title:
Four Flavor Finite Temperature Phase Transition with HYP Action: Where
  is the First Order Phase Transition Line?

abstract:
  We study the finite temperature phase transition of four flavor staggered
fermions with hypercubic fat link actions on N_t=4 and N_t=6 temporal lattices.
Our fat links are constructed with hypercubic blocking (HYP) and therefore are
very compact. We present a new algorithm for simulating fermions coupled to HYP
fat links. The algorithm has a simple form based on the standard overrelaxation
and heatbath updatings for the pure gauge action. We observe that as we
increase the smoothness of the gauge fields by changing the parameters of the
blocking the very pronounced first order phase transition of the thin link
action becomes weaker and moves to physically uninteresting values of the gauge
coupling. With our smoothest HYP action we do not find any indication of a
phase transition in the accessible temperature range on the N_t=4 or 6 lattices
even at quark masses close to the physical light quark mass. We argue that the
observed difference in the phase diagram is due to the improved flavor symmetry
of the smeared link actions.


title:
A comprehensive picture of topological excitations in finite temperature
  lattice QCD

abstract:
  We study spectra, localization properties and local chirality of eigenvectors
of the lattice Dirac operator. We analyze ensembles of quenched SU(3)
configurations on both sides of the QCD phase transition. Our Dirac operator is
a systematic expansion in path length of a solution of the Ginsparg-Wilson
equation. Analyzing the finite volume behavior of our observables and their
scaling with the gauge coupling we come up with a consistent picture of
topological excitations on both sides of the QCD phase transition. Our results
support the interpretation of the dominant gauge field excitations seen by the
Dirac operator as a fluid of instanton-like objects.


title: Adaptive Optimization of Wave Functions for Fermion Lattice Models

abstract:
  We present a simulation algorithm for Hamiltonian fermion lattice models. A
guiding trial wave function is adaptively optimized during Monte Carlo
evolution. We apply the method to the two dimensional Gross-Neveu model and
analyze systematc errors in the study of ground state properties. We show that
accurate measurements can be achieved by a proper extrapolation in the
algorithm free parameters.


title:
An Improved Upper Bound for the Ground State Energy of Fermion Lattice
  Models

abstract:
  We present an improved upper bound for the ground state energy of lattice
fermion models with sign problem. The bound can be computed by numerical
simulation of a recently proposed family of deformed Hamiltonians with no sign
problem. For one dimensional models, we expect the bound to be particularly
effective and practical extrapolation procedures are discussed. In particular,
in a model of spinless interacting fermions and in the Hubbard model at various
filling and Coulomb repulsion we show how such techniques can estimate ground
state energies and correlation function with great accuracy.


title: Two-colour QCD at non-zero quark-number density

abstract:
  We have simulated two-colour four-flavour QCD at non-zero chemical potential
$\mu$ for quark number. Simulations were performed on $8^4$ and $12^3 \times
24$ lattices. Clear evidence was seen for the formation of a colourless diquark
condensate which breaks quark number spontaneously, for $\mu > \mu_c \sim
m_\pi/2$. The transition appears to be second order. We have measured the
spectrum of scalar and pseudoscalar bosons which shows clear evidence for the
expected Goldstone boson. Our results are in qualitative agreement with those
from effective Lagrangians for the potential Goldstone excitations of this
theory.


title:
The Charge and Matter radial distributions of Heavy-Light mesons
  calculated on a lattice

abstract:
  For a heavy-light meson with a static heavy quark, we can explore the light
quark distribution. The charge and matter radial distributions of these
heavy-light mesons are measured on a 16^3 * 24 lattice at beta=5.7 and a
hopping parameter corresponding to a light quark mass about that of the strange
quark. Both distributions can be well fitted up to 4 lattice spacings (r approx
0.7 fm) with the exponential form w_i^2(r), where w_i(r)=A exp(-r/r_i). For the
charge(c) and matter(m) distributions r_c approx 0.32(2) fm and r_m approx
0.24(2) fm. We also discuss the normalisation of the total charge and matter
integrated over all space, finding 1.30(5) and 0.4(1) respectively.


title: Finite-size-scaling functions for 3d O(4) and O(2) spin models and QCD

abstract:
  We calculate numerically universal finite-size-scaling functions for the
three-dimensional O(4) and O(2) models. The approach of these functions to the
infinite-volume scaling functions is studied in detail on the critical and
pseudocritical lines. For this purpose we determine the pseudocritical line in
two different ways. We find that the asymptotic form of the finite-size-scaling
functions is already reached at small values of the scaling variable. A
comparison with QCD lattice data for two flavours of staggered fermions shows a
similar finite-size behaviour which is compatible with that of the spin models.


title: Noncompact gauge fields on a lattice: SU(n) theories

abstract:
  Recently it has been found that in a noncompact lattice regularization of the
SU(2) gauge theory the physical volume is larger than in the Wilson theory with
the same number of sites. In its original formulation the noncompact
regularization is directly applicable to U(n) theories for any n and to SU(n)
theories for n=2. In this paper we extend it to SU(n) for any n and investigate
some of its properties.


title:
Spectral function and excited states in lattice QCD with maximum entropy
  method

abstract:
  We apply the maximum entropy method to extract the spectral functions for
pseudoscalar and vector mesons from hadron correlators previously calculated at
four different lattice spacings in quenched QCD with the Wilson quark action.
We determine masses and decay constants for the ground and excited states of
the pseudoscalar and vector channels from position and area of peaks in the
spectral functions. We obtain the results, $m_{\pi_1} = 660(590)$ MeV and
$m_{\rho_1} = 1540(570)$ MeV for the masses of the first excited state masses,
in the continuum limit of quenched QCD. We also find unphysical states which
have infinite mass in the continuum limit, and argue that they are bound states
of two doublers of the Wilson quark action. If the interpretation is correct,
this is the first time that the state of doublers is identified in lattice QCD
numerical simulations.


title: Lattice study of the simplified model of M-theory

abstract:
  Lattice discretization of the supersymmetric Yang-Mills quantum mechanics is
reviewed and results of the Monte Carlo simulations of the simplified model are
presented. The D=4, N=2, quenched system, studied at finite temperature,
reveals existence of the two distinct regions which may correspond to a black
hole and the elementary 0-branes phases of the M-theory conjectured in the
literature. New results for higher gauge groups N < 9 lead to the similar
picture, however the nature of the transition between the two phases and its
precise scaling with N is yet unresolved.


title:
Domain wall fermion and chiral gauge theories on the lattice with exact
  gauge invariance

abstract:
  We discuss how to construct anomaly-free chiral gauge theories on the lattice
with exact gauge invariance in the framework of domain wall fermion. Chiral
gauge coupling is realized by introducing a five-dimensional gauge field which
interpolates between two different four-dimensional gauge fields at boundaries.
The five-dimensional dependence is compensated by a local and gauge-invariant
counter term. The cohomology problem to obtain the counter term is formulated
in 5+1 dimensional space, using the Chern-Simons current induced from the
five-dimensional Wilson fermion. We clarify the connection to the invariant
construction based on the Ginsparg-Wilson relation using overlap Dirac
operator. Formula for the measure and the effective action of Weyl fermions are
obtained in terms of five-dimensional lattice quantities.


title: Perfect Gauge Actions on Anisotropic Lattices

abstract:
  We present a method for constructing classically perfect anisotropic actions
for SU(3) gauge theory based on a present isotropic Fixed Point Action. The
action is parametrised using smeared (``fat'') links. The construction is done
explicitly for anisotropy $\xi=a_s/a_t=2,4$ and the renormalised anisotropies
are determined using the torelon dispersion relation. Quantities such as the
static quark-antiquark potential, the critical temperature of the deconfining
phase transition and the low-lying glueball spectrum are measured as well. It
turns out that the procedure presented works, the renormalised anisotropy is
small and the parametrisation describes the full action well. Issues such as
the application of the method for scalar fields as well as for the quadratic
approximation to gauge theory, measurements of autocorrelation times of simple
operators and of the computational overhead are also covered. A (more compact)
paper about this classically perfect anisotropic gauge action is in
preparation.


title:
Short distance current correlators: Comparing lattice simulations to the
  instanton liquid

abstract:
  Point to point correlators of currents are computed in quenched QCD using a
chiral lattice fermion action, the overlap action. I compare correlators made
of exact quark propagators with correlators restricted to low (less than 500
MeV) eigenvalue eigenmodes of the Dirac operator. In many cases they show
qualitative resemblence (typically at small values of the quark mass and
distances larger than 0.4 fm) and they differ qualitatively at larger quark
masses or at very short distance. Lattice results are in qualitative agreement
(and in the difference of vector and axial vector channels, quantitative
agreement) with the expectations of instanton liquid models. The scalar channel
shows the effects of a quenched finite volume zero mode artifact, a negative
correlator.


title: Lattice determination of the critical point of QCD at finite T and \mu

abstract:
  Based on universal arguments it is believed that there is a critical point
(E) in QCD on the temperature (T) versus chemical potential (\mu) plane, which
is of extreme importance for heavy-ion experiments. Using finite size scaling
and a recently proposed lattice method to study QCD at finite \mu we determine
the location of E in QCD with n_f=2+1 dynamical staggered quarks with
semi-realistic masses on $L_t=4$ lattices. Our result is T_E=160 \pm 3.5 MeV
and \mu_E= 725 \pm 35 MeV. For the critical temperature at \mu=0 we obtained
T_c=172 \pm 3 MeV.


title: Non-perturbative improvement of lattice QCD at large momenta

abstract:
  We propose a method to improve lattice operators composed of Wilson fermions
which allows the removal of all corrections of $O(a)$, including those
proportional to the quark mass. It requires off-shell improvement of quark
fields and composite operators, which is achieved by studying the behaviour of
quark and gluon correlation functions at large momenta.


title:
Glueball properties in anisotropic SU(3) lattice QCD with improved
  action

abstract:
  We study the glueballs properties at finite temperature using SU(3) lattice
QCD at the quenched level with the anisotropic lattice. We use the tree-level
Symanzik O(a^2) improved action. We present our preliminary results which shows
the slight reduction of the scalar glueball mass near T_c


title: Perturbative Matching of the staggered four-fermion operators for e'/e

abstract:
  Using staggered fermions, we calculate the perturbative corrections to the
bilinear and four-fermion operators that are used in the numerical study of
weak matrix elements for $\epsilon'/\epsilon$. We present results for one-loop
matching coefficients between continuum operators, calculated in the Naive
Dimensional Regularization (NDR) scheme, and gauge invariant staggered fermion
operators. These results, combined with existing results for penguin diagrams,
provide the complete one-loop renormalization of the staggered four-fermion
operators.


