaly in lattice abelian gauge theory is investigated by
applying the geometric and topological method in noncommutative differential
geometry(NCDG). A new kind of double complex and descent equation are proposed
on infinite hypercubic lattice in arbitrary even dimensional Euclidean space,
in the framework of NCDG. Using the general solutions to proposed descent
equation, we derive the chiral anomaly in Abelian lattice gauge theory. The
topological origin of anomaly is nothing but the Chern classes in NCDG.


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

abstract:
  We generalize overlap fermion by Narayanan and Neuberger by introducing a
hopping parameter t. This lattice fermion has desirable properties as the
original overlap fermion. We expand "Dirac" operator of this fermion in powers
of t. Higher-order terms of t are long-distance terms and this t-expansion is a
kind of the hopping expansion. It is shown that the Ginsparg-Wilson relation is
satisfied at each order of t. We show that this t-expansion is useful for study
of the strong-coupling gauge theory. We apply this formalism to the lattice QCD
and study its chiral phase structure at strong coupling. We find that there are
(at least) two phases one of which has desired chiral properties of QCD.
Possible phase structure of the lattice QCD with the overlap fermions is
proposed.


title: Light Hadron Weak Matrix Elements

abstract:
  Recent developments in lattice QCD calculation of weak matrix elements
involving light quarks are described. We focus on four topics: $B_K$ with the
Kogut-Susskind and Wilson quark actions, $\Delta I=1/2$ rule, proton decay
matrix elements and the application of domain wall QCD to calculation of weak
matrix elements.


title: The Vortex-Finding Property of Maximal Center (and Other) Gauges

abstract:
  We argue that the ``vortex-finding'' property of maximal center gauge, i.e.
the ability of this gauge to locate center vortices inserted by hand on any
given lattice, is the key to its success in extracting the vortex content of
thermalized lattice configurations. We explain how this property comes about,
and why it is expected not only in maximal center gauge, but also in an
infinite class of gauge conditions based on adjoint-representation link
variables. In principle, the vortex-finding property can be foiled by Gribov
copies. This fact is relevant to a gauge-fixing procedure devised by Kovacs and
Tomboulis, where we show that the loss of center dominance, found in their
procedure, is explained by a corresponding loss of the vortex-finding property.
The association of center dominance with the vortex-finding property is
demonstrated numerically in a number of other gauges.


title:
An exact representation of the fermion dynamics in terms of Poisson
  processes

abstract:
  We present a simple derivation of a Feynman-Kac type formula to study
fermionic systems. In this approach the real time or the imaginary time
dynamics is expressed in terms of the evolution of a collection of Poisson
processes. A computer implementation of this formula leads to a family of
algorithms parametrized by the values of the jump rates of the Poisson
processes. From these an optimal algorithm can be chosen which coincides with
the Green Function Monte Carlo (GFMC) method in the limit when the latter
becomes exact.


title: Spectrum of Mesons and Baryons with $b$ Quarks

abstract:
  We present highlights of the spectrum of mesons and baryons calculated using
NRQCD for heavy quarks and tadpole improved clover action for the light quarks.


title:
Index of a family of lattice Dirac operators and its relation to the
  non-abelian anomaly on the lattice

abstract:
  In the continuum, a topological obstruction to the vanishing of the
non-abelian anomaly in 2n dimensions is given by the index of a certain Dirac
operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family
of Dirac operators in 2n dimensions. In this paper an analogous result is
derived for chiral fermions on the lattice in the Overlap formulation. This
involves deriving an Index Theorem for a family of lattice Dirac operators
satisfying the Ginsparg--Wilson relation. The index density is proportional to
Luescher's topological field in 2n+2 dimensions.


title:
Lorentz gauge fixing and the Gribov problem: the fermion correlator in
  lattice compact QED with Wilson fermions

abstract:
  For the Lorentz gauge the influence of Gribov copies on the fermion
propagator is investigated in quenched lattice compact QED. In the Coulomb
phase zero-momentum modes of the gauge fields are shown to be the main reason
for a significant deviation from ordinary perturbation theory.


