title: A Study of the 't Hooft Model with the Overlap Dirac Operator

abstract:
  We present the results of an exploratory numerical study of two dimensional
QCD with overlap fermions. We have performed extensive simulations for U(N_c)
and SU(N_c) color groups with N_c=2, 3, 4 and coupling constants chosen to
satisfy the 't Hooft condition g^2 N_c =const=4/3. We have computed the meson
spectrum and decay constants, the topological susceptibility and the chiral
condensate. For U(N_c) gauge groups, our results indicate that the
Witten-Veneziano relation is satisfied within our statistical errors and that
the chiral condensate for N_f=1 is compatible with a non-zero value. Our
results exhibit universality in N_c and confirm once more the excellent chiral
properties of the overlap-Dirac operator.


title: CP Violation and the CKM Matrix

abstract:
  This lecture provides a general overview of CP violation, emphasizing CP
violation in flavour-violating interactions, such as due to the
Kobayashi-Maskawa mechanism.


title: Strings, quantum gravity and non-commutative geometry on the lattice

abstract:
  I review recent progress in understanding non-perturbative aspects of string
theory, quantum gravity and non-commutative geometry using lattice methods.


title: 3d Lorentzian, Dynamically Triangulated Quantum Gravity

abstract:
  The model of Lorentzian three-dimensional dynamical triangulations provides a
non-perturbative definition of three-dimensional quantum gravity. The theory
has two phases: a weak-coupling phase with quantum fluctuations around a
``semiclassical'' background geometry which is generated dynamically despite
the fact that the formulation is explicitly background-independent, and a
strong-coupling phase where ``classical'' space disintegrates into a foam of
baby universes.


title: Mesonic Wavefunctions in the three-dimensional Gross-Neveu model

abstract:
  We present results from a numerical study of bound state wavefunctions in the
(2+1)-dimensional Gross-Neveu model with staggered lattice fermions at both
zero and nonzero temperature. Mesonic channels with varying quantum numbers are
identified and analysed. In the strongly coupled chirally broken phase at T=0
the wavefunctions expose effects due to varying the interaction strength more
effectively than straightforward spectroscopy. In the weakly coupled chirally
restored phase information on fermion - antifermion scattering is recovered. In
the hot chirally restored phase we find evidence for a screened interaction.
The T=0 chirally symmetric phase is most readily distinguished from the
symmetric phase at high T via the fermion dispersion relation.


title: On the quality of random number generators with taps

abstract:
  Recent exact analytical results developed for the random number generators
with taps are reported. These results are applicable to a wide class of
algorithms, including random walks, cluster algorithms, Ising models. Practical
considerations on the improvement of the quality of random numbers are
discussed as well.


title: A Perturbative Study of a General Class of Lattice Dirac Operators

abstract:
  A perturbative study of a general class of lattice Dirac operators is
reported, which is based on an algebraic realization of the Ginsparg-Wilson
relation in the form
  $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} =
  2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer.
The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation
and thus to the overlap operator. We study one-loop fermion contributions to
the self-energy of the gauge field, which are related to the fermion
contributions to the one-loop $\beta$ function and to the Weyl anomaly. We
first explicitly demonstrate that the Ward identity is satisfied by the
self-energy tensor. By performing careful analyses, we then obtain the correct
self-energy tensor free of infra-red divergences, as a general consideration of
the Weyl anomaly indicates. This demonstrates that our general operators give
correct chiral and Weyl anomalies. In general, however, the Wilsonian effective
action, which is supposed to be free of infra-red complications, is expected to
be essential in the analyses of our general class of Dirac operators for
dynamical gauge field.


title: Quenched lattice QCD at finite isospin density and related theories

abstract:
  We study quenched QCD at finite chemical potential, $\mu_I$, for the third
component of isospin and quenched two-colour QCD at finite chemical potential,
$\mu$, for quark number. In contrast to the quenched approximation to QCD at
finite quark-number chemical potential, the quenched approximations to these
theories behave similarly to the full theories. The reason is that these
theories have real positive fermion determinants. In both of these theories
there is some critical chemical potential above which the charge coupled to the
chemical potential is spontaneously broken. In each case, the transition
appears to be second order. We study the scaling properties near the critical
point using scaling functions suggested by effective (chiral) Lagrangians and
find evidence for scaling with mean-field critical exponents in each case. The
subtleties associated with observing the critical scaling of these theories are
discussed.


title: Monopoles in Lattice QCD with Abelian Projection as Quantum Monopoles

abstract:
  Within the context of the Abelian Projection of QCD monopole-like quantum
excitations of gauge fields are studied. We start with certain classical
solutions, of the SU(2) Yang-Mills field equations, which are not monopole-like
and whose energy density diverges as $r \to \infty$. These divergent classical
solutions are then quantized using a modified version of Heisenberg's
quantization technique for strongly interacting, nonlinear fields. The modified
Heisenberg quantization technique leads to a system of equations with mixed
quantum and classical degrees of freedom. By applying a Feynman path
integration over the quantum degrees of freedom the quantum-averaged solution
gives a nondivergent, monopole-like configuration after Abelian Projection.


title: Chiral perturbation theory for the Wilson lattice action

abstract:
  We extend chiral perturbation theory to include linear dependence on the
lattice spacing $a$ for the Wilson action. The perturbation theory is written
as a double expansion in the small quark mass $m_q$ and lattice spacing $a$. We
present formulae for the mass and decay constant of a flavor-non-singlet meson
in this scheme to order $a$ and $m_q^2$. The extension to the partially
quenched theory is also described.


title: Monopole-like Quantum Excitations in the Non-abelian Vacuum

abstract:
  It is offered to consider monopoles in Abelian Projection as quantum
excitations which are solutions of the quantized Yang-Mills equations.
According to the Heisenberg quantization method these equations are equivalent
an infinite set of equations for Green's functions. A procedure for cutting off
these infinite series of differential equations after some assumptions is
offered. The received equations are identical to equations describing a dyon.


title:
Moments of Nucleon Light Cone Quark Distributions Calculated in Full
  Lattice QCD

abstract:
  Moments of the quark density, helicity, and transversity distributions are
calculated in unquenched lattice QCD. Calculations of proton matrix elements of
operators corresponding to these moments through the operator product expansion
have been performed on $16^3 \times 32$ lattices for Wilson fermions at $\beta
= 5.6$ using configurations from the SESAM collaboration and at $\beta = 5.5$
using configurations from SCRI. One-loop perturbative renormalization
corrections are included. At quark masses accessible in present calculations,
there is no statistically significant difference between quenched and full QCD
results, indicating that the contributions of quark-antiquark excitations from
the Dirac Sea are small. Close agreement between calculations with cooled
configurations containing essentially only instantons and the full gluon
configurations indicates that quark zero modes associated with instantons play
a dominant role. Naive linear extrapolation of the full QCD calculation to the
physical pion mass yields results inconsistent with experiment. Extrapolation
to the chiral limit including the physics of the pion cloud can resolve this
discrepancy and the requirements for a definitive chiral extrapolation are
described.


title: Witten-Veneziano Relation, Quenched QCD, and Overlap Fermions

abstract:
  The quarks in quenched QCD have an anomalous self-interaction in the flavor
singlet Goldstone boson channel. This coupling is extracted from a graph with
disconnected quark lines, and is used to infer the mass of the eta-prime meson
in full QCD. When the fermions are described by an overlap action, the
Witten-Veneziano relation is an exact relation between the topological
susceptibility (as defined through fermionic zero modes) and the inferred value
of the eta-prime mass. Using an overlap action we compute the hairpin amplitude
and determine the fermion zero-mode susceptibility, the inferred eta-prime mass
and other parameters characterizing the low energy chiral properties of
quenched QCD.


title:
Testing the self-duality of topological lumps in SU(3) lattice gauge
  theory

abstract:
  We discuss a simple formula which connects the field-strength tensor to a
spectral sum over certain quadratic forms of the eigenvectors of the lattice
Dirac operator. We analyze these terms for the near zero-modes and find that
they give rise to contributions which are essentially either self-dual or anti
self-dual. Modes with larger eigenvalues in the bulk of the spectrum are more
dominated by quantum fluctuations and are less (anti) self-dual. In the high
temperature phase of QCD we find considerably reduced (anti) self-duality for
the modes near the edge of the spectral gap.


title: Overlap Quark Propagator in Landau Gauge

abstract:
  The properties of the quark propagator in Landau gauge in quenched QCD are
examined for the overlap quark action. The overlap quark action satisfies the
Ginsparg-Wilson relation and as such provides an exact lattice realization of
chiral symmetry. This in turn implies that the quark action is free of ${\cal
O}(a)$ errors. We present results using the standard Wilson fermion kernel in
the overlap formalism on a $12^3\times 24$ lattice at a spacing of 0.125 fm. We
obtain the nonperturbative momentum-dependent wavefunction renormalization
function $Z(p)$ and the nonperturbative mass function $M(p)$ for a variety of
bare masses. We perform a simple extrapolation to the chiral limit for these
functions. We clearly observe the dynamically generated infrared mass and
confirm the qualitative behavior found for the Landau gauge quark propagator in
earlier studies. We attempt to extract the quark condensate from the asymptotic
behavior of the mass function in the chiral limit.


title: Charmed hadron physics in quenched anisotropic lattice QCD

abstract:
  We investigate the anisotropic lattice with $O(a)$ improved quark action as a
candidate of framework in which we can treat both the heavy and light quark
region in the same manner and systematically reduce the systematic
uncertainties. To examine applicability of anisotropic lattice, we calculate
the charmed meson spectrum and decay constants in quenched approximation. We
find consistent result with most advanced results on isotropic lattices.