title: Non-perturbative singularity structure of gluon and quark propagators

abstract:
  A gauge invariant, non-local observable is constructed in lattice pure gauge
theory, which is identical to the gluon propagator in a particular gauge. The
transfer matrix formalism is used to show that this correlator decays
exponentially with eigenvalues of the Hamiltonian. This implies a gauge
invariant singularity structure of the propagator in momentum space, permitting
a non-perturbative definition of a parton mass. The relation to gauge fixing
and the extension to matter fields are discussed.


title: Renormalization Constants using Quark States in Fixed Gauge

abstract:
  We present a status report on our calculation of the renormalization
constants for the quark bilinears in quenched (O(a)) improved Wilson theory at
(beta=6.4) using quark states in Landau gauge.


title: Chiral Loops and Ghost States in the Quenched Scalar Propagator

abstract:
  The scalar, isovector meson propagator is analyzed in quenched QCD, using the
MQA pole-shifting ansatz to study the chiral limit. In addition to the expected
short-range exponential falloff characteristic of a heavy scalar meson, the
propagator also exhibits a longer-range, negative metric contribution which
becomes pronounced for smaller quark masses. We show that this is a quenched
chiral loop effect associated with the anomalous structure of the $\eta '$
propagator in quenched QCD. Both the time dependence and the quark mass
dependence of this effect are well-described by a chiral loop diagram
corresponding to an $\eta '- \pi$ intermediate state, which is light and
effectively of negative norm in the quenched approximation. The relevant
parameters of the effective Lagrangian describing the scalar sector of the
quenched theory are determined.


title: Numerical Simulations of PT-Symmetric Quantum Field Theories

abstract:
  Many non-Hermitian but PT-symmetric theories are known to have a real
positive spectrum. Since the action is complex for there theories, Monte Carlo
methods do not apply. In this paper the first field-theoretic method for
numerical simulations of PT-symmetric Hamiltonians is presented. The method is
the complex Langevin equation, which has been used previously to study complex
Hamiltonians in statistical physics and in Minkowski space. We compute the
equal-time one-point and two-point Green's functions in zero and one dimension,
where comparisons to known results can be made. The method should also be
applicable in four-dimensional space-time. Our approach may also give insight
into how to formulate a probabilistic interpretation of PT-symmetric theories.


title:
Topological Susceptibility in Lattice QCD with Two Flavors of Dynamical
  Quarks

abstract:
  We present a study of the topological susceptibility in lattice QCD with two
degenerate flavors of dynamical quarks. The topological charge is measured on
gauge configurations generated with a renormalization group improved gauge
action and a mean field improved clover quark action at three values of
$\beta=6/g^2$, corresponding to lattice spacings of $a \approx 0.22$, 0.16 and
0.11 fm, with four sea quark masses at each $\beta$. The study is supplemented
by simulations of pure SU(3) gauge theory with the same gauge action at 5
values of $\beta$ with lattice spacings 0.09 fm$\simlt a \simlt$0.27 fm. We
employ a field theoretic definition of the topological charge together with
cooling. For the topological susceptibility in the continuum limit of pure
SU(3) gauge theory we obtain $\chi_t^{1/4} = 197^{+13}_{-16}$ MeV where the
error shows statistical and systematic ones added in quadrature. In full QCD
$\chi_t$ at heavy sea quark masses is consistent with that of pure SU(3) gauge
theory. A decrease of $\chi_t$ toward light quark masses, as predicted by the
anomalous Ward-Takahashi identity for U(1) chiral symmetry, becomes clearer for
smaller lattice spacings. The cross-over in the behavior of $\chi_t$ from heavy
to light sea quark masses is discussed.


title:
Non-perturbative renormalization of the quark condensate in
  Ginsparg-Wilson regularizations

abstract:
  We present a method to compute non-perturbatively the renormalization
constant of the scalar density for Ginsparg-Wilson fermions. It relies on
chiral symmetry and is based on a matching of renormalization group invariant
masses at fixed pseudoscalar meson mass, making use of results previously
obtained by the ALPHA Collaboration for O(a)-improved Wilson fermions. Our
approach is quite general and enables the renormalization of scalar and
pseudoscalar densities in lattice regularizations that preserve chiral symmetry
and of fermion masses in any regularization. As an application we compute the
non-perturbative factor which relates the renormalization group invariant quark
condensate to its bare counterpart, obtained with overlap fermions at beta=5.85
in the quenched approximation.


title: The Index of a Ginsparg-Wilson Dirac operator

abstract:
  A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed.
Unlike the Dirac operator for massless fermions in the continuum, this lattice
Dirac operator does not possess topological zero modes for any
topologically-nontrivial background gauge fields, even though it is
exponentially-local, doublers-free, and reproduces correct axial anomaly for
topologically-trivial gauge configurations.


title: Two-loop critical mass for Wilson fermions

abstract:
  We have redone a recent two-loop computation of the critical mass for Wilson
fermions in lattice QCD by evaluating Feynman integrals with the
coordinate-space method. We present the results for different types of infrared
regularization. We confirm both the previous numerical estimates and the power
of the coordinate-space method whenever high accuracy is needed.


title: Two Flavors of Staggered Fermions with Smeared Links

abstract:
  Staggered fermions with smeared links can have greatly improved chiral
properties. In a recent paper we introduced a simple and effective method to
simulate four flavors of staggered smeared link fermions. In this work we
extend the four flavor method to two flavors. We define the two flavor action
by the square root of the four flavor fermionic determinant and show that by
using a polynomial approximation the two flavor action can be evaluated with
the necessary accuracy. We test this method by studying the finite temperature
phase structure with hypercubic smeared (HYP) link staggered action on N_t=4
temporal lattices.


title: Does the XY Model have an integrable continuum limit?

abstract:
  The quantum field theory describing the massive O(2) nonlinear sigma-model is
investigated through two non-perturbative constructions: The form factor
bootstrap based on integrability and the lattice formulation as the XY model.
The S-matrix, the spin and current two-point functions, as well as the 4-point
coupling are computed and critically compared in both constructions. On the
bootstrap side a new parafermionic super selection sector is found; in the
lattice theory a recent prediction for the (logarithmic) decay of lattice
artifacts is probed.


title: On the low fermionic eigenmode dominance in QCD on the lattice

abstract:
  We demonstrate the utility of a spectral approximation to fermion loop
operators using low-lying eigenmodes of the hermitian Dirac-Wilson matrix, Q.
The investigation is based on a total of 400 full QCD vacuum configurations,
with two degenerate flavors of dynamical Wilson fermions at beta =5.6, at two
different sea quark masses. The spectral approach is highly competitive for
accessing both topological charge and disconnected diagrams, on large lattices
and small quark masses. We propose suitable partial summation techniques that
provide sufficient saturation for estimating Tr Q^{-1}, which is related to the
topological charge. In the effective mass plot of the eta' meson we achieved a
consistent early plateau formation, by ground state projecting the connected
piece of its propagator.


title: Direct Laplacian Center Gauge

abstract:
  We introduce a variation of direct maximal center gauge fixing: the ``direct
Laplacian'' center gauge. The new procedure overcomes certain shortcomings of
maximal center gauge, associated with Gribov copies, that were pointed out by
Bornyakov et al. in hep-lat/0009035.


title: Quenched divergences in the deconfined phase of SU(2) gauge theory

abstract:
  The spectrum of the overlap Dirac operator in the deconfined phase of
quenched gauge theory is known to have three parts: exact zeros arising from
topology, small nonzero eigenvalues that result in a non-zero chiral
condensate, and the dense bulk of the spectrum, which is separated from the
small eigenvalues by a gap. In this paper, we focus on the small nonzero
eigenvalues in an SU(2) gauge field background at $\beta=2.4$ and $N_T=4$. This
low-lying spectrum is computed on four different spatial lattices ($12^3$,
$14^3$, $16^3$, and $18^3$). As the volume increases, the small eigenvalues
become increasingly concentrated near zero in such a way as to strongly suggest
that the infinite volume condensate diverges.


title: Lattice QCD at High Temperature and Density

abstract:
  After a brief introduction into basic aspects of the formulation of lattice
regularized QCD at finite temperature and density we discuss our current
understanding of the QCD phase diagram at finite temperature. We present
results from lattice calculations that emphasize the deconfining as well as
chiral symmetry restoring features of the QCD transition, and discuss the
thermodynamics of the high temperature phase.


title: Radial Correlations between two quarks

abstract:
  In nuclear many-body problems the short-range correlation between two
nucleons is well described by the corresponding correlation in the {two}-body
problem. Therefore, as a first step in any attempt at an analogous description
of many-quark systems, it is necessary to know the two-quark correlation. With
this in mind, we study the light quark distribution in a heavy-light meson with
a static heavy quark. The charge and matter radial distributions of these
heavy-light mesons are measured on a lattice with a light quark mass about that
of the strange quark. Both distributions can be well fitted upto r approx 0.7
fm with the exponential form w_i^2(r), where w_i(r)=A exp(-r/r_i). For the
charge(c) and matter(m) distributions r_c approx 0.32(2) fm and r_m \approx
0.24(2) fm. We also discuss the normalisation of the total charge (defined to
be unity in the continuum limit) and matter integrated over all space, finding
1.30(5) and 0.4(1) respectively for a lattice spacing approx 0.17 fm.


title:
Monopoles, confinement and deconfinement of (2+1)D compact lattice QED
  in external fields

abstract:
  The compact Abelian model in three space--time dimensions is studied in the
presence of external electromagnetic fields at finite temperatures. We show
that the deconfinement phase transition is independent on the strength of the
external fields. This result is in agreement with our observation that the
external fields create small--size magnetic dipoles from the vacuum which do
not influence the confining properties of the model. Contrary to the
deconfinement phase, the internal field in the direction of the applied
external field is attenuated in the confinement phase, this screening becomes
stronger with decreasing temperature.


title: Negative-parity Baryon Masses using an O(a)-improved Fermion Action

abstract:
  We present a calculation of the mass of the lowest-lying negative-parity
J=1/2- state in quenched QCD. Results are obtained using a non-perturbatively
O(a)-improved clover fermion action, and a splitting is found between the mass
of the nucleon and its parity partner. The calculation is performed on two
lattice volumes and at three lattice spacings, enabling a study of both
finite-volume and finite lattice-spacing uncertainties. A comparison is made
with results obtained using the unimproved Wilson fermion action.


title: Improved Smoothing Algorithms for Lattice Gauge Theory

abstract:
  The relative smoothing rates of various gauge field smoothing algorithms are
investigated on ${\cal O}(a^2)$-improved $\suthree$ Yang--Mills gauge field
configurations. In particular, an ${\cal O}(a^2)$-improved version of APE
smearing is motivated by considerations of smeared link projection and cooling.
The extent to which the established benefits of improved cooling carry over to
improved smearing is critically examined. We consider representative gauge
field configurations generated with an ${\cal O}(a^2)$-improved gauge field
action on $\1$ lattices at $\beta=4.38$ and $\2$ lattices at $\beta=5.00$
having lattice spacings of 0.165(2) fm and 0.077(1) fm respectively. While the
merits of improved algorithms are clearly displayed for the coarse lattice
spacing, the fine lattice results put the various algorithms on a more equal
footing and allow a quantitative calibration of the smoothing rates for the
various algorithms. We find the relative rate of variation in the action may be
succinctly described in terms of simple calibration formulae which accurately
describe the relative smoothness of the gauge field configurations at a
microscopic level.