title: Topology and chiral symmetry breaking in QCD

abstract:
  We construct a model to study the impact of instantons on the low lying
eigenvalue spectrum of the Dirac operator. The model is by necessity,
approximate, though it does incorporate the important symmetries of the
underlying field theory. The model also reproduces classical results in the
appropriate limits. We find that generic instanton ensembles lead to an
accumulation of eigenvalues around zero, and hence, break chiral symmetry. The
eigenvalue spectrum is divergent however, as the eigenvalue approaches zero.
This leads to a divergent chiral condensate in quenched QCD, and hence, shows
the theory to be pathological. In full QCD we find the novel result of a
divergent spectral density leading to chiral symmetry breaking, but, with a
finite condensate. This result holds for both $N_{f}=1$ and $N_{f}=2$. We also
compute correlation functions and find a massive $\eta^{'}$ and $\sigma$ in the
chiral limit. Whilst the divergence follows a power law, the strength of the
divergence is inversely proportional to the instanton density. To investigate
the impact of the divergence further, we analyse instanton ensembles derived by
"cooling" lattice gauge configurations. An important negative result is that
the chiral condensate is strongly dependent upon the number of cooling sweeps
performed. Whether the problem lies with cooling or with the identification of
topological objects is yet to be resolved.


title: Lattice QCD and chiral mesons

abstract:
  The standard QCD action is improved by the addition of irrelevant operators
built with chiral composites. An effective Lagrangian is derived in terms of
auxiliary fields, which has the form of the phenomenological chiral
Lagrangians. Our improved QCD action appears promising for numerical
simulations as the pion physics is explicitely accounted for by the auxiliary
fields.


title: The Overlap Dirac Operator

abstract:
  This introductory presentation describes the Overlap Dirac Operator, why it
could be useful in numerical QCD, and how it can be implemented.


title: Chiral Condensate in the Deconfined Phase of Quenched Gauge Theories

abstract:
  We compute the low lying spectrum of the overlap Dirac operator in the
deconfined phase of finite-temperature quenched gauge theory. It suggests the
existence of a chiral condensate which we confirm with a direct stochastic
estimate. We show that the part of the spectrum responsible for the chiral
condensate can be understood as arising from a dilute gas of instantons and
anti-instantons.


title: A New Gauge Fixing Method for Abelian Projection

abstract:
  We formulate a stochastic gauge fixing method to study the gauge dependence
of the Abelian projection. We consider a gauge which interpolates between the
maximal Abelian gauge and no gauge fixing. We have found that Abelian dominance
for the heavy quark potential holds even in a gauge which is far from maximally
Abelian one. The heavy quark potentials from monopole and photon contribution
are calculated at several values of the gauge parameter, and the former part
shows always the confinement behavior.


title: Lattice Gauge Theories and the Heisenberg Antiferromagnetic Chain

abstract:
  We study the strongly coupled 2-flavor lattice Schwinger model and the
SU(2)-color QCD_2. The strong coupling limit, even with its inherent
nonuniversality, makes accurate predictions of the spectrum of the continuum
models and provides an intuitive picture of the gauge theory vacuum. The
massive excitations of the gauge model are computable in terms of spin-spin
correlators of the quantum Heisenberg antiferromagnetic spin-1/2 chain.


title: The Static Potential in the SU(2) Higgs Model

abstract:
  The static potential in the confinement ``phase'' of the SU(2) Higgs model is
studied. In particular, the observation of the screening (called string
breaking) of the static quarks by the dynamical light quarks leading to the
formation of two static-light mesons was not observed before my work in
non-Abelian gauge theories. The tool that I employ is lattice gauge simulation.
The observable from which the spectrum of the Hamiltonian in presence of two
static quarks can be extracted, is a matrix correlation whose elements are
constructed not only from string-type states represented by Wilson loops (like
in pure gauge theories). Additional matrix elements representing transitions
from string-type to meson-type states and the propagation of meson-type states
are taken into account. From this basis of states it is possible to extract the
ground state and first excited state static potentials employing a variational
method. The crossing of these two energy levels in the string breaking region
is clearly visible and the inadequacy of the Wilson loops alone can be
demonstrated. I also address the question of the lattice artifacts. For this
purpose lines of constant physics in the confinement ``phase'' of the model
have to be constructed. This problem has only partially been solved.
Nevertheless it is possible to show that the static potentials have remarkable
scaling properties under a variation of the lattice spacing by a factor two and
are almost independent of the quartic Higgs coupling.