title: Critical behaviour in QCD at finite isovector chemical potential

abstract:
  We report an investigation of criticality in QCD at finite isovector chemical
potential, mu_3, and at zero temperature. At the critical point, mu_3^c = m_pi,
we find that an uncharged scalar and pseudoscalar and a charged pseudoscalar
meson become massless within the resolution of our measurement. The effective
long distance theory therefore breaks O(4) symmetry by charged pion
condensation. This results in a rising quark number susceptibility. The baryon
remains massive, as indicated by a vanishing baryon number susceptibility.


title: The continuum limit of quark number susceptibilities

abstract:
  We report the continuum limit of quark number susceptibilities in quenched
QCD. Deviations from ideal gas behaviour at temperature T increase as the
lattice spacing is decreased from T/4 to T/6, but a further decrease seems to
have very little effect. The measured susceptibilities are 20% lower than the
ideal gas values, and also 10% below the hard thermal loop (HTL) results. The
off-diagonal susceptibility is several orders of magnitude smaller than the HTL
results. We verify a strong correlation between the lowest screening mass and
the susceptibility. We also show that the quark number susceptibilities give a
reasonable account of the Wroblewski parameter, which measures the strangeness
yield in a heavy-ion collision.


title: High performance Beowulf computer for lattice QCD

abstract:
  We describe the construction of a high performance parallel computer composed
of PC components, as well as the performance test in lattice QCD.


title: Progress in understanding confinement

abstract:
  A few aspects of the mechanism of confinement of color by monopole
condensation are reviewed.


title: Chiral symmetry restoration and the Z3 sectors of QCD

abstract:
  Quenched SU(3) lattice gauge theory shows three phase transitions, namely the
chiral, the deconfinement and the Z3 phase transition. Knowing whether or not
the chiral and the deconfinement phase transition occur at the same temperature
for all Z3 sectors could be crucial to understand the underlying microscopic
dynamics. We use the existence of a gap in the Dirac spectrum as an order
parameter for the restoration of chiral symmetry. We find that the spectral gap
opens up at the same critical temperature in all Z3 sectors in contrast to
earlier claims in the literature.


title: QCD, Gauge Fixing, and the Gribov Problem

abstract:
  The standard techniques of gauge-fixing, such as covariant gauge fixing, are
entirely adequate for the purposes of studies of perturbative QCD. However,
they fail in the nonperturbative regime due to the presence of Gribov copies.
These copies arise because standard local gauge fixing methods do not
completely fix the gauge. Known Gribov-copy-free gauges, such as Laplacian
gauge, are manifestly non-local. These issues are examined and the implications
of non-local gauge-fixing for ghost fields, BRST invariance, and the proof of
renormalizability of QCD are considered.


title: Quark propagator in a covariant gauge

abstract:
  Using mean--field improved gauge field configurations, we compare the results
obtained for the quark propagator from Wilson fermions and Overlap fermions on
a $\3$ lattice at a spacing of $a=0.125(2)$ fm.


title:
Light Hadron Masses in QCD with Valence Wilson Quarks at beta=6.25 from
  a Parallel PC Cluster

abstract:
  We present results for $\pi$, $\rho$ and proton and $\Delta$ masses from our
recently built Pentium cluster. The previous results for quenched Wilson
fermions by MILC and GF11 collaborations are compared at $\beta=6/g^2$=5.7 and
5.85 with the same parameters on the $8^3\times32$ lattice. New data are shown
at $\beta$=6.25 on the $12^3\times36$ and $16^3\times32$ lattices. Such a
larger $\beta$ value is useful for extrapolating the lattice results to the
continuum limit. The smearing technique is systematically investigated and
shown to greatly improve the spectrum data.


title: Nucleon-Nucleon Interactions on the Lattice

abstract:
  We consider the nucleon-nucleon potential in quenched and partially-quenched
QCD. The leading one-meson exchange contribution to the potential is found to
fall off exponentially at long-distances, in contrast with the Yukawa-type
behaviour found in QCD. This unphysical component of the two-nucleon potential
has important implications for the extraction of nuclear properties from
lattice simulations.


title:
Density Matrix Renormalisation Group Approach to the Massive Schwinger
  Model

abstract:
  The massive Schwinger model is studied, using a density matrix
renormalisation group approach to the staggered lattice Hamiltonian version of
the model. Lattice sizes up to 256 sites are calculated, and the estimates in
the continuum limit are almost two orders of magnitude more accurate than
previous calculations. Coleman's picture of `half-asymptotic' particles at
background field theta = pi is confirmed. The predicted phase transition at
finite fermion mass (m/g) is accurately located, and demonstrated to belong in
the 2D Ising universality class.


title: Form and index of Ginsparg-Wilson fermions

abstract:
  We clarify the questions rised by a recent example of a lattice Dirac
operator found by Chiu. We show that this operator belongs to a class based on
the Cayley transformation and that this class on the finite lattice generally
does not admit a nonvanishing index, while in the continuum limit, due to
operator properties in Hilbert space, this defect is no longer there. Analogous
observations are made for the chiral anomaly. We also elaborate on various
aspects of the underlying sum rule for the index.


title: Thermodynamics from Monte Carlo Hamiltonian

abstract:
  We construct an effective low-energy Hamiltonian from the classical action
via Monte Carlo with importance sampling. We use Monte Carlo (i) to compute
matrix elements of the transition amplitude and (ii) to construct
stochastically a basis. The MC Hamiltonian allows to obtain energies and wave
functions of low-lying states. It allows also to compute thermodynamical
observables in some temperature window (starting from temperature zero). We
present examples from lattice field theory (Klein-Gordon model).


title: Ginsparg-Wilson operators and a no-go theorem

abstract:
  If one uses a general class of Ginsparg-Wilson operators, it is known that CP
symmetry is spoiled in chiral gauge theory for a finite lattice spacing and the
Majorana fermion is not defined in the presence of chiral symmetric Yukawa
couplings. We summarize these properties in the form of a theorem for the
general Ginsparg-Wilson relation.


title: Effects of Dynamical Quarks in UKQCD Simulations

abstract:
  Recent results from the UKQCD Collaboration's dynamical simulations are
presented. The main feature of these ensembles is that they have a fixed
lattice spacing and volume, but varying sea quark mass from infinite
(corresponding to the quenched simulation) down to roughly that of the strange
quark mass. The main aim of this work is to uncover dynamical quark effects
from these ``matched'' ensembles. We obtain some evidence of dynamical quark
effects in the static quark potential with less effects in the hadronic
spectrum.


title:
The phase diagram of QCD with two and four flavors: results with HYP
  fermions

abstract:
  We study the finite temperature phase transition of four and two flavor
staggered fermions with hypercubic smeared link actions. These preliminary
studies suggest that the improved flavor symmetry of the fermionic action can
have a significant effect on the finite temperature phase diagram.


title: Lattice monopoles in hot SU(2) gluodynamics as blocked continuum defects

abstract:
  We propose to consider lattice monopoles in gluodynamics as continuum
monopoles blocked to the lattice. In this approach the lattice is associated
with a measuring device consisting of finite-sized detectors of monopoles
(lattice cells). Thus a continuum monopole theory defines the dynamics of the
lattice monopoles. We apply this idea to the static monopoles in high
temperature gluodynamics. We show that our suggestion allows to describe the
numerical data both for the density of the lattice monopoles and for the
lattice monopole action in terms of a continuum Coulomb gas model.


title:
Series expansion of the quark determinant in the number of
  quark-antiquark pairs

abstract:
  We propose a formulation of the QCD partition function which leads to a
series expansion of the quark determinant in any given baryonic sector. The
r-th term gives the gauge-invariant contribution of the valence quarks plus r
quark-antiquark pairs. This expansion can be used to investigate any baryonic
sector, starting from the nucleon up to high baryonic densities.


title: Excited Baryons in Lattice QCD

abstract:
  We present first results for the masses of positive and negative parity
excited baryons calculated in lattice QCD using an O(a^2)-improved gluon action
and a fat-link irrelevant clover (FLIC) fermion action in which only the
irrelevant operators are constructed with APE-smeared links. The results are in
agreement with earlier calculations of N^* resonances using improved actions
and exhibit a clear mass splitting between the nucleon and its chiral partner.
An correlation matrix analysis reveals two low-lying J^P=(1/2)^- states with a
small mass splitting. The study of different Lambda interpolating fields
suggests a similar splitting between the lowest two Lambda1/2^- octet states.
However, the empirical mass suppression of the Lambda^*(1405) is not evident in
these quenched QCD simulations, suggesting a potentially important role for the
meson cloud of the Lambda^*(1405) and/or a need for more exotic interpolating
fields.


title: Monopole and vortex content of a meron pair

abstract:
  We investigate the monopole and vortex content of a meron pair by calculating
the points at which the transformation to the Laplacian Center Gauge is
ill-defined and by studying the behavior of Wilson loops. These techniques
reveal complementary aspects of the vortex and monopole structure, including
the presence of closed monopole lines and closed vortex surfaces joining the
two merons, and evidence for intersecting vortex surfaces at each meron.


title:
Spectral Functions, Maximum Entropy Method and Unconventional Methods in
  Lattice Field Theory

abstract:
  We present two unconventional methods of extracting information from hadronic
2-point functions produced by Monte Carlo simulations. The first is an
extension of earlier work by Leinweber which combines a QCD Sum Rule approach
with lattice data. The second uses the Maximum Entropy Method to invert the
2-point data to obtain estimates of the spectral function. The first approach
is applied to QCD data, and the second method is applied to the
Nambu--Jona-Lasinio model in (2+1)D. Both methods promise to augment the
current approach where physical quantities are extracted by fitting to pure
exponentials.


title:
Numerical Methods for the QCD Overlap Operator: I. Sign-Function and
  Error Bounds

abstract:
  The numerical and computational aspects of the overlap formalism in lattice
quantum chromodynamics are extremely demanding due to a matrix-vector product
that involves the sign function of the hermitian Wilson matrix. In this paper
we investigate several methods to compute the product of the matrix
sign-function with a vector, in particular Lanczos based methods and partial
fraction expansion methods. Our goal is two-fold: we give realistic comparisons
between known methods together with novel approaches and we present error
bounds which allow to guarantee a given accuracy when terminating the Lanczos
method and the multishift-CG solver, applied within the partial fraction
expansion methods.


title: Finite Density Algorithm in Lattice QCD -- a Canonical Ensemble Approach

abstract:
  I will review the finite density algorithm for lattice QCD based on finite
chemical potential and summarize the associated difficulties. I will propose a
canonical ensemble approach which projects out the finite baryon number sector
from the fermion determinant. For this algorithm to work, it requires an
efficient method for calculating the fermion determinant and a Monte Carlo
algorithm which accommodates unbiased estimate of the probability. I shall
report on the progress made along this direction with the Pad\'{e} - Z$_2$
estimator of the determinant and its implementation in the newly developed
Noisy Monte Carlo algorithm.