title:
Differential decay rate of $B \to \pi l \nu$ semileptonic decay with
  lattice NRQCD

abstract:
  We present a lattice QCD calculation of $B\to \pi l \nu$ semileptonic decay
form factors in the small pion recoil momentum region. The calculation is
performed on a quenched $16^3 \times 48$ lattice at $\beta=5.9$ with the NRQCD
action including the full 1/M terms. The form factors $f_1(v\cdot k_{\pi})$ and
$f_2(v\cdot k_{\pi})$ defined in the heavy quark effective theory for which the
heavy quark scaling is manifest are adpoted, and we find that the 1/M
correction to the scaling is small for the $B$ meson. The dependence of form
factors on the light quark mass and on the recoil energy is found to be mild,
and we use a global fit of the form factors at various quark masses and recoil
energies to obtain model independent results for the physical differential
decay rate. We find that the $B^*$ pole contribution dominates the form factor
$f^+(q^2)$ for small pion recoil energy, and obtain the differential decay rate
integrated over the kinematic region $q^2 >$ 18 GeV$^2$ to be $|V_{ub}|^2
\times (1.18 \pm 0.37 \pm 0.08 \pm 0.31)$ psec$^{-1}$, where the first error is
statistical, the second is that from perturbative calculation, and the third is
the systematic error from finite lattice spacing and the chiral extrapolation.
We also discuss the systematic errors in the soft pion limit for
$f^0(q^2_{max})$ in the present simulation.


title: Schr"odinger functional at negative flavour number

abstract:
  The scaling of the Schr"odinger functional coupling is studied numerically
and perturbatively for an SU(3) lattice gauge field coupled to an O(a) improved
bosonic spinor field. This corresponds to QCD with minus two light flavours and
is used as a numerically less costly test case for real QCD. A suitable
algorithm is developed, and the influence of the matter fields on the continuum
limit and the lattice artefacts are studied in detail.


title:
Numerical study of O(a) improved Wilson quark action on anisotropic
  lattice

abstract:
  The $O(a)$ improved Wilson quark action on the anisotropic lattice is
investigated. We carry out numerical simulations in the quenched approximation
at three values of lattice spacing ($a_{\sigma}^{-1}=1$--2 GeV) with the
anisotropy $\xi=a_{\sigma}/a_{\tau}=4$, where $a_{\sigma}$ and $a_{\tau}$ are
the spatial and the temporal lattice spacings, respectively. The bare
anisotropy $\gamma_F$ in the quark field action is numerically tuned by the
dispersion relation of mesons so that the renormalized fermionic anisotropy
coincides with that of gauge field. This calibration of bare anisotropy is
performed to the level of 1 % statistical accuracy in the quark mass region
below the charm quark mass. The systematic uncertainty in the calibration is
estimated by comparing the results from different types of dispersion
relations, which results in 3 % on our coarsest lattice and tends to vanish in
the continuum limit. In the chiral limit, there is an additional systematic
uncertainty of 1 % from the chiral extrapolation.
  Taking the central value $\gamma_F=\gamma_F^*$ from the result of the
calibration, we compute the light hadron spectrum. Our hadron spectrum is
consistent with the result by UKQCD Collaboration on the isotropic lattice. We
also study the response of the hadron spectrum to the change of anisotropic
parameter, $\gamma_F \to \gamma_F^* + \delta\gamma_F$. We find that the change
of $\gamma_F$ by 2 % induces a change of 1 % in the spectrum for physical quark
masses. Thus the systematic uncertainty on the anisotropic lattice, as well as
the statistical one, is under control.


title: Responses of hadrons to chemical potential at finite temperature

abstract:
  We present a framework to compute the responses of hadron masses to the
chemical potential in lattice QCD simulations. As a first trial, the screening
mass of the pseudoscalar meson and its first and second responses are
evaluated. We present results on a $16\times 8^2\times 4$ lattice with two
flavors of staggered quarks below and above $T_c$. The responses to both the
isoscalar and isovector chemical potentials are obtained. They show different
behavior in the low and the high temperature phases, which may be explained as
a consequence of chiral symmetry breaking and restoration, respectively.


title: The flavour singlet mesons in QCD

abstract:
  We study the flavour singlet mesons from first principles using lattice QCD.
We explore the splitting between flavour singlet and non-singlet for vector and
axial mesons as well as the more commonly studied cases of the scalar and
pseudoscalar mesons.


title:
The (2+1)-dimensional Gross-Neveu model with a U(1) chiral symmetry at
  non-zero temperature

abstract:
  We present results from numerical simulations of the (2+1)-dimensional
Gross-Neveu model with a U(1) chiral symmetry and N_f=4 fermion species at
non-zero temperature. We provide evidence that there are two different chirally
symmetric phases, one critical and one with finite correlation length,
separated by a Berezinskii-Kosterlitz-Thouless transition. We have also
identified a regime above the critical temperature in which the fermions
acquire a screening mass even in the absence of chiral symmetry breaking,
analogous to the pseudogap behaviour observed in cuprate superconductors.


title:
Tuning the Tadpole Improved Clover Wilson Action on Coarse Anisotropic
  Lattices

abstract:
  Wilson quark action, with tadpole improved clover term added, is studied on
coarse anisotropic lattices. The bare velocity of light parameter in this
action is determined non-perturbatively using the pseudo-scalar and vector
meson dispersion relations for various values of the gauge coupling $\beta$ and
bare quark mass parameter $\kappa$.


title: The static three-quark SU(3) and four-quark SU(4) potentials

abstract:
  We present results on the static three- and four-quark potentials in SU(3)
and SU(4) respectively within quenched lattice QCD. We use an analytic
multi-hit procedure for the time links and a variational approach to determine
the ground state. The three- and four-quark potentials extracted are consistent
with a sum of two-body potentials, possibly with a weak many-body component.
The results give support to the $\Delta$ ansatz for the baryonic area law.


title: Confining strings in SU(N) gauge theories

abstract:
  We calculate the string tensions of $k$-strings in SU($N$) gauge theories in
both 3 and 4 dimensions. In D=3+1, we find that the ratio of the $k=2$ string
tension to the $k = 1$ fundamental string tension is consistent, at the $2
\sigma$ level, with both the M(-theory)QCD-inspired conjecture and with
`Casimir scaling'. In D=2+1 we see a definite deviation from the MQCD formula,
as well as a much smaller but still significant deviation from Casimir scaling.
We find that in both D=2+1 and D=3+1 the high temperature spatial $k$-string
tensions also satisfy approximate Casimir scaling. We point out that
approximate Casimir scaling arises naturally if the cross-section of the flux
tube is nearly independent of the flux carried, and that this will occur in an
effective dual superconducting description, if we are in the deep-London limit.
We estimate, numerically, the intrinsic width of $k$-strings in D=2+1 and
indeed find little variation with $k$. In addition to the stable $k$-strings we
investigate some ofthe unstable strings, finding in D=2+1 that they satisfy
(approximate) Casimir scaling. We also investigate the basic assumption that
confining flux tubes are described by an effective string theory at large
distances. We estimate the coefficient of the universal L\"uscher correction
from periodic strings that are longer than 1 fermi, and find $c_L=0.98(4)$ in
D=3+1 and $c_L=0.558(19)$ in D=2+1. These values are within $2 \sigma$ of the
simple bosonic string values and are inconsistent with other simple effective
string theories.


title: SU(3) Lattice QCD Study for Static Three-Quark Potential

abstract:
  We study the static three-quark (3Q) potential in detail using SU(3) lattice
QCD with $12^3 \times 24$ at $\beta=5.7$ and $16^3 \times 32$ at $\beta=5.8,
6.0$ at the quenched level. For more than 200 patterns of the 3Q systems, we
numerically derive 3Q ground-state potential $V_{3Q}$ from the 3Q Wilson loop
with the smearing technique, which reduces excited-state contaminations. The
lattice QCD data of $V_{3Q}$ are well reproduced within a few % deviation by a
sum of a constant, the two-body Coulomb term and the three-body linear
confinement term $\sigma_{3Q} L_{min}$, with $L_{min}$ the minimal value of
total length of color flux tubes linking the three quarks.
  From the comparison with the Q-$\bar {Q}$ potential, we find a universality
of the string tension as $\sigma_{3Q} \simeq \sigma_{\rm Q \bar Q}$ and the
one-gluon-exchange result for Coulomb coefficients, $A_{3Q} \simeq \frac12
A_{\rm Q \bar Q}$.


title: Relativistic Heavy Quarks on the Lattice

abstract:
  Lattice QCD should allow quantitative predictions for the heavy quark physics
from first principles. Up to now, however, most approaches have based on the
nonrelativistic effective theory, with which the continuum limit can not be
taken in principle. In this paper we investigate feasibility of relativistic
approaches to the heavy quark physics in lattice QCD. We first examine validity
of the idea that the use of the anisotropic lattice could be advantageous to
control the $m_Q a$ corrections. Our perturbative calculation, however, reveals
that this is not true. We instead propose a new relativistic approach to handle
heavy quarks on the isotropic lattice. We explain how power corrections of $m_Q
a$ can be avoided and remaining uncertainties are reduced to be of order
$(a\Lambda_{QCD})^2$.


title: Understanding Hadron Structure Using Lattice QCD

abstract:
  Numerical evaluation of the path integral for QCD on a discrete space-time
lattice has been used to calculate ground state matrix elements specifying
moments of quark density and spin distributions. This talk will explain how
these matrix elements have been calculated in full QCD using dynamical quarks,
show how physical extrapolation to the chiral limit including the physics of
the pion cloud resolves previous apparent conflicts with experiment, and
describe the computational resources required for a definitive comparison with
experiment.


title: Bottomonium Decay Matrix Elements from Lattice QCD with Two Light Quarks

abstract:
  We calculate the long-distance matrix elements for the decays of the Upsilon
(eta_b) and chi_b (h_b) states in lattice QCD with two flavors of light
dynamical quarks. We relate the lattice matrix elements to their continuum
counterparts through one-loop order in perturbation theory. In the case of the
leading S-wave matrix element, we compare our result with a phenomenological
value that we extract from the experimental leptonic decay rate by using the
theoretical expression for the decay rate, accurate through relative order
alpha_s. Whereas estimates of the leading S-wave matrix element from quenched
QCD are 40--45% lower than the phenomenological value, the two-flavor estimate
of the same matrix element is close to the phenomenological value.
Extrapolating to the real world of 2+1 light flavors, we find that this matrix
element is approximately 6% higher than the phenomenological value, but that
the phenomenological value lies within our error bars. We also compute the
color-singlet and color-octet matrix elements for P-wave decays. We find the
value of the color-singlet matrix element for 2+1 flavors to be approximately
70% larger than the quenched value and the value of the color-octet matrix
element for 2+1 flavors to be approximately 40% larger than the quenched value.