title: Lanczos Approach to the Inverse Square Root of a Large and Sparse Matrix

abstract:
  I construct a Lanczos process on a large and sparse matrix and use the
results of this iteration to compute the inverse square root of the same
matrix. The algorithm is a stable version of an earlier proposal by the author.
It can be used for problems related to the matrix sign and polar decomposition.
The application here comes from the theory of chiral fermions on the lattice.


title: Fixed-point pure gauge action using $ b= \sqrt{3} $ RGT

abstract:
  We present a status report on the construction of the classical perfect
action using the $ b=\sqrt{3} $ renormalization group transformation (RGT). We
investigate finite volume corrections and map the locality of the fixed-point
action by tuning the RGT parameter, $\kappa$. We compare results with the
previous calculation for b=2 RGT.


title: Finite size scaling of the balls in boxes model

abstract:
  We discuss the finite size behaviour in the canonical ensemble of the balls
in boxes model. We compare theoretical predictions and numerical results for
the finite size scaling of cumulants of the energy distribution in the
canonical ensemble and perform a detailed analysis of the first and third order
phase transitions which appear for different parameter values in the model.


title: A Study of Meson Correlators at Finite Temperature

abstract:
  We present results for mesonic propagators in temporal and spatial directions
at T below and above the deconfining transition in quenched QCD. Anisotropic
lattices are used to get enough information in the temporal direction. We use
the Wilson fermion action for light quarks and Fermilab action for heavy
quarks.


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

abstract:
  Results from the Columbia lattice group study of the QCD finite temperature
phase transition with dynamical domain wall fermions on $16^3 \times 4$
lattices are presented. These results include an investigation of the U(1)
axial symmetry breaking above but close to the transition, the use of zero
temperature calculations that set the scale at the transition and preliminary
measurements close to the transition.


title: The glueball spectrum from novel improved actions

abstract:
  Results for the inter-quark potential and low-lying SU(3) glueball spectrum
from simulations using a new improved action are presented. The action,
suitable for highly anisotropic lattices, contains a two-plaquette term
coupling with a negative coefficient as well as incorporating Symanzik
improvement.


title: Bounds on the Wilson Dirac Operator

abstract:
  New exact upper and lower bounds are derived on the spectrum of the square of
the hermitian Wilson Dirac operator. It is hoped that the derivations and the
results will be of help in the search for ways to reduce the cost of
simulations using the overlap Dirac operator. The bounds also apply to the
Wilson Dirac operator in odd dimensions and are therefore relevant to domain
wall fermions as well.


title:
The Phase Diagram and Spectrum of Gauge-Fixed Abelian Lattice Gauge
  Theory

abstract:
  We consider a lattice discretization of a covariantly gauge-fixed abelian
gauge theory. The gauge fixing is part of the action defining the theory, and
we study the phase diagram in detail. As there is no BRST symmetry on the
lattice, counterterms are needed, and we construct those explicitly. We show
that the proper adjustment of these counterterms drives the theory to a new
type of phase transition, at which we recover a continuum theory of (free)
photons. We present both numerical and (one-loop) perturbative results, and
show that they are in good agreement near this phase transition. Since
perturbation theory plays an important role, it is important to choose a
discretization of the gauge-fixing action such that lattice perturbation theory
is valid. Indeed, we find numerical evidence that lattice actions not
satisfying this requirement do not lead to the desired continuum limit. While
we do not consider fermions here, we argue that our results, in combination
with previous work, provide very strong evidence that this new phase transition
can be used to define abelian lattice chiral gauge theories.