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


title: Instanton vacuum at finite density of quark matter

abstract:
  We study light quark interactions in the instanton liquid at finite
quark/baryon number density analyzing chiral and diquark condensates and
investigate the behaviors of quark dynamical mass and both condensates together
with instanton liquid density as a function of quark chemical potential. We
conclude the quark impact (estimated in the tadpole approximation) on the
instanton liquid could shift color superconducting phase transition to higher
values of the chemical potential bringing critical quark matter density to the
values essentially higher than conventional nuclear one.


title: Lattice QCD at finite isospin density at zero and finite temperature

abstract:
  We simulate lattice QCD with dynamical $u$ and $d$ quarks at finite chemical
potential, $\mu_I$, for the third component of isospin ($I_3$), at both zero
and at finite temperature. At zero temperature there is some $\mu_I$, $\mu_c$
say, above which $I_3$ and parity are spontaneously broken by a charged pion
condensate. This is in qualitative agreement with the prediction of effective
(chiral) Lagrangians which also predict $\mu_c=m_\pi$. This transition appears
to be second order, with scaling properties consistent with the mean-field
predictions of such effective Lagrangian models. We have also studied the
restoration of $I_3$ symmetry at high temperature for $\mu_I > \mu_c$. For
$\mu_I$ sufficiently large, this finite temperature phase transition appears to
be first order. As $\mu_I$ is decreased it becomes second order connecting
continuously with the zero temperature transition.


title:
Semi-leptonic decays of heavy mesons and the Isgur-Wise function in
  quenched lattice QCD

abstract:
  The form factors for the semi-leptonic B->D and B->D* decays are evaluated in
quenched lattice QCD at two different values of the coupling, beta=6.0 and 6.2.
The action and the operators are fully O(a) non-perturbatively improved. The
slope of the Isgur-Wise function is evaluated, and found to be
rho^2=0.83^{+15+24}_{-11-1} (quoted errors are statistical and systematic
respectively). Ratios of form factors are evaluated and compared to
experimental determinations.


title:
Better than $1/Mflops sustained: a scalable PC-based parallel computer
  for lattice QCD

abstract:
  We study the feasibility of a PC-based parallel computer for medium to large
scale lattice QCD simulations. The E\"otv\"os Univ., Inst. Theor. Phys. cluster
consists of 137 Intel P4-1.7GHz nodes with 512 MB RDRAM. The 32-bit, single
precision sustained performance for dynamical QCD without communication is 1510
Mflops/node with Wilson and 970 Mflops/node with staggered fermions. This gives
a total performance of 208 Gflops for Wilson and 133 Gflops for staggered QCD,
respectively (for 64-bit applications the performance is approximately halved).
The novel feature of our system is its communication architecture. In order to
have a scalable, cost-effective machine we use Gigabit Ethernet cards for
nearest-neighbor communications in a two-dimensional mesh. This type of
communication is cost effective (only 30% of the hardware costs is spent on the
communication). According to our benchmark measurements this type of
communication results in around 40% communication time fraction for lattices
upto 48^3\cdot96 in full QCD simulations. The price/sustained-performance ratio
for full QCD is better than $1/Mflops for Wilson (and around $1.5/Mflops for
staggered) quarks for practically any lattice size, which can fit in our
parallel computer. The communication software is freely available upon request
for non-profit organizations.


title: Thermal Dilepton Rates and Meson Spectral Functions from Lattice QCD

abstract:
  Pseudo-scalar and vector meson correlation functions were calculated at
temperatures below and above the deconfinement transition using ${\cal O}(a)$
improved Wilson fermions in quenched lattice QCD. The spectral functions were
reconstructed from the correlator given only at discrete points in Euclidean
time by means of the Maximum Entropy Method without a priori assumptions on the
spectral shape. The deviation of the spectral functions from the one of a
freely propagating quark anti-quark pair is examined above the critical
temperature. At 1.5 and 3 $T_c$ the vector spectral function yields an
enhancement of the dilepton rate over the Born rate in the energy interval $4 <
\omega/T < 8$ and a sharp drop at energies below 2-3 T.


title:
Lattice quark propagator with staggered quarks in Landau and Laplacian
  gauges

abstract:
  We report on the lattice quark propagator using standard and improved
Staggered quark actions, with the standard, Wilson gauge action. The standard
Kogut-Susskind action has errors of \oa{2} while the ``Asqtad'' action has
\oa{4}, \oag{2}{2} errors. The quark propagator is interesting for studying the
phenomenon of dynamical chiral symmetry breaking and as a test-bed for
improvement. Gauge dependent quantities from lattice simulations may be
affected by Gribov copies. We explore this by studying the quark propagator in
both Landau and Laplacian gauges. Landau and Laplacian gauges are found to
produce very similar results for the quark propagator.


title:
Moments of singlet parton densities on the lattice in the Schroedinger
  Functional scheme

abstract:
  A non perturbative computation of the evolution of singlet parton densities
without gauge--fixing requires a gauge invariant gluon source operator. Within
the Schr\"odinger Functional scheme (SF), such a source can be defined in terms
of path ordered products of gauge links, connected to the time boundaries. In
this paper we adopt this definition and perform a one loop lattice computation
of the renormalization constants of the twist--2 operators that correspond to
the second moment of singlet parton densities. This calculation fixes the
connection between the lattice SF scheme where a non perturbative evaluation of
the absolute normalization of singlet parton densities can be made at low
energy and the $\bar{MS}$ scheme where one can extract the experimental values.


title: Nucleons in Two-Flavor Partially-Quenched Chiral Perturbation Theory

abstract:
  Properties of the proton and the neutron are explored in partially-quenched
chiral perturbation theory with two non-degenerate light flavors. Masses,
magnetic moments, matrix elements of isovector twist-2 operators and
axial-vector currents are computed at the one-loop level in the chiral
expansion.


title: Contents of Lattice 2001 Proceedings

abstract:
  We give here the contents pages for the Proceedings of the Lattice 2001
conference (19th International Symposium on Lattice Field Theory) that took
place in August 2001 in Berlin, Germany. The contents are in HTML form with
clickable links to the papers that exist on the arXiv, mostly in hep-lat.
  Corrections and comments should be sent to bunk@physik.hu-berlin.de.


title: Proposal for the numerical solution of planar QCD

abstract:
  Using quenched reduction, we propose a method for the numerical calculation
of meson correlation functions in the planar limit of QCD. General features of
the approach are outlined, and an example is given in the context of
two-dimensional QCD.


title: The Laplacian Gauge Gluon Propagator in SU(N_c)

abstract:
  We examine the gluon propagator in the Laplacian gauge in quenched lattice
QCD as a function of the number of colours. We observe a weak dependence on
$N_c$ over the whole momentum range. This implies an almost $N_c$-independent
gluon pole mass in units of the string tension.


title:
Finite-size scaling and deconfinement transition: the case of 4D SU(2)
  pure gauge theory

abstract:
  A recently introduced method for determining the critical indices of the
deconfinement transition in gauge theories, already tested for the case of 3D
SU(3) pure gauge theory, is applied here to 4D SU(2) pure gauge theory. The
method is inspired by universality and based on the finite size scaling
behavior of the expectation value of simple lattice operators, such as the
plaquette. We obtain an accurate determination of the critical index $\nu$, in
agreement with the prediction of the Svetitsky-Yaffe conjecture.


title: Highly-improved lattice field-strength tensor

abstract:
  We derive an O(a^4)-improved lattice version of the continuum field-strength
tensor. Discretization errors are reduced via the combination of several clover
terms of various sizes, complemented by tadpole improvement. The resulting
improved field-strength tensor is used to construct O(a^4)-improved topological
charge and action operators. We compare the values attained by these operators
as we cool several configurations to self-duality with a previously defined
highly-improved action and assess the relative scale of the remaining
discretization errors.


title: Cost of QCD simulations with n_f=2 dynamical Wilson fermions

abstract:
  Cost estimates for simulations of full QCD with n_f=2 Wilson fermions by
hybrid Monte Carlo are presented. The extrapolations are based on the average
number of iterations of the iterative solver within the fermionic part of the
HMC molecular dynamics, which is closely related to the minimal eigenvalue of
M^+M The cost formula is determined as a product of the scaling functions of
iterative solver and integrated autocorrelation time as function of the inverse
lattice pseudoscalar mass. Timings by SESAM/TxL allow to fix the pre-factor. It
is demonstrated that a 2-flavor dynamical determination of light hadron masses
with a statistical precision comparable to the corresponding quenched results
from CP-PACS can be an appropriate task for a 100 Tflops system.