title: Gauge fixed domain wall fermions on lattice at small Yukawa coupling

abstract:
  Gauge fixed domain wall fermions are investigated in the reduced model at
small Yukawa couplings. We present chiral propagators at the waveguide
boundaries using quenched numerical simulations and analytic methods. There is
no evidence of mirror chiral modes at the waveguide boundaries.


title: Thermodynamical quantities of lattice full QCD from an efficient method

abstract:
  I extend to QCD an efficient method for lattice gauge theory with dynamical
fermions. Once the eigenvalues of the Dirac operator and the density of states
of pure gluonic configurations at a set of plaquette energies (proportional to
the gauge action) are computed, thermodynamical quantities deriving from the
partition function can be obtained for arbitrary flavor number, quark masses
and wide range of coupling constants, without additional computational cost.
Results for the chiral condensate and gauge action are presented on the $10^4$
lattice at flavor number $N_f=0$, 1, 2, 3, 4 and many quark masses and coupling
constants. New results in the chiral limit for the gauge action and its
correlation with the chiral condensate, which are useful for analyzing the QCD
chiral phase structure, are also provided.


title: Another determination of the quark condensate from an overlap action

abstract:
  I use the technique of Hernandez, et al (hep-lat/0106011) to convert a recent
calculation of the lattice-regulated quark condensate from an overlap action to
a continuum-regulated number. I find Sigma(MSbar)(mu = 2 GeV) = (282(6)
MeV)-cubed times (a-inverse/1766 MeV)-cubed from a calculation with the Wilson
gauge action at beta=5.9.


title:
Spectrum of the Dirac operator coupled to two-dimensional quantum
  gravity

abstract:
  We implement fermions on dynamical random triangulation and determine
numerically the spectrum of the Dirac-Wilson operator D for the system of
Majorana fermions coupled to two-dimensional Euclidean quantum gravity. We
study the dependence of the spectrum of the operator (epsilon D) on the hopping
parameter. We find that the distributions of the lowest eigenvalues become
discrete when the hopping parameter approaches the value 1/sqrt{3}. We show
that this phenomenon is related to the behavior of the system in the
'antiferromagnetic' phase of the corresponding Ising model. Using finite size
analysis we determine critical exponents controlling the scaling of the lowest
eigenvalue of the spectrum including the Hausdorff dimension d_H and the
exponent kappa which tells us how fast the pseudo-critical value of the hopping
parameter approaches its infinite volume limit.


title: Properties of near-zero modes and chiral symmetry breaking

abstract:
  We study localization and chirality properties of eigenvectors of the lattice
Dirac operator. In particular we focus on the dependence of our observables on
the size of the corresponding eigenvalue, which allows us to study the
transition of a near-zero mode into a bulk mode. We analyze ensembles of
quenched SU(3) configurations using a Dirac operator which is a systematic
expansion in path length of a solution of the Ginsparg-Wilson equation. Our
results support the interpretation of the excitations relevant for chiral
symmetry breaking as interacting instantons and anti-instantons.


title:
Parallel Supercomputing PC Cluster and Some Physical Results in Lattice
  QCD

abstract:
  We describe the construction of a high performance parallel computer composed
of PC components, present some physical results for light hadron and hybrid
meson masses from lattice QCD. We also show that the smearing technique is very
useful for improving the spectrum calculations.


title:
't Hooft Loops, Electric Flux Sectors and Confinement in SU(2)
  Yang-Mills Theory

abstract:
  We use 't Hooft loops of maximal size on finite lattices to calculate the
free energy in the sectors of SU(2) Yang-Mills theory with fixed electric flux
as a function of temperature and (spatial) volume. Our results provide evidence
for the mass gap. The confinement of electric fluxes in the low temperature
phase and their condensation in the high temperature phase are demonstrated. In
a surprisingly large scaling window around criticality, the transition is
quantitatively well described by universal exponents and amplitude ratios
relating the properties of the two phases.


title: Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions

abstract:
  We propose a modification of the Hybrid-Monte-Carlo algorithm that allows for
a larger step-size of the integration scheme at constant acceptance rate. The
key ingredient is that the pseudo-fermion action is split into two parts. We
test our proposal at the example of the two-dimensional lattice Schwinger model
with two degenerate flavours of Wilson-fermions.


title: The Chiral Critical Point in 3-Flavour QCD

abstract:
  We determine the second order endpoint of the line of first order phase
transitions, which occur in the light quark mass regime of 3-flavour QCD at
finite temperature, and analyze universal properties of this chiral critical
point. A detailed analysis of Binder cumulants and the joint probability
distributions of energy like and ordering-field like observables confirms that
the chiral critical point belongs to the universality class of the three
dimensional Ising model. From a calculation with improved gauge and staggered
fermion actions we estimate that the transition is first order for
pseudo-scalar meson masses less than about 200 MeV.


title:
Effects of non-perturbatively improved dynamical fermions in QCD at
  fixed lattice spacing

abstract:
  We present results for the static inter-quark potential, lightest glueballs,
light hadron spectrum and topological susceptibility using a non-perturbatively
improved action on a $16^3\times 32$ lattice at a set of values of the bare
gauge coupling and bare dynamical quark mass chosen to keep the lattice size
fixed in physical units ($\sim 1.7$ fm). By comparing these measurements with a
matched quenched ensemble, we study the effects due to two degenerate flavours
of dynamical quarks. With the greater control over residual lattice spacing
effects which these methods afford, we find some evidence of charge screening
and some minor effects on the light hadron spectrum over the range of quark
masses studied ($M_{PS}/M_{V}\ge0.58$). More substantial differences between
quenched and unquenched simulations are observed in measurements of topological
quantities.


title: Quenched QCD at finite temperature with chiral Fermions

abstract:
  We study physics at temperatures just above the QCD phase transition (Tc)
using chiral (overlap) Fermions in the quenched approximation of lattice QCD.
Exact zero modes of the overlap Dirac operator are localized and their
frequency of occurrence drops with temperature. This is closely related to
axial U(1) symmetry, which remains broken up to 2Tc. After subtracting the
effects of these zero modes, chiral symmetry is restored, as indicated by the
behavior of the chiral condensate. The pseudoscalar and vector screening masses
are close to ideal gas values.


title: Is the up-quark massless?

abstract:
  We report on determinations of the low-energy constants alpha5 and alpha8 in
the effective chiral Lagrangian at O(p^4), using lattice simulations with N_f=2
flavours of dynamical quarks. Precise knowledge of these constants is required
to test the hypothesis whether or not the up-quark is massless. Our results are
obtained by studying the quark mass dependence of suitably defined ratios of
pseudoscalar meson masses and matrix elements. Although comparisons with an
earlier study in the quenched approximation reveal small qualitative
differences in the quark mass behaviour, numerical estimates for alpha5 and
alpha8 show only a weak dependence on the number of dynamical quark flavours.
Our results disfavour the possibility of a massless up-quark, provided that the
quark mass dependence in the physical three-flavour case is not fundamentally
different from the two-flavour case studied here.


title: Comparing lattice Dirac operators in smooth instanton backgrounds

abstract:
  We compare the behavior of different lattice Dirac operators in gauge
backgrounds which are lattice discretizations of a classical instanton. In
particular we analyze the standard Wilson operator, a chirally improved Dirac
operator and the overlap operators constructed from these two operators. We
discuss the flow of real eigenvalues as a function of the instanton size. An
analysis of the eigenvectors shows that overlap fermions with the Wilson
operator as input operator have difficulties with reproducing the continuum
zero mode already for moderately small instantons. This problem is greatly
reduced when using the chirally improved operator for the overlap projection.


title: Parton distributions from lattice QCD

abstract:
  We extract the x dependence of the nonsinglet u-d distribution function in
the nucleon from the lowest few moments calculated on the lattice, using an
extrapolation formula which ensures the correct behavior in the chiral and
heavy quark limits. We discuss the implications for the quark mass dependence
of meson masses lying on the J(PC)=1(--) Regge trajectory.


title: Partially quenched chiral perturbation theory without $\Phi_0$

abstract:
  This paper completes the argument that lattice simulations of partially
quenched QCD can provide quantitative information about QCD itself, with the
aid of partially quenched chiral perturbation theory. A barrier to doing this
has been the inclusion of $\Phi_0$, the partially quenched generalization of
the $\eta'$, in previous calculations in the partially quenched effective
theory. This invalidates the low energy perturbative expansion, gives rise to
many new unknown parameters, and makes it impossible to reliably calculate the
relation between the partially quenched theory and low energy QCD. We show that
it is straightforward and natural to formulate partially quenched chiral
perturbation theory without $\Phi_0$, and that the resulting theory contains
the effective theory for QCD without the $\eta'$. We also show that previous
results, obtained including $\Phi_0$, can be reinterpreted as applying to the
theory without $\Phi_0$. We contrast the situation with that in the quenched
effective theory, where we explain why it is necessary to include $\Phi_0$.
  We also compare the derivation of chiral perturbation theory in partially
quenched QCD with the standard derivation in unquenched QCD. We find that the
former cannot be justified as rigorously as the latter, because of the absence
of a physical Hilbert space. Finally, we present an encouraging result:
unphysical double poles in certain correlation functions in partially quenched
chiral perturbation theory can be shown to be a property of the underlying
theory, given only the symmetries and some plausible assumptions.


title: Center vortices on SU(2) lattices

abstract:
  We show that gauge invariant definition of thin, thick and hybrid center
vortices, defined by Kovacs and Tomboulis on SO(3) x Z(2) configurations, can
also be defined in SU(2). We make this connection using the freedom of choosing
a particular SU(2) representative of SO(3). We further show that in another
representative the Tomboulis \sigma - \eta thin vortices are P (projection)
vortices. The projection approximation corresponds to dropping the perimeter
factor of a Wilson loop after appropriate gauge fixing. We present results for
static quark potentials based on these vortex counters and compare pojection
vortex counters with gauge invariant ones on the same configuration.