title: First Evidence for Center Dominance in SU(3) Lattice Gauge Theory

abstract:
  The dominance of center degrees of freedom is observed in SU(3) lattice gauge
theory in maximal center gauge. The full asymptotic string tension is
reproduced, after center projection, by the center elements alone. When center
vortices are removed from lattice configurations, the string tension tends to
zero. This provides further evidence for the role played by center vortices in
the mechanism of color confinement in quantum chromodynamics, but more
extensive simulations with a better gauge-fixing procedure are still needed.


title: Quark Confinement and Surface Critical Phenomena

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


title: Static SU(3) potentials for sources in various representations

abstract:
  The potentials and string tensions between static sources in a variety of
representations (fundamental, 8, 6, 15-antisymmetric, 10, 27 and 15-symmetric)
have been computed by measuring Wilson loops in pure gauge SU(3). The
simulations have been done primarily on anisotropic lattices, using a tadpole
improved action improved to O(a_{s}^4). A range of lattice spacings (0.43 fm,
0.25 fm and 0.11 fm) and volumes ($8^3\times 24$, $10^3 \times 24$, $16^3
\times 24$ and $18^3 \times 24$) has been used in an attempt to control
discretization and finite volume effects. At intermediate distances, the
results show approximate Casimir scaling. Finite lattice spacing effects
dominate systematic error, and are particularly large for the representations
with the largest string tensions.


title: Anomaly Cancellation Condition in Abelian Lattice Gauge Theories

abstract: This paper has been withdrawn by the author.


title: The topological characteristics of lattice Dirac operators

abstract:
  We show that even if a lattice Dirac operator satisfies the conditions
consisting of locality, free of species doublings, correct continuum behavior,
$\gm5$-hermiticity and the Ginsparg-Wilson relation, it does not necessarily
have exact zero modes in nontrivial gauge backgrounds. This implies that each
lattice Dirac operator has its own topological characteristics which cannot be
fixed by these conditions. The role of topological characteristics in the axial
anomaly is derived explicitly.


title: Improved B -> pi l nu_l form factors from the lattice

abstract:
  We present the results of a lattice computation of the form factors for B^0
->pi^- l^+nu_l decays near zero-recoil. These results will allow a
determination of the CKM matrix element |Vub| when measurements of the
differential decay rate become available. We also provide models for
extrapolation of the form factors and rate to the full recoil range. Our
computation is performed in the quenched approximation to QCD on a 24^3x48
lattice at beta=6.2, using a non-perturbatively O(a)-improved action. The
masses of all light valence quarks involved are extrapolated to their physical
values.


title: The Abelian Higgs Model in Three Dimensions with Improved Action

abstract:
  We study the Abelian Higgs Model using an improved form of the action in the
scalar sector. The subleading corrections are carefully analysed and the
connection between lattice and continuous parameters is worked out. The
simulation shows a remarkable improvement of the numerical performance.


title: Noise Methods for Flavor Singlet Quantities

abstract:
  A discussion of methods for reducing the noise variance of flavor singlet
quantities ("disconnected diagrams") in lattice QCD is given. After an
introduction, the possible advantage of partitioning the Wilson fermion matrix
into disjoint spaces is discussed and a numerical comparison of the variance
for three possible partitioning schemes is carried out. The measurement
efficiency of lattice operators is examined and shown to be strongly influenced
by the Dirac and color partitioning choices. Next, the numerical effects of an
automated subtraction algorithm on the noise variance of various disconnected
loop matrix elements are examined. It is found that there is a dramatic
reduction in the variance of the Wilson point-split electromagnetic currents
and that this reduction persists at small quark mass.


title: Least-squares optimized polynomials for fermion simulations

abstract:
  Least-squares optimized polynomials are discussed which are needed in the
two-step multi-bosonic algorithm for Monte Carlo simulations of quantum field
theories with fermions. A recurrence scheme for the calculation of necessary
coefficients in the recursion and for the evaluation of these polynomials is
introduced.