title: Simulation of dynamical fermions with smeared links

abstract:
  Smearing the gauge links of dynamical configurations removes small scale
unphysical vacuum fluctuations und thus improves the chiral properties of
lattice fermions. We present a new algorithm for the simulation of dynamical
fermions coupled via smeared links based on the standard pure gauge
overrelaxation and heatbath updatings. Smeared links play a fundamental role in
making this algorithm effective. At fixed lattice spacing the computational
cost of the algorithm has an extra volume factor due to the finite volume of
the lattice region which can be updated. As the continuum limit is approached
the physical volume of the updated region remains constant. We simulated four
flavors of staggered fermions coupled via hypercubic (HYP) smeared links. The
simulation cost of the new algorithm on 10 fm^4 volumes is a factor 2-8 larger
than with the standard Hybrid Monte Carlo but the improved properties of the
HYP action allow to gain a factor 2 in the lattice spacing. The new algorithm
could be applicable to simulations of more complicated chiral fermionic
actions, like overlap or perfect actions.


title:
Scaling laws for the 2d 8-state Potts model with Fixed Boundary
  Conditions

abstract:
  We study the effects of frozen boundaries in a Monte Carlo simulation near a
first order phase transition. Recent theoretical analysis of the dynamics of
first order phase transitions has enabled to state the scaling laws governing
the critical regime of the transition. We check these new scaling laws
performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In
particular, our results support a pseudo-critical beta finite-size scaling of
the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d +
d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not
coincide with the latent heat analytically derived for the same model if
periodic boundary conditions are assumed, which is 0.486358...


title:
On the dependence of the gauge-invariant field-strength correlators in
  QCD on the shape of the Schwinger string

abstract:
  We study, by numerical simulations on a lattice, the dependence of the
gauge-invariant two-point field-strength correlators in QCD on the path used to
perform the color parallel transport between the two points.


title: The topological susceptibility of SU(3) gauge theory near T_c

abstract:
  We compute the topological susceptibility chi_t in SU(3) lattice gauge theory
using fermionic methods based on the Atiyah-Singer index theorem. Near the
phase transition we find a smooth crossover behavior for chi_t with values
decreasing from (191(5) MeV)^4 to (100(5) MeV)^4 as we increase the temperature
from 0.88 T_c to 1.31 T_c, showing that topological excitations exist far above
T_c. Our study is the first large scale analysis of the topological
susceptibility at high temperature based on the index theorem and the results
agree well with field theoretical methods.


title:
Gauge fixing, families index theory, and topological features of the
  space of lattice gauge fields

abstract:
  The families index theory for the overlap lattice Dirac operator is applied
to derive topological features of the space of SU(N) lattice gauge fields on
the 4-torus: The topological sectors, specified by the fermionic topological
charge, are shown to contain noncontractible even-dimensional spheres when
$N\ge3$, and noncontractible circles in the N=2 case. We describe how certain
obstructions to the existence of gauge fixings without the Gribov problem in
the continuum setting correspond on the lattice to obstructions to the
contractibility of these spheres and circles. We also point out a canonical
connection on the space of lattice gauge fields with monopole-like
singularities associated with the spheres.


title: On The Deconfinement Transition in SU(4) Lattice Gauge Theory

abstract:
  The deconfinement transition in SU(4) lattice gauge theory is investigated on
N_s^3 X N_t lattices for N_s = 8-16 and N_t = 4-8 using a modified Wilson
action which is expected to be free of any bulk transitions. The susceptibility
chi_{|L|}^{max}, where L is the order parameter for deconfinement, is found to
increase linearly with spatial volume for N_t = 4, 5, and 6, indicating a first
order deconfinement phase transition. The latent heat of the transition is
estimated to be approximately 2/3 of the corresponding ideal gas energy density
at T_c.


title: CP breaking in lattice chiral gauge theories

abstract:
  The CP symmetry is not manifestly implemented for the local and doubler-free
Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify
where the effects of this CP breaking appear. We show that they appear in: (I)
Overall constant phase of the fermion generating functional. (II) Overall
constant coefficient of the fermion generating functional. (III) Fermion
propagator appearing in external fermion lines and the propagator connected to
Yukawa vertices. The first effect appears from the transformation of the path
integral measure and it is absorbed into a suitable definition of the constant
phase factor for each topological sector; in this sense there appears no ``CP
anomaly''. The second constant arises from the explicit breaking in the action
and it is absorbed by the suitable weights with which topological sectors are
summed. The last one in the propagator is inherent to this formulation and
cannot be avoided by a mere modification of the projection operator, for
example, in the framework of the Ginsparg-Wilson operator. This breaking
emerges as an (almost) contact term in the propagator when the Higgs field,
which is treated perturbatively, has no vacuum expectation value. In the
presence of the vacuum expectation value, however, a completely new situation
arises and the breaking becomes intrinsically non-local, though this breaking
may still be removed in a suitable continuum limit. This non-local CP breaking
is expected to persist for a non-perturbative treatment of the Higgs coupling.


title: New proposal for numerical simulations of theta-vacuum like systems

abstract:
  We propose a new approach to perform numerical simulations of theta-vacuum
like systems, test it in two analytically solvable models, and apply it to
CP^3. The main new ingredient in our approach is the method used to compute the
probability distribution function of the topological charge at theta=0. We do
not get unphysical phase transitions (flattening behavior of the free energy
density) and reproduce the exact analytical results for the order parameter in
the whole theta-range within a few percent.


title: Non-perturbative formulation of the static color octet potential

abstract:
  By dressing Polyakov lines with appropriate functionals of the gauge fields,
we construct observables describing a fundamental representation static
quark-antiquark pair in the singlet, adjoint and average channels of SU(N) pure
gauge theory. Each of the potentials represents a gauge invariant eigenvalue of
the Hamiltonian. Numerical simulations are performed for SU(2) in 2+1
dimensions. The adjoint channel is found to be repulsive at small and confining
at large separations, suggesting the existence of a metastable (N^2-1)-plet
bound state. For small distances and temperatures above the deconfinement
transition, the leading order perturbative prediction for the ratio of singlet
and adjoint potentials is reproduced by the lattice data.


title:
Ginsparg-Wilson Relation and Lattice Chiral Symmetry in Fermionic
  Interacting Theories

abstract:
  We derive Ginsparg-Wilson relation for a lattice chiral symmetry in theories
with self-interacting fermions. Auxiliary scalar and pseudo-scalar fields are
introduced on a coarse lattice to give an effective description of the
fermionic interactions. We obtain particular solutions to the Ginsparg-Wilson
relation and other
  Ward-Takahashi identities in a closed form. These non-perturbative solutions
can be used to construct a chiral invariant action and an invariant
path-integral measure on the coarse lattice. The resulting partition function
exhibits the exact chiral symmetry in the fermionic system with the auxiliary
fields.


title: Unexpected Results in the Chiral Limit with Staggered Fermions

abstract:
  A cluster algorithm is constructed and applied to study the chiral limit of
the strongly coupled lattice Schwinger model involving staggered fermions. The
algorithm is based on a novel loop representation of the model. Finite size
scaling of the chiral susceptibility based on data from lattices of size up to
$64\times 64$ indicates the absence of long range correlations at strong
couplings. Assuming that there is no phase transition at a weaker coupling, the
results imply that all mesons acquire a mass at non-zero lattice spacings.
Although this does not violate any known physics, it is surprising since
typically one expects a single pion to remain massless at non-zero lattice
spacings in the staggered fermion formulation.


title: Cost of dynamical quark simulations: O(a) improved Wilson fermions

abstract:
  I report on cost estimates and algorithmic performance in simulations using 2
flavours of non-perturbatively O(a) improved Wilson quarks together with the
Wilson plaquette action.


title: Study of Confinement Using the Schroedinger Functional

abstract:
  We use a gauge-invariant effective action defined in terms of the lattice
Schroedinger functional to investigate vacuum dynamics and confinement in pure
lattice gauge theories. After a brief introduction to the method, we report
some numerical results.


title: Abelian projection in SU(N) gauge theories

abstract:
  The abelian projection in SU(N) gauge theories is discussed in detail, as
well as the construction of a disorder parameter to study dual
superconductivity as a mechanism for color confinement. If the ideas of the
large N limit are correct, a universal N-independent behavior is expected for
the suitable rescaled disorder parameter as a function of lambda = g^2 N.


title: Higher Order Hybrid Monte Carlo at Finite Temperature

abstract:
  The standard hybrid Monte Carlo algorithm uses the second order integrator at
the molecular dynamics step. This choice of the integrator is not always the
best. Using the Wilson fermion action, we study the performance of the hybrid
Monte Carlo algorithm for lattice QCD with higher order integrators in both
zero and finite temperature phases and find that in the finite temperature
phase the performance of the algorithm can be raised by use of the 4th order
integrator.


title: Heavy quark action on the anisotropic lattice

abstract:
  We investigate the $O(a)$ improved quark action on anisotropic lattice as a
potential framework for the heavy quark, which may enable precision computation
of hadronic matrix elements of heavy-light mesons. The relativity relations of
heavy-light mesons as well as of heavy quarkonium are examined on a quenched
lattice with spatial lattice cutoff $a_\sigma^{-1} \simeq$ 1.6 GeV and the
anisotropy $\xi=4$. We find that the bare anisotropy parameter tuned for the
massless quark describes both the heavy-heavy and heavy-light mesons within 2%
accuracy for the quark mass $a_\sigma m_Q < 0.8$, which covers the charm quark
mass. This bare anisotropy parameter also successfully describes the
heavy-light mesons in the quark mass region $a_\sigma m_Q \leq 1.2$ within the
same accuracy. Beyond this region, the discretization effects seem to grow
gradually. The anisotropic lattice is expected to extend by a factor $\xi$ the
quark mass region in which the parameters in the action tuned for the massless
limit are applicable for heavy-light systems with well controlled systematic
errors.