title: Classically Perfect Gauge Actions on Anisotropic Lattices

abstract:
  We present a method for constructing classically perfect anisotropic actions
for SU(3) gauge theory based on an isotropic Fixed Point Action. The action is
parametrised using smeared (``fat'') links. The construction is done explicitly
for anisotropy $\xi=a_s/a_t=2$ and 4. The corresponding renormalised
anisotropies are determined using the torelon dispersion relation. The
renormalisation of the anisotropy is small and the parametrisation describes
the true action well. Quantities such as the static quark-antiquark potential,
the critical temperature of the deconfining phase transition and the low-lying
glueball spectrum are measured on lattices with anisotropy $\xi=2$. The mass of
the scalar $0^{++}$ glueball is determined to be 1580(60) MeV, while the tensor
$2^{++}$ glueball is at 2430(60) MeV.


title: The topological susceptibility and f_pi from lattice QCD

abstract:
  We study the topological susceptibility, chi, in QCD with two quark flavours
using lattice field configurations that have been produced with an O(a)
improved quark action. We find clear evidence for the expected suppression at
small quark mass, and examine the variation of chi with this mass. The
resulting estimate of the pion decay constant, f_pi = 105 +/- 6 ^{+18}_{-10}
MeV, is consistent with the experimental value of ~93 MeV. We compare chi to
the large-N_c prediction and find consistency over a large range of quark
masses. We discuss the benefits of the non-perturbative action improvement
scheme and of the stategy of keeping the lattice spacing (nearly) fixed as the
quark mass is varied. We compare our results with other studies and suggest why
such a quark mass dependence has not always been seen.


title: Light Quark Masses with Overlap Fermions in Quenched QCD

abstract:
  We present the results of a computation of the sum of the strange and average
up-down quark masses with overlap fermions in the quenched approximation. Since
the overlap regularization preserves chiral symmetry at finite cutoff and
volume, no additive quark mass renormalization is required and the results are
O(a) improved. Our simulations are performed at beta=6.0 and volume V=16^3X32,
which correspond to a lattice cutoff of ~2 GeV and to an extension of ~1.4 fm.
The logarithmically divergent renormalization constant has been computed
non-perturbatively in the RI/MOM scheme. By using the K-meson mass as
experimental input, we obtain (m_s + m_l)^RI(2 GeV) = 120(7)(21) MeV, which
corresponds m_s^MS (2 GeV) = 102(6)(18) MeV if continuum perturbation theory
and ChiPT are used. By using the GMOR relation we also obtain <psi psi>^MS(2
GeV)/N_f = - 0.0190(11)(33) GeV^3 = - [267(5)(15) MeV]^3.


title: The Nf=0 heavy quark potential from short to intermediate distances

abstract:
  We study the potential of a static quark anti-quark pair in the range 0.05fm
\leq r \leq 0.8fm, employing a sequence of lattices up to 64^4. Lattice
artifacts in potential and force are investigated theoretically as well as
numerically and continuum quantities are obtained by extrapolation of the
results at finite lattice spacing. Consistency of the numerical results with
the form of scaling violations predicted by an analysis `a la Symanzik is
found. The scale r_0/a is determined for the Wilson action up to beta=6.92.


title: The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions

abstract:
  We show how it is possible to give a precise and unambiguous implementation
of the Witten--Veneziano formula for the eta' mass on the lattice, which looks
like the formal continuum one, if the expression of the topological charge
density operator, suggested by fermions obeying the Ginsparg--Wilson relation,
is employed. By using recent numerical results from simulations with overlap
fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions, one obtains
values for the mass of the lightest pseudo-scalar flavour-singlet state that
agree within errors with theoretical expectations and experimental data,
respectively.


title: Effects of Quenching and Partial Quenching on Penguin Matrix Elements

abstract:
  In the calculation of non-leptonic weak decay rates, a "mismatch" arises when
the QCD evolution of the relevant weak hamiltonian down to hadronic scales is
performed in unquenched QCD, but the hadronic matrix elements are then computed
in (partially) quenched lattice QCD. This mismatch arises because the
transformation properties of penguin operators under chiral symmetry change in
the transition from unquenched to (partially) quenched QCD. Here we discuss
QCD-penguin contributions to $\Delta S=1$ matrix elements, and show that new
low-energy constants contribute at leading order in chiral perturbation theory
in this case. In the partially quenched case (in which sea quarks are present),
these low-energy constants are related to electro-magnetic penguins, while in
the quenched case (with no sea quarks) no such relation exists. As a simple
example, we give explicit results for $K^+\to\pi^+$ and $K^0\to vacuum$ matrix
elements, and discuss the implications for lattice determinations of
$K\to\pi\pi$ amplitudes from these matrix elements.


title: Majorana fermions on the lattice

abstract:
  The Monte Carlo simulation of Majorana fermions is discussed on the example
of supersymmetric Yang-Mills (SYM) theory.


title: Odd-flavor Hybrid Monte Carlo Algorithm for Lattice QCD

abstract:
  We discuss hybrid Monte Carlo algorithms for odd-flavor lattice QCD
simulations. The algorithms include a polynomial approximation which enables us
to simulate odd-flavor QCD in the framework of the hybrid Monte Carlo
algorithm. In order to make the algorithms exact, the correction factor to the
polynomial approximation is also included in an economical, stochastic way. We
test the algorithms for $n_f=1$, 1+1 and 2+1 flavors and compare results with
other algorithms.


title:
Calculation of Non-Leptonic Kaon Decay Amplitudes from $K\to\pi$ Matrix
  Elements in Quenched Domain-Wall QCD

abstract:
  We explore application of the domain wall fermion formalism of lattice QCD to
calculate the $K\to\pi\pi$ decay amplitudes in terms of the $K\to\pi$ and $K\to
0$ hadronic matrix elements through relations derived in chiral perturbation
theory. Numerical simulations are carried out in quenched QCD using domain-wall
fermion action for quarks and an RG-improved gauge action for gluons on a
$16^3\times 32\times 16$ and $24^3\times 32\times 16$ lattice at $\beta=2.6$
corresponding to the lattice spacing $1/a\approx 2$GeV. Quark loop contractions
which appear in Penguin diagrams are calculated by the random noise method, and
the $\Delta I=1/2$ matrix elements which require subtractions with the quark
loop contractions are obtained with a statistical accuracy of about 10%. We
confirm the chiral properties required of the $K\to\pi$ matrix elements.
Matching the lattice matrix elements to those in the continuum at $\mu=1/a$
using the perturbative renormalization factor to one loop order, and running to
the scale $\mu=m_c=1.3$ GeV with the renormalization group for $N_f=3$ flavors,
we calculate all the matrix elements needed for the decay amplitudes. With
these matrix elements, the $\Delta I=3/2$ decay amplitude shows a good
agreement with experiment in the chiral limit. The $\Delta I=1/2$ amplitude, on
the other hand, is about 50--60% of the experimental one even after chiral
extrapolation. In view ofthe insufficient enhancement of the $\Delta I=1/2$
contribution, we employ the experimental values for the real parts of the decay
amplitudes in our calculation of $\epsilon'/\epsilon$. We find that the $\Delta
I=3/2$ contribution is larger than the $\Delta I=1/2$ contribution so that
$\epsilon'/\epsilon$ is negative and has a magnitude of order $10^{-4}$.
Possible reasons for these unsatisfactory results are discussed.


title:
Locality and exponential error reduction in numerical lattice gauge
  theory

abstract:
  In non-abelian gauge theories without matter fields, expectation values of
large Wilson loops and loop correlation functions are difficult to compute
through numerical simulation, because the signal-to-noise ratio is very rapidly
decaying for increasing loop sizes. Using a multilevel scheme that exploits the
locality of the theory, we show that the statistical errors in such
calculations can be exponentially reduced. We explicitly demonstrate this in
the SU(3) theory, for the case of the Polyakov loop correlation function, where
the efficiency of the simulation is improved by many orders of magnitude when
the area bounded by the loops exceeds 1 fm^2.


title: Simple check of the vacuum structure in full QCD lattice simulations

abstract:
  Given the increasing availability of lattice data for (unquenched) QCD with
$N_f=2$, it is worth while to check whether the generated vacuum significantly
deviates from the quenched one. I discuss a specific attempt to do this on the
basis of topological susceptibility data gained at various sea-quark masses,
since for this observable detailed predictions are available. The upshot is
that either discretization effects in dynamical simulations are still
untolerably large or the vacuum structure in 2-flavour QCD substantially
deviates from that in the theory with 3 (or 2+1) light quarks.


title: Composite Reweighting the Glasgow Method for Finite Density QCD

abstract:
  The reweighting method developed in Glasgow to circumvent the lattice action
becoming complex at finite density suffers from a pathological onset transition
thought to be due to the reweighting. We present a new reweighting scheme based
on this approach in which we combine ensembles to alleviate the sampling bias
we identify in the polynomial coefficients of the fugacity expansion.


title: Vortex waistlines and long range fluctuations

abstract:
  We examine the manner in which a linear potential results from fluctuations
due to vortices linked with the Wilson loop. Our discussion is based on exact
relations and inequalities between the Wilson loop and the vortex and electric
flux order parameters. We show that, contrary to the customary naive picture,
only vortex fluctuations of thickness of the order of the spatial linear size
of the loop are capable of producing a strictly linear potential. An effective
theory of these long range fluctuations emerges naturally in the form of a
strongly coupled Z(N) lattice gauge theory. We also point out that dynamical
fermions introduced in this medium undergo chiral symmetry breaking.


title: Heavy Quark Effective Theory at one-loop order: An explicit example

abstract:
  We consider correlation functions containing the axial current of one light
and one heavy quark in the static approximation as well as in full QCD, using
the lattice regularization. Up to one-loop order of perturbation theory, we
study the difference between the full and the effective theory in the continuum
limit. In the full theory we find a term non-analytic in 1/m, revealing the
asymptotic character of the 1/m-expansion. In general, deviations from the
m-to-infinity limit turn out to be small and are well described by the first
non-trivial terms when m is a factor 2-3 above the external scale. We also
investigate the mass dependence of discretization errors, and find that the
behaviour of the correlation functions at finite lattice spacing differs
significantly from that in the continuum limit when the quark mass is large.


title: Cutoff effects in twisted mass lattice QCD

abstract:
  We present a first numerical study of lattice QCD with O(a) improved Wilson
quarks and a chirally twisted mass term. Renormalized correlation functions are
derived from the Schroedinger functional and evaluated in an intermediate
space-time volume of size 0.75^3 x 1.5 fm^4. In the quenched approximation
precise results are then obtained with a moderate computational effort,
allowing for a detailed study of the continuum approach. The latter is
discussed in terms of observables which converge to meson masses and decay
constants in the limit of large space-time volume. In the O(a) improved theory
we find residual cutoff effects to be at the level of a few percent for lattice
spacings of about 0.1 fm.