title: Perfect Scalars on the Lattice

abstract:
  We perform renormalization group transformations to construct optimally local
perfect lattice actions for free scalar fields of any mass. Their couplings
decay exponentially. The spectrum is identical to the continuum spectrum, while
thermodynamic quantities have tiny lattice artifacts. To make such actions
applicable in simulations, we truncate the couplings to a unit hypercube and
observe that spectrum and thermodynamics are still drastically improved
compared to the standard lattice action. We show how preconditioning techniques
can be applied successfully to this type of action. We also consider a number
of variants of the perfect lattice action, such as the use of an anisotropic or
triangular lattice, and modifications of the renormalization group
transformations motivated by wavelets. Along the way we illuminate the
consistent treatment of gauge fields, and we find a new fermionic fixed point
action with attractive properties.


title: Future Perspectives in Lattice Field Theory

abstract:
  I review some of the contributions which lattice simulations are likely to
make during the next five years or so to the development of our understanding
of particle physics. Particular emphasis is given to the evaluation of
non-perturbative QCD effects in experimentally measurable amplitudes, and the
corresponding extraction of fundamental parameters.


title:
A comment on the index of the lattice Dirac operator and the
  Ginsparg-Wilson relation

abstract:
  We pursue Ginsparg and Wilsons' block spin approach in the derivation of the
Ginsparg-Wilson relation and study the correspondence of the eigenmodes of the
Dirac operators in the continuum and lattice theories. After introducing a
suitable cut-off in the continuum theory, we identify unphysical modes of the
lattice Dirac operator which do not correspond to any physical modes of the
regulated continuum Dirac operator. We also consider zero modes in the
continuum and lattice theories. Our studies give a physical interpretation of
the expression of the index defined on a lattice and a formal argument on the
relation of the indices between the continuum and lattice theories.


title: Two Loop Computation of the Schroedinger Functional in Lattice QCD

abstract:
  We compute the Schroedinger functional (SF) for the case of lattice QCD with
Wilson fermions (with and without SW improvement) at two-loop order in lattice
perturbation theory. This allows us to extract the three-loop beta-function in
the SF-scheme. These results are required to compute the running coupling, the
Lambda-parameter and quark masses by finite size techniques with negligible
systematic errors. In addition our results enable the implementation of
two-loop O(a) improvement in SF-simulations.


title: Matrix elements of the plaquette operator of Lattice Gauge Theory

abstract:
  We show that in the spin-network basis it is possible to compute the matrix
elements of any given operator of the Hamiltonian formulation of Lattice Gauge
Theory (LGT). We give the explicit calculation for the case of the plaquette
operator.


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

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


title: A New Finite-lattice study of the Massive Schwinger Model

abstract:
  A new finite lattice calculation of the low lying bound state energies in the
massive Schwinger model is presented, using a Hamiltonian lattice formulation.
The results are compared with recent analytic series calculations in the low
mass limit, and with a new higher order non-relativistic series which we
calculate for the high mass limit. The results are generally in good agreement
with these series predictions, and also with recent calculations by light cone
and related techniques.


title: Overlap

abstract:
  The overlap formulation of regulated vectorial and chiral gauge theories is
reviewed. Ostensibly new constructions, based on the Ginsparg-Wilson relation
are essentially just overlap with new notation. At present there exists no
satisfactory realization of chiral symmetries outside perturbation theory which
is structurally different from the overlap.


title: Pion decay constant in quenched QCD with Kogut-Susskind quarks

abstract:
  We present a non-perturbative calculation for the pion decay constant with
quenched Kogut-Susskind quarks. Numerical simulations are carried out at $\beta
= 6.0$ and 6.2 with various operators extending over all flavors. The
renormalization correction is applied for each flavor by computing
non-perturbative renormalization constants, and it is compared with a
perturbative calculation. We also study the behavior of $f_\pi$ in the
continuum limits for both non-perturbative and perturbative calculations. The
results in the continuum limit is also discussed.