title: Evaluating the Fermionic Determinant of Dynamical Configurations

abstract:
  We propose and study an improved method to calculate the fermionic
determinant of dynamical configurations. The evaluation or at least stochastic
estimation of ratios of fermionic determinants is essential for a recently
proposed updating method of smeared link dynamical fermions. This update
creates a sequence of configurations by changing a subset of the gauge links by
a pure gauge heat bath or over relaxation step. The acceptance of the proposed
configuration depends on the ratio of the fermionic determinants on the new and
original configurations. We study this ratio as the function of the number of
links that are changed in the heat bath update. We find that even when every
link of a given direction and parity of a 10fm^4 configuration is updated, the
average of the determinant ratio is still close to one and with the improved
stochastic estimator the proposed change is accepted with about 20%
probability. This improvement suggests that the new updating technique can be
efficient even on large lattices.


title: On the Local Structure of Topological Charge Fluctuations in QCD

abstract:
  We consider the lattice topological charge density introduced by Hasenfratz,
Laliena and Niedermayer and propose its eigenmode expansion as a tool to
investigate the structure of topological charge fluctuations in QCD. The
resulting effective density is built from local chiralities studied previously.
At every order of the expansion the density exactly sums up to the global
topological charge, and the leading term describes the maximally smooth
space-time distribution of charge relevant for propagating light fermions. We
use this framework to demonstrate our previous suggestion that the bulk of
topological charge in QCD does not effectively appear in the form of quantized
unit lumps. Our conclusion implies that it is unlikely that the mixing of
"would-be" zeromodes associated with such lumps is the prevalent microscopic
mechanism for spontaneous chiral symmetry breaking in QCD. We also present
first results quantitatively characterizing the space-time behavior of
effective densities. For coherent fluctuations contained in spherical regions
we find a continuous distribution of associated charges essentially ending at
~0.5.


title: Hadronic Parity-Violation on the Lattice

abstract:
  We motivate lattice QCD studies of the parity-violating pion-nucleon coupling
constant and extend flavor-conserving hadronic parity-violation from QCD to
partially-quenched QCD. The parity-violating pion-nucleon coupling and the
anapole form factor (and moment) of the proton are computed to one-loop order
in the partially-quenched chiral expansion. For the parity-violating
pion-nucleon interaction, we include the contributions from total derivative
operators necessary to match the kinematics that will be used in lattice
simulations.


title: From enemies to friends: chiral symmetry on the lattice

abstract:
  The physics of strong interactions is invariant under the exchange of
left-handed and right-handed quarks, at least in the massless limit. This
invariance is reflected in the chiral symmetry of quantum chromodynamics.
Surprisingly, it has become clear only recently how to implement this important
symmetry in lattice formulations of quantum field theories. We will discuss
realizations of exact lattice chiral symmetry and give an example of the
computation of a physical observable in quantum chromodynamics where chiral
symmetry is important. This calculation is performed by relying on finite size
scaling methods as predicted by chiral perturbation theory.


title: Topology and chiral symmetry breaking in SU(N) gauge theories

abstract:
  We study the low-lying eigenmodes of the lattice overlap Dirac operator for
SU(N) gauge theories with N=2,3,4 and 5 colours. We define a fermionic
topological charge from the zero-modes of this operator and show that, as N
grows, any disagreement with the topological charge obtained by cooling the
fields, becomes rapidly less likely. By examining the fields where there is a
disagreement, we are able to show that the Dirac operator does not resolve
instantons below a critical size of about rho = 2.5 a, but resolves the larger,
more physical instantons. We investigate the local chirality of the near-zero
modes and how it changes as we go to larger N. We observe that the local
chirality of these modes, which is prominent for SU(2) and SU(3), becomes
rapidly weaker for larger N and is consistent with disappearing entirely in the
limit of N -> infinity. We find that this is not due to the observed
disappearance of small instantons at larger N.


title: QCD vacuum and confinement

abstract:
  This course consists of two lectures. In the first lecture I discuss why a
non perturbative formulation of QCD is needed, and I show that lattice
formulation copes with this need, even if it mainly produces numerical results.
In the second lecture I discuss how lattice can help to understand the
deconfinement transition.Such understanding is also important to predict
parameters that can help in the interpretation of heavy ions high energy
experiments.


title:
Center vortex model for the infrared sector of Yang-Mills theory -
  Quenched Dirac spectrum and chiral condensate

abstract:
  The Dirac operator describing the coupling of continuum quark fields to SU(2)
center vortex world-surfaces composed of elementary squares on a hypercubic
lattice is constructed. It is used to evaluate the quenched Dirac spectral
density in the random vortex world-surface model, which previously has been
shown to quantitatively reproduce both the confinement properties and the
topological susceptibility of SU(2) Yang-Mills theory. Under certain conditions
on the modeling of the vortex gauge field, a behavior of the quenched chiral
condensate as a function of temperature is obtained which is consistent with
measurements in SU(2) lattice Yang-Mills theory.


title:
Blocking of lattice monopoles from the continuum in hot lattice
  gluodynamics

abstract:
  The Abelian monopoles in lattice gluodynamics are associated with continuum
monopoles blocked to the lattice. This association allows to predict the
lattice monopole action and density of the (squared) monopole charges from a
continuum monopole model. The method is applied to the static monopoles in high
temperature gluodynamics. We show that the numerical data both for the density
and the action of the lattice monopoles can be described in terms of a Coulomb
gas of Abelian monopoles in the continuum.


title:
Spectral density analysis of time correlation functions in lattice QCD
  using the maximum entropy method

abstract:
  We study various aspects of extracting spectral information from time
correlation functions of lattice QCD by means of Bayesian inference with an
entropic prior, the maximum entropy method (MEM). Correlator functions of a
heavy-light meson-meson system serve as a repository for lattice data with
diverse statistical quality. Attention is given to spectral mass density
functions, inferred from the data, and their dependence on the parameters of
the MEM. We propose to employ simulated annealing, or cooling, to solve the
Bayesian inference problem, and discuss practical issues of the approach.


title: Chiral Magnetism of the Nucleon

abstract:
  We study the quark mass expansion of the magnetic moments of the nucleon in a
chiral effective field theory including nucleons, pions and delta resonances as
explicit degrees of freedom. We point out that the usual powercounting applied
so far to this problem misses important quark mass structures generated via an
intermediate isovector M1 nucleon-delta transition. We propose a modified
powercounting and compare the resulting chiral extrapolation function to
available (quenched) lattice data. The extrapolation is found to work
surprisingly well, given that the lattice data result from rather large quark
masses. Our calculation raises the hope that extrapolations of lattice data
utilizing chiral effective field theory might be applicable over a wider range
in quark masses than previously thought, and we discuss some open questions in
this context. Furthermore, we observe that within the current lattice data
uncertainties the extrapolations presented here are consistent with the Pade
fit ansatz introduced by the Adelaide group a few years ago.


title:
Gluon propagators and the choice of the gauge field in SU(2) theory on
  the lattice

abstract:
  We study numerically magnetic $G_M(p)$ and electric $G_E(p)$ gluon
propagators and their dependence on the choice of the lattice gauge field
$\caa_{x\mu}$ in SU(2) gauge theory, especially, in the low--momentum limit. We
find that two different $\caa_{x\mu}$ definitions are equivalent up to a
trivial renormalization of the propagator, at least, in the main approximation.


title:
A library of extended high-temperature expansions of basic observables
  for the spin S Ising models on two- and three-dimensional lattices

abstract:
  We present an on-line library of unprecedented extension for high-temperature
expansions of basic observables in the Ising models of general spin S, with
nearest-neighbor interactions.
  We have tabulated through order beta^{25} the series for the nearest-neighbor
correlation function, the susceptibility and the second correlation moment in
two dimensions on the square lattice, and, in three dimensions, on the
simple-cubic and the body-centered cubic lattices. The expansion of the second
field derivative of the susceptibility is also tabulated through beta^{23} for
the same lattices. We have thus added several terms (from four up to thirteen)
to the series already published for spin
  S=1/2,1,3/2,2,5/2,3,7/2,4,5,infinity.


title: More chiral operators on the lattice

abstract:
  Instead of the Ginsparg-Wilson (GW) relation we only require generalized
chiral symmetry and show that this results in a larger class of Dirac operators
describing massless fermions, which in addition to GW fermions and to the ones
proposed by Fujikawa includes many more general ones. The index turns out to
depend solely on a basic unitary operator. We use spectral representations to
analyze the new class and to obtain detailed properties. We also show that our
weaker conditions still lead properly to Weyl fermions and to chiral gauge
theories.


title: Quenched chiral logarithms in lattice QCD with exact chiral symmetry

abstract:
  We examine quenched chiral logarithms in lattice QCD with overlap Dirac
quark. For 100 gauge configurations generated with the Wilson gauge action at $
\beta = 5.8 $ on the $ 8^3 \times 24 $ lattice, we compute quenched quark
propagators for 12 bare quark masses. The pion decay constant is extracted from
the pion propagator, and from which the lattice spacing is determined to be
0.147 fm. The presence of quenched chiral logarithm in the pion mass is
confirmed, and its coefficient is determined to be $ \delta = 0.203 \pm 0.014
$, in agreement with the theoretical estimate in quenched chiral perturbation
theory. Further, we obtain the topological susceptibility of these 100 gauge
configurations by measuring the index of the overlap Dirac operator. Using a
formula due to exact chiral symmetry, we obtain the $ \eta' $ mass in quenched
chiral perturbation theory, $ m_{\eta'} = (901 \pm 64) $ Mev, and an estimate
of $ \delta = 0.197 \pm 0.027 $, which is in good agreement with that
determined from the pion mass.