title:
Chiral Properties of Pseudoscalar Mesons on a Quenched $20^4$ Lattice
  with Overlap Fermions

abstract:
  The chiral properties of the pseudoscalar mesons are studied numerically on a
quenched $20^4$ lattice with the overlap fermion. We elucidate the role of the
zero modes in the meson propagators, particularly that of the pseudoscalar
meson. The non-perturbative renormalization constant $Z_A$ is determined from
the axial Ward identity and is found to be almost independent of the quark mass
for the range of quark masses we study; this implies that the $O(a^2)$ error is
small. The pion decay constant, $f_{\pi}$, is calculated from which we
determine the lattice spacing to be 0.148 fm. We look for quenched chiral log
in the pseudoscalar decay constants and the pseudoscalar masses and we find
clear evidence for its presence. The chiral log parameter $\delta$ is
determined to be in the range 0.15 -- 0.4 which is consistent with that
predicted from quenched chiral perturbation theory.


title: The Critical Hopping Parameter in O(a) improved Lattice QCD

abstract:
  We calculate the critical value of the hopping parameter, $\kappa_c$, in O(a)
improved Lattice QCD, to two loops in perturbation theory. We employ the
Sheikholeslami-Wohlert (clover) improved action for Wilson fermions.
  The quantity which we study is a typical case of a vacuum expectation value
resulting in an additive renormalization; as such, it is characterized by a
power (linear) divergence in the lattice spacing, and its calculation lies at
the limits of applicability of perturbation theory.
  The dependence of our results on the number of colors $N$, the number of
fermionic flavors $N_f$, and the clover parameter $c_{SW}$, is shown
explicitly. We compare our results to non perturbative evaluations of
$\kappa_c$ coming from Monte Carlo simulations.


title: On the glueball spectrum in O(a)-improved lattice QCD

abstract:
  We calculate the light `glueball' mass spectrum in N_f=2 lattice QCD using a
fermion action that is non-perturbatively O(a) improved. We work at lattice
spacings a ~0.1 fm and with quark masses that range down to about half the
strange quark mass. We find the statistical errors to be moderate and under
control on relatively small ensembles. We compare our mass spectrum to that of
quenched QCD at the same value of a. Whilst the tensor mass is the same (within
errors), the scalar mass is significantly smaller in the dynamical lattice
theory, by a factor of ~(0.84 +/- 0.03). We discuss what the observed m_q
dependence of this suppression tells us about the dynamics of glueballs in QCD.
We also calculate the masses of flux tubes that wind around the spatial torus,
and extract the string tension from these. As we decrease the quark mass we see
a small but growing vacuum expectation value for the corresponding flux tube
operators. This provides clear evidence for `string breaking' and for the
(expected) breaking of the associated gauge centre symmetry by sea quarks.


title:
Simulations of Discrete Random Geometries: Simplicial Quantum Gravity
  and Quantum String Theory

abstract:
  I investigate two discrete models of random geometries, namely simplicial
quantum gravity and quantum string theory. In four-dimensional simplicial
quantum gravity, I show that the addition of matter gauge fields to the model
is capable of changing its phase structure by replacing the branched polymers
of the pure gravity model with a new phase that has a negative string
susceptibility exponent and a fractal dimension of four. Some of the results
are derived from a strong coupling expansion of the model, a technique which is
used here for the first time in this context. In quantum string theory, I study
a discrete version of the IIB superstring. I show that the divergences
encountered in the discretization of the bosonic string are eliminated in the
supersymmetric case. I give theoretical arguments for the appearance of
one-dimensional structures in the region of large system extents that manifest
as a power-law tail in the link length distribution; this is confirmed by
numerical simulations of the model. I also examine a lower-dimensional version
of the IKKT matrix model, in which a similar effect can be observed.


title: Exact Lattice Supersymmetry: the Two-Dimensional N=2 Wess-Zumino Model

abstract:
  We study the two-dimensional Wess-Zumino model with extended N=2
supersymmetry on the lattice. The lattice prescription we choose has the merit
of preserving {\it exactly} a single supersymmetric invariance at finite
lattice spacing $a$. Furthermore, we construct three other transformations of
the lattice fields under which the variation of the lattice action vanishes to
$O(ga^2)$ where $g$ is a typical interaction coupling. These four
transformations correspond to the two Majorana supercharges of the continuum
theory. We also derive lattice Ward identities corresponding to these exact and
approximate symmetries. We use dynamical fermion simulations to check the
equality of the massgaps in the boson and fermion sectors and to check the
lattice Ward identities. At least for weak coupling we see no problems
associated with a lack of reflection positivity in the lattice action and find
good agreement with theory. At strong coupling we provide evidence that
problems associated with a lack of reflection positivity are evaded for small
enough lattice spacing.


title: Hamiltonian Lattice QCD with Wilson Fermions at Strong Coupling

abstract:
  Hamiltonian lattice QCD with Wilson fermions is investigated systematically
by strong-coupling expansion up to the second order. The effective Hamiltonian
is diagonalized by Bogoliubov transformation. The vacuum energy, chiral
condensate, pseudo-scalar and vector meson masses are calculated. The
comparison with the unitary transformation method by Luo and Chen is also made.
The method discussed in this paper has potential application to QCD at finite
density.


title: Monte Carlo Hamiltonian: Generalization to Quantum Field Theory

abstract:
  Monte Carlo techniques with importance sampling have been extensively applied
to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is
extremely difficult to compute the excited states using the conventional Monte
Carlo algorithm. Our recently developed approach: the Monte Carlo Hamiltonian
method, has been designed to overcome the difficulties of the conventional
approach. In this paper, we extend the method to many body systems and quantum
field theory. The Klein-Gordon field theory is used as a testing ground.


title: Abelian projected monopoles - to be or not to be

abstract:
  We analyse what happens with two merging constituent monopoles for the SU(3)
caloron. Identified through degenerate eigenvalues (the singularities or
defects of the abelian projection) of the Polyakov loop, it follows that there
are defects that are not directly related to the actual constituent monopoles.


title: Perturbative renormalization for overlap fermions

abstract:
  Using lattice overlap fermions, we have computed the 1-loop renormalization
factors of several operators that measure DIS structure functions and weak
amplitudes. Computer codes written in the algebraic manipulation language FORM
have been used. The improvement of the operators is also discussed.


title: Using Lattice QCD and ChPT to obtain non-leptonic K-decay amplitudes

abstract:
  We summarize some of the difficulties that confront lattice calculations of
non-leptonic kaon decay matrix elements. We review some of the methods that
have been proposed to overcome these difficulties, and discuss the importance
of one-loop ChPT in this respect, including the role of O(p^4) operators.


title: Numerical Portrait of a Relativistic Thin Film BCS Superfluid

abstract:
  We present results of numerical simulations of the 2+1d Nambu - Jona-Lasinio
model with a non-zero baryon chemical potential mu including the effects of a
diquark source term. Diquark condensates, susceptibilities and masses are
measured as functions of source strength j. The results suggest that diquark
condensation does not take place in the high density phase mu>mu_c, but rather
that the condensate scales non-analytically with j implying a line of critical
points and long range phase coherence. Analogies are drawn with the low
temperature phase of the 2d XY model. The spectrum of the spin-1/2 sector is
also studied yielding the quasiparticle dispersion relation. There is no
evidence for a non-zero gap; rather the results are characteristic of a normal
Fermi liquid with Fermi velocity less than that of light. We conclude that the
high density phase of the model describes a relativistic gapless thin film BCS
superfluid.

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


title: The (11112) model on a 1+1 dimensional lattice

abstract:
  We study the chiral gauge model (11112) of four left-movers and one
right-mover with strong interactions in the 1+1 dimensional lattice. Exact
computations of relevant $S$-matrix elements demonstrate a loophole that so
constructed model and its dynamics can possibly evade the ``no-go'' theorem of
Nielsen and Ninomiya.


title: Constructing States and Effective Hamiltonians in Lattice QCD

abstract:
  We formulate SU(3) Hamiltonian lattice QCD in terms of the plaquette
variables and determine the relevant subspaces of the Hilbert space for the
vacuum wave functional and its approximations. We analyze the one- and
two-plaquette problems.


title: First results from a parametrized Fixed-Point QCD action

abstract:
  We have constructed a new fermion action which is an approximation to the
(chirally symmetric) Fixed-Point action, containing the full Clifford algebra
with couplings inside a hypercube and paths built from renormalization group
inspired fat links. We present an exploratory study of the light hadron
spectrum and the energy-momentum dispersion relation.


title: Adaptive Optimization of Wave Functions for Lattice Field Models

abstract:
  The accuracy of Green Function Monte Carlo (GFMC) simulations can be greatly
improved by a clever choice of the approximate ground state wave function that
controls configuration sampling. This trial wave function typically depends on
many free parameters whose fixing is a non trivial task. Here, we discuss a
general purpose adaptive algorithm for their non-linear optimization. As a non
trivial application we test the method on the two dimensional Wess-Zumino
model, a relativistically invariant supersymmetric field theory with
interacting bosonic and fermionic degrees of freedom.


title: The Isgur-Wise function on the lattice

abstract:
  The h+, h_A1 form factors for the semi-leptonic B->D and B->D* decays are
evaluated in quenched lattice QCD with beta=6.2. The action and the operators
are fully O(a) non-perturbatively improved. The Isgur-Wise function is
evaluated and fitted to extract its slope; the latter is found to be
rho^2=1.1(2)(3) from the B->D* decay and rho^2=1.0(2)(3) from the B->D decay.
The form factors ratios R_1, R_2 are evaluated and found to be in agreement
with experimental determinations.


title:
Chiral measurements with the Fixed-Point Dirac operator and construction
  of chiral currents

abstract:
  In this preliminary study, we examine the chiral properties of the
parametrized Fixed-Point Dirac operator D^FP, see how to improve its chirality
via the Overlap construction, measure the renormalized quark condensate Sigma
and the topological susceptibility chi_t, and investigate local chirality of
near zero modes of the Dirac operator. We also give a general construction of
chiral currents and densities for chiral lattice actions.


title: Heatbath Noise Methods in Lattice QCD

abstract:
  In a recent paper, de Forcrand has pointed out that matrix inversions using
Gaussian noise need not be iterated to full convergence, but instead may be
solved approximately and treated as a heatbath. Gaussian noise however is not
optimal for minimizing variance. It shown here how his algorithm may be
generalized to a mixture of Gaussian and Z(N) noise, resulting in a smaller
effective variance for some operators.


title: Deflation of Eigenvalues for GMRES in Lattice QCD

abstract:
  Versions of GMRES with deflation of eigenvalues are applied to lattice QCD
problems. Approximate eigenvectors corresponding to the smallest eigenvalues
are generated at the same time that linear equations are solved. The
eigenvectors improve convergence for the linear equations, and they help solve
other right-hand sides.