title: U(1) Problem at Finite Temperature

abstract:
  We model the effects of a large number of zero and near-zero modes in the QCD
partition function by using sparse chiral matrix models with an emphasis on the
quenched topological susceptibility in the choice of the measure. At finite
temperature, the zero modes are not affected by temperature but are allowed to
pair into topologically neutral near-zero modes which are gapped at high
temperature. In equilibrium, chiral and U(1) symmetry are simultaneously
restored for total pairing, evading mean-field arguments. We analyze a number
of susceptibilities versus the light quark masses. At the transition point the
topological susceptibility vanishes, and the dependence on the vacuum angle
$\theta$ drops out. Our results are briefly contrasted with recent lattice
simulations.


title: I=2 Pion Scattering Length with Wilson Fermions

abstract:
  We present results for I=2 pion scattering length with the Wilson fermions in
the quenched approximation. The finite size method presented by L\"uscher is
employed, and calculations are carried out at $\beta=5.9$, 6.1, and 6.3. In the
continuum limit, we obtain a result in reasonable agreement with the
experimental value.


title: Nucleon Decay Matrix Elements from Lattice QCD

abstract:
  We present a model-independent calculation of hadron matrix elements for all
dimension-six operators associated with baryon number violating processes using
lattice QCD. The calculation is performed with the Wilson quark action in the
quenched approximation at $\beta=6/g^2=6.0$ on a $28^2\times 48\times 80$
lattice. Our results cover all the matrix elements required to estimate the
partial lifetimes of (proton,neutron)$\to$($\pi,K,\eta$) +(${\bar
\nu},e^+,\mu^+$) decay modes. We point out the necessity of disentangling two
form factors that contribute to the matrix element; previous calculations did
not make the separation, which led to an underestimate of the physical matrix
elements. With a correct separation, we find that the matrix elements have
values 3-5 times larger than the smallest estimates employed in
phenomenological analyses of the nucleon decays, which could give strong
constraints on several GUT models. We also find that the values of the matrix
elements are comparable with the tree-level predictions of chiral lagrangian.


title:
Gauge Theory and String Theory; An Introduction to the AdS/CFT
  Correspondence

abstract:
  Plenary talk at the conference, LATTICE 99, held in Pisa, Itay from June 29
to July 3, 1999.


title:
Goldstone-mode effects and scaling function for the three-dimensional
  O(4) model

abstract:
  We investigate numerically the three-dimensional O(4) model on 24^3-120^3
lattices as a function of the magnetic field H. We verify explicitly the
singularities induced by Goldstone modes in the low-temperature phase of the
model, and show that they are also observed close to the critical temperature.
Our results are well described by the perturbative form of the model's magnetic
equation of state, with coefficients determined nonperturbatively from our
data. The resulting expression is used to generate the magnetization's scaling
function parametrically.


title: Chiral Gauge Theory on Lattice with Domain Wall Fermions

abstract:
  We investigate a U(1) lattice chiral gauge theory with domain wall fermions
and compact gauge fixing. In the reduced model limit, our perturbative and
numerical investigations show that there exist no extra mirror chiral modes.
The longitudinal gauge degrees of freedom have no effect on the free domain
wall fermion spectrum consisting of opposite chiral modes at the domain wall
and at the anti-domain wall which have an exponentially damped overlap.


title:
From Black Holes to Glueballs: The QCD_3 Tensor Glueball at Strong
  Coupling

abstract:
  A strong coupling calculation of glueball masses based on the duality between
supergravity and Yang-Mills theory is presented. Earlier work is extended to
non-zero spin. Fluctuations in the gravitational metric lead to the 2^{++}
state on the leading Pomeron trajectory with a mass relation: m(0^{++}) <
m(2^{++}) < m(1^{-+}). Contrary to expectation, the mass of our new 0^{++}
state (m^2=5.4573) associated with the graviton is smaller than the mass of the
${\tilde 0}^{++}$ state (m^2=11.588) from the dilaton, which in fact is exactly
degenerate with the tensor 2^{++}.