title:
The QCD thermal phase transition in the presence of a small chemical
  potential

abstract:
  We propose a new method to investigate the thermal properties of QCD with a
small quark chemical potential $\mu$. Derivatives of the phase transition point
with respect to $\mu$ are computed at $\mu=0$ for 2 flavors of p-4 improved
staggered fermions with $ma=0.1,0.2$ on a $16^3\times4$ lattice. The resulting
Taylor expansion is well behaved for the small values of $\mu_{\rm
q}/T_c\sim0.1$ relevant for RHIC phenomenology, and predicts a critical curve
$T_c(\mu)$ in reasonable agreement with estimates obtained using exact
reweighting. In addition, we contrast the case of isoscalar and isovector
chemical potentials, quantify the effect of $\mu\not=0$ on the equation of
state, and comment on the complex phase of the fermion determinant in QCD with
$\mu\not=0$.


title: Detailed Analysis of the Three Quark Potential in SU(3) Lattice QCD

abstract:
  The static three-quark (3Q) potential is studied 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 300 different patterns of
the 3Q systems, we perform the accurate measurement of the 3Q Wilson loop with
the smearing method, which reduces excited-state contaminations, and present
the lattice QCD data of the 3Q ground-state potential $V_{\rm 3Q}$. We perform
the detailed fit analysis on $V_{\rm 3Q}$ in terms of the Y-ansatz both with
the continuum Coulomb potential and with the lattice Coulomb potential, and
find that the lattice QCD data of the 3Q potential $V_{\rm 3Q}$ are well
reproduced within a few % deviation by the sum of a constant, the two-body
Coulomb term and the three-body linear confinement term $\sigma_{\rm 3Q} L_{\rm
min}$, with $L_{\rm min}$ the minimal value of the total length of color flux
tubes linking the three quarks.
  From the comparison with the Q-$\bar {\rm Q}$ potential, we find a
universality of the string tension as $\sigma_{\rm 3Q} \simeq \sigma_{\rm Q
\bar Q}$ and the one-gluon-exchange result for the Coulomb coefficients as
$A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar Q}$. We investigate also the several
fit analyses with the various ans\"atze: the Y-ansatz with the Yukawa
potential, the $\Delta$-ansatz and a more general ansatz including the Y and
the $\Delta$ ans\"atze in some limits. All these fit analyses support the
Y-ansatz on the confinement part in the 3Q potential $V_{\rm 3Q}$, although
$V_{\rm 3Q}$ seems to be approximated by the $\Delta$-ansatz with
$\sigma_\Delta \simeq 0.53 \sigma$.


title:
Center-Vortex Solutions of the Yang-Mills Effective Action in Three and
  Four Dimensions

abstract:
  We calculate the one-loop effective action of the SU(2) Yang-Mills theory for
center-vortex configurations, both in 3d and 4d. We find that in both cases
there are minima of the effective action, corresponding to vortices of the
transverse size approximately 4/g_3^2 and 1.7/Lambda_MS, respectively. The
values of the effective actions at the minima are negative, suggesting that the
Euclidian vacuum may be unstable with respect to creation of vortices.


title: Responses of quark condensates to the chemical potential

abstract:
  The responses of quark condensates to the chemical potential, as a function
of temperature T and chemical potential \mu, are calculated within the
Nambu--Jona-Lasinio (NJL) model. We compare our results with those from the
recent lattice QCD simulations [QCD-TARO Collaboration, Nucl. Phys. B (Proc.
Suppl.) 106, 462 (2002)]. The NJL model and lattice calculations show
qualitatively similar behavior, and they will be complimentary ways to study
hadrons at finite density. The behavior above T_c requires more elaborated
analyses.


title: SU(3) lattice QCD study for octet and decuplet baryon spectra

abstract:
  The spectra of octet and decuplet baryons are studied using SU(3) lattice QCD
at the quenched level. As an implementation to reduce the statistical
fluctuation, we employ the anisotropic lattice with $O(a)$ improved quark
action. In relation to $\Lambda(1405)$, we measure also the mass of the SU(3)
flavor-singlet negative-parity baryon, which is described as a three quark
state in the quenched lattice QCD, and its lowest mass is measured about 1.6
GeV. Since the experimentally observed negative-parity baryon $\Lambda(1405)$
is much lighter than 1.6 GeV, $\Lambda(1405)$ may include a large component of
a $N \bar K$ bound state rather than the three quark state. The mass splitting
between the octet and the decuplet baryons are also discussed in terms of the
current quark mass.


title:
Light hadron spectroscopy in quenched lattice QCD with chiral
  Fixed-Point fermions

abstract:
  The classically perfect Fixed-Point fermion action for lattice QCD, a highly
improved discretization of the continuum theory that preserves chiral symmetry,
is constructed in this thesis and a parallel work by T. Jorg. In the framework
of the BGR collaboration, we perform studies in quenched light hadron
spectroscopy with this new action in order to examine its chiral and scaling
properties and investigate in detail the chiral limit of pseudoscalar mesons.
Topological finite-volume artifacts are identified and removed, and the
coefficient of the quenched chiral logarithm is measured. The results show that
the Fixed-Point action allows to simulate at quark masses corresponding to
PS/V<0.3, has small scaling violations in hadron masses and reproduces the
continuum energy-momentum dispersion relation very well.


title: Convergence Rate and Locality of Improved Overlap Fermions

abstract:
  We construct new Ginsparg-Wilson fermions for QCD by inserting an
approximately chiral Dirac operator - which involves ingredients of a perfect
action - into the overlap formula. This accelerates the convergence of the
overlap Dirac operator by a factor of 5 compared to the standard construction,
which inserts the Wilson fermion as a point of departure. Taking into account
the effort for treating the improved fermion, we are left with an total
computational overhead of about a factor 3. This remaining factor is likely to
be compensated by other virtues; here we show that the level of locality is
clearly improved, so that the exponent of the correlation decay is doubled. We
also show that approximate rotation invariance is drastically improved, but a
careful scaling test has to be postponed.


title: Gauge Invariant Monopoles in SU(2) Gluodynamics

abstract:
  We introduce a gauge invariant topological definition of monopole charge in
pure SU(2) gluodynamics. The non-trivial topology is provided by hedgehog
configurations of the non-Abelian field strength tensor on the two-sphere
surrounding the monopole. It is shown that this definition can be formulated
entirely in terms of Wilson loops which makes the gauge invariance manifest.
Moreover, it counts correctly the monopole charge in case of spontaneously
broken gauge symmetry and of pure Abelian gauge fields.


title: Gauge Invariant Monopoles in Lattice SU(2) Gluodynamics

abstract:
  We consider lattice implementation of the recently proposed gauge invariant
definition of the monopole charge. Because of the lattice discretization the
algorithm gives rise to specific lattice artifacts and an effective Ising
model. The Ising-model problem might in principle be solved and we discuss the
role of the Maximal Abelian gauge in this respect. The lattice artifacts are
much more difficult to deal with since they are mixed up with monopoles thus
obscuring the physical observables. Nevertheless, it is possible to extract the
density of physical monopoles which seems to scale correctly towards the
continuum limit.


title: Unquenched domain wall quarks with multi-bosons

abstract:
  The numerical simulation of domain wall quarks with the two-step multi-boson
(TSMB) algorithm is considered. The inclusion of single quark flavours, as
required for strange quarks, is discussed. The usage of computer memory can be
kept relatively low, independently of the order of polynomial approximations.
Tests are performed with two flavours (N_f=2) of degenerate quarks near the
N_t=4 thermodynamical cross over.


title: Status of center dominance in various center gauges

abstract:
  We review arguments for center dominance in center gauges where vortex
locations are correctly identified. We introduce an appealing interpretation of
the maximal center gauge, discuss problems with Gribov copies, and a cure to
the problems through the direct Laplacian center gauge. We study correlations
between direct and indirect Laplacian center gauges.


title: Center vortex model for nonperturbative strong interaction physics

abstract:
  A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic
vortex degrees of freedom represented by (closed) random world-surfaces, is
presented. The model quantitatively describes both the confinement properties
(including the finite-temperature transition to a deconfined phase) and the
topological susceptibility of the Yang-Mills ensemble. A (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:
Scaling Laws and Effective Dimension in Lattice SU(2) Yang-Mills Theory
  with a Compactified Extra Dimension

abstract:
  Monte Carlo simulations are performed in a five-dimensional lattice SU(2)
Yang-Mills theory with a compactified extra dimension, and scaling laws are
studied. Our simulations indicate that as the compactification radius $R$
decreases, the confining phase spreads more and more to the weak coupling
regime, and the effective dimension of the theory changes gradually from five
to four. Our simulations also indicate that the limit $a_4 to 0$ with $R/a_4$
kept fixed exists both in the confining and deconfining phases if $R/a_4$ is
small enough, where $a_4$ is the lattice spacing in the four-dimensional
direction. We argue that the color degrees of freedom in QCD are confined only
for $R < R_{\rm max}$, where a rough estimate shows that $1/R_{\rm max}$ lies
in the TeV range. Comments on deconstructing extra dimensions are given.


title: Abelian chromomagnetic fields and confinement

abstract:
  We study vacuum dynamics of SU(3) lattice gauge theory at finite temperature
using the lattice Schr\"odinger functional. The SU(3) vacuum is probed by means
of an external constant Abelian chromomagnetic field. We find that by
increasing the strength of the applied external field the deconfinement
temperature decreases towards zero. This means that strong enough Abelian
chromomagnetic fields destroy confinement of color. We discuss some
consequences of this phenomenon on confinement and quark stars.


title: Continuum Moment Equations on the Lattice

abstract:
  An analysis is given as to why one can not directly evaluate continuum moment
equations, i.e., equations involving powers of the position variable times
charge, current, or energy/momentum operators, on the lattice. I examine two
cases: a three point function evaluation of the nucleon magnetic moment and a
four point function (charge overlap) evaluation of the pseudoscalar charge
radius.