title: I=2 Pion Scattering Length from a Coarse Anisotropic Lattice Calculation

abstract:
  Using the tadpole improved clover Wilson quark action on coarse anisotropic
lattices, the $\pi\pi$ scattering length in the I=2 channel is calculated
within quenched approximation. We show that such a calculation is feasible
using small lattices on small computers provided that the finite volume and
finite lattice spacing errors are under control. Our results are extrapolated
towards the chiral, infinite volume and continuum limit. Comparisons of our
results with previous lattice results from JLQCD collaboration, the new results
from E865 experiment, and the results from Chiral Perturbation Theory are made.
Good agreements are found.


title:
Scalar Glueball Mass Reduction at Finite Temperature in SU(3)
  Anisotropic Lattice QCD

abstract:
  We report the first study of the glueball properties at finite temperatures
below T_c using SU(3) anisotropic lattice QCD with beta=6.25, the renormalized
anisotropy xi \equiv a_s/a_t = 4 and 20^3 \times N_t
(N_t=35,36,37,38,40,43,45,50,72) at the quenched level. From the temporal
correlation analysis with the smearing method, about 20 % mass reduction is
observed for the lowest scalar glueball as m_G(T)=1250 \pm 50MeV for 0.8 T_c <
T < T_c in comparison with m_G \simeq 1500 \sim 1700MeV at T \simeq 0.


title: Atomic Bose Condensation and the Lattice

abstract:
  I show how interaction corrections to the Bose condensation temperature of an
atomic gas can be computed using a combination of perturbative effective field
theory and lattice techniques.


title: Specific heat and energy for the three-dimensional O(2) model

abstract:
  We investigate the three-dimensional O(2) model on lattices of size 8^3 to
160^3 close to the critical point at zero magnetic field. We confirm explicitly
the value of the critical coupling J_c found by Ballesteros et al. and estimate
there the universal values of g_r and xi/L. At the critical point we study the
finite size dependencies of the energy density epsilon and the specific heat C.
We find that the nonsingular part of the specific heat C_{ns} is linearly
dependent on 1/alpha. From the critical behaviour of the specific heat for T
not T_c on the largest lattices we determine the universal amplitude ratio
A+/A-. The alpha- dependence of this ratio is close to the phenomenological
relation A+/A- = 1-4alpha.


title: Spin splittings among charmed hadrons

abstract:
  The mass differences between spin-1/2 and spin-3/2 baryons are compared to
the mass differences between spin-0 and spin-1 mesons. Results of simulations
for charmed hadrons in the quenched approximation from a tadpole-improved
anisotropic action are discussed in the context of other lattice calculations,
quark model predictions, heavy quark symmetry predictions and experimental
data.


title: Lattice results for the decay constant of heavy-light vector mesons

abstract:
  We compute the leptonic decay constants of heavy-light vector mesons in the
quenched approximation. The reliability of lattice computations for heavy
quarks is checked by comparing the ratio of vector to pseudoscalar decay
constant with the prediction of Heavy Quark Effective Theory in the limit of
infinitely heavy quark mass. Good agreement is found. We then calculate the
decay constant ratio for B mesons: $f_{B^*}/f_B= 1.01(0.01)(^{+0.04}_{-0.01})$.
We also quote quenched $f_{B^*}=177(6)(17)$ MeV.


title:
Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson
  lattice Dirac operator

abstract:
  A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac
operator does not possess any topological zero modes in
topologically-nontrivial gauge backgrounds, it can reproduce correct axial
anomaly for sufficiently smooth gauge configurations, provided that it is
exponentially-local, doublers-free, and has correct continuum behavior. In this
paper, we calculate the axial anomaly of this lattice Dirac operator in weak
coupling perturbation theory, and show that it recovers the topological charge
density in the continuum limit.


title: Thermodynamics of 2 and 3 flavour QCD

abstract:
  We discuss recent results on the thermodynamics of QCD in the presence of
light dynamical quark degrees of freedom. In particular, we concentrate on an
analysis of the flavour and quark mass dependence of the QCD phase diagram, the
equation of state and the transition temperature. Moreover, we present recent
results on the heavy quark free energy.


title: Cluster Percolation and Explicit Symmetry Breaking in Spin Models

abstract:
  Many features of spin models can be interpreted in geometrical terms by means
of the properties of well defined clusters of spins. In case of spontaneous
symmetry breaking, the phase transition of models like the q-state Potts model,
O(n), etc., can be equivalently described as a percolation transition of
clusters. We study here the behaviour of such clusters when the presence of an
external field H breaks explicitly the global symmetry of the Hamiltonian of
the theory. We find that these clusters have still some interesting
relationships with thermal features of the model.


title: Families index theory for Overlap lattice Dirac operator. I

abstract:
  The index bundle of the Overlap lattice Dirac operator over the orbit space
of lattice gauge fields is introduced and studied. Obstructions to the
vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge
theory have a natural description in this context. Our main result is a formula
for the topological charge (integrated Chern character) of the index bundle
over even-dimensional spheres in the orbit space. It reduces under suitable
conditions to the topological charge of the usual (continuum) index bundle in
the classical continuum limit (this is announced and sketched here; the details
will be given in a forthcoming paper). Thus we see that topology of the index
bundle of the Dirac operator over the gauge field orbit space can be captured
in a finite-dimensional lattice setting.


title:
Calculating the I=2 Pion Scattering Length Using Tadpole Improved Clover
  Wilson Action on Coarse Anisotropic Lattices

abstract:
  In an exploratory study, using the tadpole improved clover Wilson quark
action on small, coarse and anisotropic lattices, the $\pi\pi$ scattering
length in the I=2 channel is calculated within quenched approximation. A new
method is proposed which enables us to make chiral extrapolation of our lattice
results without calculating the decay constant on the lattice. Finite volume
and finite lattice spacing errors are analyzed and the results are extrapolated
towards the infinite volume and continuum limit. Comparisons of our lattice
results with the new experiment and the results from Chiral Perturbation Theory
are made. Good agreements are found.


title: Theory of color confinement: state of the art

abstract:
  The existing evidence for dual superconductivity as mechanism of color
confinement is reviewed. We also discuss what is known on the dual excitations,
which produce confinement by condensation, and what are the open problems


title:
Chiral properties of domain-wall fermions from eigenvalues of 4
  dimensional Wilson-Dirac operator

abstract:
  We investigate chiral properties of the domain-wall fermion (DWF) system by
using the four-dimensional hermitian Wilson-Dirac operator. We first derive a
formula which connects a chiral symmetry breaking term in the five dimensional
DWF Ward-Takahashi identity with the four dimensional Wilson-Dirac operator,
and simplify the formula in terms of only the eigenvalues of the operator,
using an ansatz for the form of the eigenvectors. For a given distribution of
the eigenvalues, we then discuss the behavior of the chiral symmetry breaking
term as a function of the fifth dimensional length. We finally argue the chiral
property of the DWF formulation in the limit of the infinite fifth dimensional
length, in connection with spectra of the hermitian Wilson-Dirac operator in
the infinite volume limit as well as in the finite volume.


title: Quenched QCD at finite temperature with overlap Fermions

abstract:
  We study quenched QCD just above the phase transition temperature using
overlap Fermions. Exact zero modes of the overlap operator are localized.
Chiral symmetry is restored, as indicated by the behavior of the chiral
condensate after subtracting the effects of zero modes. The vector and
pseudo-scalar screening masses are close to ideal gas values.


title: Spectral function at high temperature

abstract:
  For a weakly coupled quantum field at high temperature the classical
approximation offers a possibility to gain insight into nonperturbative
real-time dynamics. I use this to present a nonperturbative approach to the
computation of spectral functions in real time. Results are shown for a scalar
field in 2+1 dimensions.


title:
Self-Duality and Statistical Systems without Internal Energy Scaling
  Terms at Criticality

abstract:
  It is argued that self-duality of one system leads to the zero finite-size
scaling amplitude of the critical internal energy for all system belonging to
the same universality class. For such models, we may expect that condition of
equality (up to correction-to-scaling terms) of the internal energies for
systems with different sizes will yield more accurate estimates for the
critical temperature than the scaling equation for the inverse correlation
lengths which is used in the standard phenomenological renormalization-group
approach. Analytical and numerical evidences confirming the above conjecture
are given for examples of two-dimensional next-nearest-neighbour and spin-1
Ising lattices.


title: Heavy light decay constants on the lattice

abstract:
  We present results for the leptonic decays of heavy-light mesons in the
quenched approximation and a preliminary result for f_Ds with dynamical
fermions for Nf=2. We examine the systematic effects of extrapolating the decay
constants from the charm to the bottom quark mass, and find this extrapolation
to be under control. We present a preliminary result for f_Ds{Nf=2} and compare
to f_Ds{Nf=0} matched to have the same lattice spacing set by the Sommer scale,
r0. We find no significant difference.


title: Quark-gluon vertex in a momentum subtraction scheme

abstract:
  We compute the quark-gluon vertex in quenched QCD, in the Landau gauge using
an off-shell mean-field O(a)-improved fermion action. The running coupling is
calculated in an `asymmetric' momentum subtraction scheme (MOM~). We obtain a
crude estimate for Lambda_MSbar=170+/-65 MeV, which is considerably lower than
other determinations of this quantity. However, substantial systematic errors
remain.


title: The strangeness content of the nucleon

abstract:
  We evaluate the matrix element of $\bar{q} q$ in hadron states on a lattice.
We find substantial mixing of the connected and disconnected contributions so
that the lattice result that the disconnected contribution to the nucleon is
large does not imply that the $\bar{s} s$ content is large. This has
implications for dark matter searches.


title: Diquark condensation in dense adjoint matter

abstract:
  We study SU(2) lattice gauge theory at non-zero chemical potential with one
staggered quark flavor in the adjoint representation. In this model the fermion
determinant, although real, can be both positive and negative. We have
performed numerical simulations using both hybrid Monte Carlo and two-step
multibosonic algorithms, the latter being capable of exploring sectors with
either determinant sign. We find that the positive determinant sector behaves
like a two-flavor theory, with the chiral condensate rotating into a two-flavor
diquark condensate for mu>m_pi/2, implying a superfluid ground state. Good
agreement is found with analytical predictions made using chiral perturbation
theory. In the `full' model there is no sign of either onset of baryon density
or diquark condensation for the range of chemical potentials we have
considered. The impact of the sign problem has prevented us from exploring the
true onset transition and the mode of diquark condensation, if any, for this
model.


title: External Field Dependence of Deconfinement Temperature in SU(3)

abstract:
  We study vacuum dynamics of SU(3) lattice gauge theory at finite temperature.
Using the lattice Schr\"odinger functional, SU(3) vacuum is probed by means of
an external constant Abelian chromomagnetic field. Our preliminary numerical
data suggest that, by increasing the strength of the applied external field,
deconfinement temperature decreases towards zero. This means that strong enough
Abelian chromomagnetic fields destroy confinement of color.