title: Vortex induced confinement and the Kugo-Ojima confinement criterion

abstract:
  The SU(2) Yang-Mills gluon and ghost Green-functions are studied in Landau
gauge by means of lattice gauge simulations. A focal point is their low energy
behavior since in particular the Kugo-Ojima confinement criterion relates a
diverging ghost form factor at vanishing momentum transfer to the confining
capabilities of the theory. This divergence is verified by numerical
simulations. Removing the confining vortices from the lattice ensembles
converts SU(2) Yang-Mills theory in a non-confining theory. It is shown that in
this modified theory the divergence of the ghost propagator disappears.


title: The Gluon Chain Model Revisited

abstract:
  I describe how the gluon chain model of QCD string formation meets a number
of criteria which are required of any theory of the confining force, including:
the correct center dependence and (at large-N) Casimir scaling of the string
tension, the logarithmic broadening of the QCD flux tube, and the existence of
a Luscher term in the static quark potential.


title: The Poincare Group of Discrete Minkowskian Space-Time

abstract:
  The lattice of integral points of 4-dimensional Minkowski space, together
with the inherited indefinite distance function, is considered as a model for
discrete space-time. The Lorentz and Poincare groups of this discrete
space-time are identified as subgroups of the corresponding Lie groups. The
lattice Lorentz group has irreducible projective (including linear)
representations which are restrictions of (all) finite-dimensional irreducible
projective representations of the Lorentz Lie group and hence can be used to
describe all integral and half-odd-integral helicity. The (4-torus) momentum
space has a well-defined ``light cone'' of null points and there are orbits of
the lattice Lorentz group lying entirely in the torus light cone and having the
lattice euclidean group of the plane as little group. Wigner's method for the
Poincare Lie group can then be adapted to show, in the first instance, that the
lattice Poincare group has unitary representations describing lattice free
fields of zero mass and an arbitrary Lorentz helicity, in particular chiral
fermions. There are no representations with a nonzero invariant mass.


title:
Analytical study of low temperature phase of 3D LGT in the plaquette
  formulation

abstract:
  We develop an analytical approach for non-abelian gauge models within the
plaquette representation where the plaquette matrices play the role of the
fundamental degrees of freedom. We start from the original Batrouni formulation
and show how it can be modified in such a way that each non-abelian Bianchi
identity contains two connectors instead of four. Using this representation we
construct the low-temperature expansion for U(1) and SU(N) models on a finite
lattice and discuss its uniformity in the volume. Next, we derive a dual
representation for the 't Hooft loop in the SU(2) model and describe monopoles
in the maximal axial gauge.


title: Lattice QCD results at finite T and \mu

abstract:
  We propose a method to study lattice QCD at finite temperature (T) and
chemical potential (\mu). We test the method and compare it with the Glasgow
method using n_f=4 staggered QCD with imaginary \mu. The critical endpoint (E)
of QCD on the Re(\mu)-T plane is located. We use n_f=2+1 dynamical staggered
quarks with semi-realistic masses on L_t=4 lattices. Our results are based on
{\cal{O}}(10^3-10^4) configurations.


title: Large center vortices and confinement in 3D Z(2) gauge theory

abstract:
  We study the role of large clusters of center vortices in producing
confinement in 3D Z(2) gauge theory. First, we modify each configuration of a
Monte Carlo-generated ensemble in the confined phase by removing the largest
cluster of center vortices, and show that the ensemble thus obtained does not
confine. Conversely, we show that removing all of the small clusters of center
vortices and leaving the largest one only, confinement is preserved, albeit
with a string tension significantly smaller than the original one. Remarkably,
also the string corrections due to the quantum fluctuations of the confining
flux tube are preserved by this transformation.


title: Solitons and spontaneous symmetry breaking in 2 and 4 dimensions

abstract:
  We show that mass generation in 1+1 and 3+1 dimensions may occur together
with spontaneous symmetry breaking.


title: Color confinement and dual superconductivity: an update

abstract:
  The evidence for dual superconductivity as a mechanism for color confinement
is reviewed. New developments are presented for full QCD, i.e. in the presence
of dynamical quarks.


title: Confinement-deconfinement order parameters

abstract:
  We study numerically the monopole creation operator proposed recently by
Frohlich and Marchetti. The operator is defined with the help of a three
dimensional model which generates random Mandelstam strings. These strings
imitate the Coulombic magnetic field around the monopole. We show that if the
Mandelstam strings are condensed the creation operator discriminates between
the phases with condensed and non--condensed monopoles in the Abelian Higgs
model with the compact gauge field.


title: Lattice chiral gauge theories through gauge fixing

abstract:
  After an introduction in which we review the fundamental difficulty in
constructing lattice chiral gauge theories, we discuss the analytic and
numerical evidence that abelian lattice chiral gauge theories can be
non-perturbatively constructed through the gauge-fixing approach. While a
complete non-abelian extension is still under construction, we also show how
fermion-number violating processes are realized in this approach.


title:
Connections between Thin,Thick and Projection Vortices in SU(2) Lattice
  Gauge Theory

abstract:
  We elucidate the connection between $SO(3) \times Z(2)$ and the usual SU(2)
configuration variables. By exploiting the freedom of choosing a particular
SO(3) representative we find a direct connection between the two configuration
spaces. We are then able to compare the Kovacs-Tomboulis formulation of center
vortices with the projection vortex formulation on the same configuration.
Choosing a different representative, and going to the maximal center gauge, we
show that projection vortices occur without approximation. The projection
vortex dominance approximation results from dropping a factor in an exact
expression for the Wilson loop.


title: Monopoles and Lyapunov Exponents in U(1) Lattice Gauge Theory

abstract:
  U(1) gauge fields are decomposed into a monopole and photon part across the
phase transition from the confinement to the Coulomb phase. We analyze the
leading Lyapunov exponents of such gauge field configurations on the lattice
which are initialized by quantum Monte Carlo simulations. We observe a strong
relation between the sizes of the monopole density and the Lyapunov exponent.
Evidence is found that monopole fields stay chaotic in the continuum whereas
the photon fields are regular.


title:
Center vortices, magnetic condensate and confinement in a simple gauge
  system

abstract:
  The confining mechanisms of 't Hooft and Mandelstam have a simple microscopic
realization in 3D Z2 gauge theory: the center vortex and the magnetic monopole
condensation are associated, in the set of configurations contributing to the
confining phase, to the presence of two kinds of infinite clusters. These
generate the area law of the large Wilson loops and the universal finite size
effects produced by the quantum fluctuations of the bosonic string describing
the infrared behavior of the flux tube.


title: Chiral fermions on the lattice

abstract:
  We discuss topological obstructions to putting chiral fermions on an even
dimensional lattice. The setting includes Ginsparg-Wilson fermions, but is more
general. We prove a theorem which relates the total chirality to the difference
of generalised winding numbers of chiral projection operators. For an odd
number of Weyl fermions this implies that particles and anti-particles live in
topologically different spaces.


title: Confinement in SU(3: Simple and Generalized Maximal Abelian Gauge

abstract:
  The general problem of obtaining reliable results from gauge-fixing and
projection is discussed. It is shown that the usual form of the maximal abelian
gauge gives poor results for the string tension in SU(3) lattice gauge theory.
A generalized form is suggested. Evidence is presented that monopoles in SU(3)
are associated with SU(2) subgroups, and that P-vortices pass through
monopoles, similar to what happens in SU(2).


title: Light quark masses in quenched QCD with exact chiral symmetry

abstract:
  The parameters in the pseudoscalar meson mass formula in quenched chiral
perturbation theory to one-loop order are determined by quenched lattice QCD
with overlap Dirac operator, and from which the light quark masses are
determined with the experimental inputs of pion and kaon masses, and the pion
decay constant. Our results are $ m_{u,d} = 5.3 \pm 0.3 $ MeV, and $ m_s =
115\pm 8 $ MeV, in the $ \bar{MS} $ scheme at scale $ \mu = 2 $ GeV.


title: String effects in Polyakov loop correlators

abstract:
  We compare the predictions of the effective string description of confinement
in finite temperature gauge theories to high precision Monte Carlo data for the
three-dimensional Z_2 gauge theory. First we review the predictions of the free
bosonic string model and their asymptotic behavior in the various regimes of
physical interest. Then we show that very good agreement with the Monte Carlo
data is obtained, for temperatures not too close to the deconfinement one
(typically T<T_c/3). For higher temperatures, higher order effects are not
negligible: we show that they are accurately modeled by assuming a Nambu-Goto
string action and computing its partition function at next-to-leading order.


title: Remarks on the Gauge Dependence of the RI/MOM Renormalization Procedure

abstract:
  The RI/MOM non-perturbative renormalization scheme is studied on the lattice
in SU(3) quenched QCD with Wilson fermions. The gauge dependence of some
fermion bilinear renormalization constants is discussed by comparing data which
have been gauge-fixed in two different realizations of the Landau gauge and in
a generic covariant gauge. The very good agreement between the various sets of
results and the theory indicates that the numerical uncertainty induced by the
lattice gauge-fixing procedure is moderate and below the statistical errors.


title:
Testing the fixed-point QCD action and the construction of chiral
  currents

abstract:
  We present the first set of quenched QCD measurements using the recently
parametrized fixed-point Dirac operator D^FP. We also give a general and
practical construction of covariant densities and conserved currents for chiral
lattice actions. The measurements include (a) hadron spectroscopy, (b)
corrections of small chiral deviations, (c) the renormalized quark condensate
from finite-size scaling and, independently, spectroscopy, (d) the topological
susceptibility, (e) small eigenvalue distributions and random matrix theory,
and (f) local chirality of near-zero modes and instanton-dominance.