title:
Lattice study of the simplified model of M-theory for larger gauge
  groups

abstract:
  Lattice discretization of the supersymmetric Yang-Mills quantum mechanics is
dis cussed. First results of the quenched Monte Carlo simulations, for D=4 and
with higher g auge groups (3 <= N <= 8), are presented. We confirm an earlier
(N=2) evidence tha t the system reveals different behaviours at low and high
temperatures separated by a narrow transiti on region. These two regimes may
correspond to a black hole and elementary excitations phases conjectured in the
M-theory. Dependence of the "transition temperature" on N is consistent with 't
Hooft scaling and shows a smooth saturation of lattice results towards the
large N limit. Is not yet resolved if the observed change between the two
regimes corresponds to a genuine phase transition or to a gentle crossover . A
new, noncompact formulation of the lattice model is also proposed and its
advantages are briefly discussed.


title: Center Dominance Recovered: Direct Laplacian Center Gauge

abstract:
  We introduce a variation of direct maximal center gauge fixing: the "direct
Laplacian" center gauge. The new procedure consists of first fixing to the
Laplacian adjoint Landau gauge, followed by overrelaxation to the nearby Gribov
copy of the direct maximal center gauge. Certain shortcomings of maximal center
gauge, associated with Gribov copies, are overcome in the new gauge, in
particular center dominance is recovered.


title: Confinement versus color superconductivity: a lattice investigation

abstract:
  High density YM-theory is addressed by means of an effective theory where a
Higgs type field corresponds to the diquark order parameter. The effective
Higgs theory mimics the Cooper instability at the Fermi surface. After Landau
gauge fixing, the theory possesses a global color degree of freedom. Color
superconductivity corresponds to a spontaneous breakdown of the residual global
color symmetry. Numerical simulations illustrate this mechanism of
spontaneously broken global color for the case of the standard electro-weak
phase transition and for the case of the transition between the confinement and
the Higgs phase, respectively. The latter transition is relevant for the study
of diquark condensation.


title: Lattice Matter

abstract:
  I review recent developments in the study of strongly interacting field
theories with non-zero chemical potential mu. In particular I focus on (a) the
determination of the QCD critical endpoint in the (mu,T) plane; (b) superfluid
condensates in Two Color QCD; and (c) Fermi surface effects in the NJL model.
Some remarks are made concerning the relation of superconductivity with the
sign problem.


title: Semileptonic decay of a heavy-light pseudoscalar to a light vector meson

abstract:
  We present the results of a calculation of semileptonic form factors of D and
B mesons. The calculation uses nonperturbatively order a improved quenched
lattice QCD and two values of the coupling. Results for charm mesons show
reasonable agreement with experiment. The lattice results for B -> rho l nu are
compared with high q^2 experimental results.


title:
A nonperturbative determination of c_A and the scaling of f_pi and
  m^{MSbar}

abstract:
  We calculate the $O(a)$ improvement coefficient for the axial-vector current
using the nonperturbative method proposed by the LANL group. Results for the
coefficient in the range $\beta=5.93$ to 6.2 are presented. We find $c_A$ is
close to the 1-loop tadpole-improved perturbative value. In addition, scaling
of the pseudoscalar decay constant and renormalised quark mass is improved
compared to that obtained using the (larger) $c_A$ values obtained by the ALPHA
collaboration.


title: Unquenching the topological susceptibility with an overlap action

abstract:
  We estimate the quark-mass dependence of the topological susceptibility with
dynamical overlap and clover fermions. Unquenching effects on the
susceptibility turn out to be well approximated by a reweighting of a quenched
ensemble with a low-eigenmode truncation of the fermionic determinant. We find
that it is most likely due to the explicit chiral symmetry breaking of the
fermion action that present day dynamical simulations do not show the expected
suppression of the topological susceptibility.


title:
Determining hybrid content of heavy quarkonia using lattice
  nonrelativistic QCD

abstract:
  Using lowest-order lattice NRQCD to create heavy meson propagators and
applying the spin-dependent interaction, $c_B^{}
\frac{-g}{2m_q}\vec\sigma\cdot\vec{B}$, at varying intermediate time slices, we
compute the off-diagonal matrix element of the Hamiltonian for the
quarkonium-hybrid two-state system. Diagonalizing this two-state Hamiltonian,
the admixture of hybrid ($|Q\bar{Q}g>$) in the ground state is found. We
present results from a set of quenched lattices with an interpolation in quark
mass to match the bottomonium spectrum.


title: Abelian and Center Vortex Condensation in SU(3) Lattice Gauge Theory

abstract:
  We study the condensation of Abelian and Center vortices in SU(3) lattice
gauge theory at finite temperature. We find that both vortices condense in the
confined phase of the SU(3) vacuum.


title: F_B from moving B mesons

abstract:
  We show results for the B meson decay constant calculated both for B mesons
at rest and those with non-zero momentum and using both the temporal and
spatial components of the axial vector current. It is an important check of
lattice systematic errors that all these determinations of f_B should agree. We
also describe how well different smearings for the B meson work at non-zero
momentum - the optimal smearing has a narrow smearing for the b quark.


title: Topology and Confinement in SU(N) Gauge Theories

abstract:
  The large N limit of SU(N) gauge theories in 3+1 dimensions is investigated
on the lattice by extrapolating results obtained for $2 \le N \le 5$. A
numerical determination of the masses of the lowest-lying glueball states and
of the topological susceptibility in the limit $N\to\infty$ is provided. Ratios
of the tensions of stable k-strings over the tension of the fundamental string
are investigated in various regimes and the results are compared with
expectations based on several scenarios -- in particular MQCD and Casimir
scaling. While not conclusive at zero temperature in D=3+1, in the other cases
investigated our data seem to favour the latter.


title: Understanding chiral symmetry breaking with the overlap action

abstract:
  A chiral fermion action allows one to do very clean studies of chiral
symmetry breaking in QCD. I will briefly describe how to compute with the
overlap action (relatively) cheaply, and then turn to physics: Low modes of the
Dirac operator show a ``lumped'' chiral density which peaks at the locations of
instantons and anti-instantons. These modes dominate correlation functions at
small quark mass in many channels. The picture qualitatively (and in some cases
quantitatively) resembles an instanton liquid model.


title: Matrix elements of (delta S=2) operators with Wilson fermions

abstract:
  We test the recent proposal of using the Ward identities to compute the
K0-K0bar mixing amplitude with Wilson fermions, without the problem of spurious
lattice subtractions. From our simulations, we observe no difference between
the results obtained with and without subtractions. In addition, from the
standard study of the complete set of (delta S=2) operators, we quote the
following (preliminary) results (in the MS(NDR) scheme): Bk(2 GeV)=0.70(10), <
O7^{3/2}>_{K->pi pi} = 0.10(2)(1) GeV^3, < O8^{3/2}>_{K->pi pi} = 0.49(6)(0)
GeV^3.


title: Lattice QCD on PCs?

abstract:
  Current PC processors are equipped with vector processing units and have
other advanced features that can be used to accelerate lattice QCD programs.
Clusters of PCs with a high-bandwidth network thus become powerful and
cost-effective machines for numerical simulations.


title:
Dynamics of the Scalar Condensate in thermal 4D self-interacting Scalar
  Field Theory on the Lattice

abstract:
  We simulate a four dimensional self-interacting scalar field theory on the
lattice at finite temperature. By varying temperature, the system undergoes a
phase transition from broken phase to symmetric phase. Our data show that the
zero-momentum field renormalization increases by approaching critical
temperature. On the other hand, finite-momentum wave-function renormalization
remains remarkably constant.


title: A new fermion Hamiltonian for lattice gauge theory

abstract:
  We formulate Hamiltonian vector-like lattice gauge theory using the overlap
formula for the spatial fermionic part, $H_f$. We define a chiral charge, $Q_5$
which commutes with $H_f$, but not with the electric field term. There is an
interesting relation between the chiral charge and the fermion energy with
consequences for chiral anomalies.


title: Spectrum Results with Kogut-Susskind Quarks

abstract:
  I summarize recent developments in spectrum calculations using Kogut-Susskind
quarks. Theoretical developments include one-loop computations with improved
actions. I present some recent simulation results, mostly from a MILC
collaboration project using three flavors. Effects of dynamical quarks are
clearly seen in the isovector 0++ meson propagator and in the mass ratio ``J''.


title:
Anatomy of Isolated Monopole in Abelian Projection of SU(2) Lattice
  Gauge Theory

abstract:
  We study the structure of the isolated static monopoles in the maximal
Abelian projection of SU(2) lattice gluodynamics. Our estimation of the
monopole radius is $ \approx 0.06 fm$.


title: Center vortex model for the infrared sector of Yang-Mills theory

abstract:
  A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic
vortices represented by (closed) random surfaces, is presented. The model
quantitatively describes both confinement (including the finite-temperature
transition to a deconfined phase) and the topological susceptibility of the
Yang-Mills ensemble. A first (quenched) study of the spectrum of the Dirac
operator furthermore yields a behavior for the chiral condensate which is
compatible with results obtained in lattice gauge theory.


title: Cluster Percolation and Thermal Critical Behaviour

abstract:
  Continuous phase transitions in spin systems can be formulated as percolation
of suitably defined clusters. We review this equivalence and then discuss how
in a similar way, the color deconfinement transition in SU(2) gauge theory can
be treated as a percolation phenomenon. In the presence of an external field,
spin systems cease to show thermal critical behavior, but the geometric
percolation transition persists (Kert\'esz line). For $H\not=0$, we study the
relation between percolation and pseudocritical behavior, both for continuous
and first order transitions, and show that it leads to the necessity of an
$H$-dependent cluster definition. A viable formulation of this kind could serve
as definition of deconfinement in QCD with dynamical quarks.


title:
Comparison of finite-size-scaling functions for 3d O(N) spin models to
  QCD

abstract:
  We calculate numerically universal finite-size-scaling functions of the
magnetization for the three-dimensional O(4) and O(2) spin models. The approach
of these functions to the infinite-volume scaling functions is studied in
detail on the critical and pseudocritical lines. For this purpose we determine
the pseudocritical line in two different ways. We find that the asymptotic form
of the finite-size-scaling functions is already reached at small values of the
scaling variable. A comparison with QCD lattice data for two flavours of
staggered fermions shows a similar finite-size behaviour which is compatible
with that of the spin models.


title:
Chirally improved Dirac operators: Studying the sensitivity to
  topological excitations for zero and finite temperature

abstract:
  We discuss the construction and properties of an approximate solution of the
Ginsparg-Wilson equation, the so-called chirally improved lattice Dirac
operator. In particular we study the behavior of its eigenmodes in smooth
instanton backgrounds as well as for thermalized gauge configurations on both
sides of the QCD phase transition. We compare with results from other Dirac
operators including the overlap operator. The results support the picture of
chiral symmetry breaking being closely related to instantons.