title: Lattice QCD with Suppressed High Momentum Modes of the Dirac Operator

abstract:
  I define lattice fermions in five Euclidean dimensions and the corresponding
effective theory in four dimensions. The main properties of these theories
include the suppression of high momentum modes of the lattice Dirac operator
and their ability to continuously interpolate between quenched and dynamical
fermions. In particular, the standard formulation of lattice QCD can be viewed
as a limiting case of the theory.


title:
Low-Lying Dirac Eigenmodes, Topological Charge Fluctuations and the
  Instanton Liquid Model

abstract:
  The local structure of low-lying eigenmodes of the overlap Dirac operator is
studied. It is found that these modes cannot be described as linear
combinations of 't Hooft "would-be" zeromodes associated with instanton
excitations that underly the Instanton Liquid Model. This implies that the
instanton liquid scenario for spontaneous chiral symmetry breaking in QCD is
not accurate. More generally, our data suggests that the vacuum fluctuations of
topological charge are not effectively dominated by localized lumps of unit
charge with which the topological "would-be" zeromodes could be associated.


title: Exact duality transformations for sigma models and gauge theories

abstract:
  We present an exact duality transformation in the framework of Statistical
Mechanics for various lattice models with non-Abelian global or local
symmetries. The transformation applies to sigma models with variables in a
compact Lie group G with global GxG-symmetry (the chiral model) and with
variables in coset spaces G/H and a global G-symmetry (for example, the
non-linear O(N) or RP^N models) in any dimension d>=1. It is also available for
lattice gauge theories with local gauge symmetry in dimensions d>=2 and for the
models obtained from minimally coupling a sigma model of the type mentioned
above to a gauge theory. The duality transformation maps the strong coupling
regime of the original model to the weak coupling regime of the dual model.
Transformations are available for the partition function, for expectation
values of fundamental variables (correlators and generalized Wilson loops) and
for expectation values in the dual model which correspond in the original
formulation to certain ratios of partition functions (free energies of
dislocations, vortices or monopoles). Whereas the original models are
formulated in terms of compact Lie groups G and H, coset spaces G/H and
integrals over them, the configurations of the dual model are given in terms of
representations and intertwiners of G. They are spin networks and spin foams.
The partition function of the dual model describes the group theoretic aspects
of the strong coupling expansion in a closed form.


title: Connecting the Quenched and Unquenched Worlds via the Large N_c World

abstract:
  In the large N_c(number of colors) limit, quenched QCD and QCD are identical.
This implies that, in the effective field theory framework, some of the low
energy constants in (N_c=3) quenched QCD and QCD are the same up to
higher-order corrections in the 1/N_c expansion. Thus the calculation of the
nonleptonic kaon decays relevant for the Delta I=1/2 rule in the quenched
approximation is expected to differ from the unquenched one by an O(1/N_c)
correction. However, the calculation relevant to the CP-violation parameter
epsilon'/epsilon would have a relatively big higher-order correction due to the
large cancellation in the leading order. Some important weak matrix elements
are poorly known that even constraints with 100% errors are interesting. In
those cases, quenched calculations will be very useful.


title: Center vortices and k-strings

abstract:
  The vortex contribution to the $k$-string tensions is computed for SU($N$)
gauge theories. We deduce the surface densities needed to reproduce the sine
scaling and the Casimir scaling formulae, recently obtained from numerical
simulations on the lattice. We find that such densities need to grow linearly
in $N$, which in turn suggests that the vortex scenario can hardly reproduce
the physics of confinement at large $N$.


title:
The QCD phase diagram for small densities from imaginary chemical
  potential

abstract:
  We present results on the QCD phase diagram for mu_B <= pi T. Our simulations
are performed with an imaginary chemical potential mu_I for which the fermion
determinant is positive. On an 8^3 x 4 lattice with 2 flavors of staggered
quarks, we map out the phase diagram and identify the pseudo-critical
temperature T_c(mu_I). For mu_I/T <= pi/3, this is an analytic function, whose
Taylor expansion is found to converge rapidly, with truncation errors far
smaller than statistical ones. The truncated series may then be continued to
real mu, yielding the corresponding phase diagram for mu_B <~ 500 MeV. This
approach provides control over systematics and avoids reweighting. We compare
it with other recent work.


title: Chiral Analysis of Quenched Baryon Masses

abstract:
  We extend to quenched QCD an earlier investigation of the chiral structure of
the masses of the nucleon and the delta in lattice simulations of full QCD.
Even after including the meson-loop self-energies which give rise to the
leading and next-to-leading non-analytic behaviour (and hence the most rapid
variation in the region of light quark mass), we find surprisingly little
curvature in the quenched case. Replacing these meson-loop self-energies by the
corresponding terms in full QCD yields a remarkable level of agreement with the
results of the full QCD simulations. This comparison leads to a very good
understanding of the origins of the mass splitting between these baryons.


title:
Gauge-invariant field-strength correlators in pure Yang-Mills and full
  QCD at finite temperature

abstract:
  We study by numerical simulations on a lattice the behaviour of the
gauge-invariant two-point correlation functions of the gauge-field strengths
across the deconfinement phase transition, both for the pure-gauge SU(3) theory
and for full QCD with two flavours. Quenched data agree within errors with
previous determinations, but have much higher statistics. A best-fit analysis
of the data has been performed, both for the quenched and the full-QCD case,
showing that the electric gluon condensate drops to zero at the deconfining
phase transition.


title:
The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero
  Chemical Potential and Temperature

abstract:
  SU(2) lattice gauge theory with four flavors of quarks is simulated at
nonzero chemical potential $\mu$ and temperature $T$ and the results are
compared to the predictions of Effective Lagrangians. Simulations on $16^4$
lattices indicate that at zero $T$ the theory experiences a second order phase
transition to a diquark condensate state. Several methods of analysis,
including equation of state fits suggested by Chiral Perturbation Theory,
suggest that mean-field scaling describes this critical point. Nonzero $T$ and
$\mu$ are studied on $12^3 \times 6$ lattices. For low $T$, increasing $\mu$
takes the system through a line of second order phase transitions to a diquark
condensed phase. Increasing $T$ at high $\mu$, the system passes through a line
of first order transitions from the diquark phase to the quark-gluon plasma
phase. Metastability is found in the vicinity of the first order line. There is
a tricritical point along this line of transitions whose position is consistent
with theoretical predictions.


title: Spectra of Lattice Dirac Operators in Non-Trivial Topology Backgrounds

abstract:
  Dirac operators in non-trivial topology backgrounds in a finite box are
reviewed. We analyze how the formalism translates to the lattice, with special
emphasis on uniform field backgrounds.


title: Uses of Effective Field Theory in Lattice QCD

abstract:
  Several physical problems in particle physics, nuclear physics, and
astrophysics require information from non-perturbative QCD to gain a full
understanding. In some cases the most reliable technique for quantitative
results is to carry out large-scale numerical calculations in lattice gauge
theory. As in any numerical technique, there are several sources of
uncertainty. This chapter explains how effective field theories are used to
keep them under control and, then, obtain a sensible error bar. After a short
survey of the numerical technique, we explain why effective field theories are
necessary and useful. Then four important cases are reviewed: Symanzik's
effective field theory of lattice spacing effects; heavy-quark effective theory
as a tool for controlling discretization effects of heavy quarks; chiral
perturbation theory as a tool for reaching the chiral limit; and a general
field theory of hadrons for deriving finite volume corrections.


title: Imaginary chemical potential in QCD at finite temperature

abstract:
  After presenting a brief review of how simulations of QCD with imaginary
chemical potential can be used to extract physical results, we analyse the
phase structure of QCD with four flavours of dynamical fermions in the finite
temperature - imaginary chemical potential plane, and discuss perspectives for
realistic calculations.


title: Ising spins coupled to a four-dimensional discrete Regge skeleton

abstract:
  Regge calculus is a powerful method to approximate a continuous manifold by a
simplicial lattice, keeping the connectivities of the underlying lattice fixed
and taking the edge lengths as degrees of freedom. The discrete Regge model
employed in this work limits the choice of the link lengths to a finite number.
To get more precise insight into the behavior of the four-dimensional discrete
Regge model, we coupled spins to the fluctuating manifolds. We examined the
phase transition of the spin system and the associated critical exponents. The
results are obtained from finite-size scaling analyses of Monte Carlo
simulations. We find consistency with the mean-field theory of the Ising model
on a static four-dimensional lattice.


title: Generalized Ginsparg-Wilson algebra and index theorem on the lattice

abstract:
  Recent studies of the topological properties of a general class of lattice
Dirac operators are reported. This is based on a specific algebraic realization
of the Ginsparg-Wilson relation in the form
  $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} =
  2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer.
The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation
and thus to the overlap operator. It is shown that local chiral anomaly and the
instanton-related index of all these operators are identical. The locality of
all these Dirac operators for vanishing gauge fields is proved on the basis of
explicit construction, but the locality with dynamical gauge fields has not
been established yet. We suggest that the Wilsonian effective action is
essential to avoid infrared singularities encountered in general perturbative
analyses.


title: Color confinement and dual superconductivity in full QCD

abstract:
  We report on evidence that confinement is related to dual superconductivity
of the vacuum in full QCD, as in quenched QCD. The vacuum is a dual
superconductor in the confining phase, whilst the U(1) magnetic symmetry is
realized a la Wigner in the deconfined phase.


title: SO(3) versus SU(2) lattice gauge theory

abstract:
  We consider the SO(3) lattice gauge theory at weak coupling, in the Villain
action. We exhibit an analytic path in coupling space showing the equivalence
of the SO(3) theory with SU(2) summed over all twist sectors. This clarifies
the ``mysterious phase'' of SO(3). As order parameter, we consider the dual
string tension or center vortex free energy, which we measure in SO(3) using
multicanonical Monte Carlo. This allows us to set the scale, indicating that
${\cal O}(700)^4$ lattices are necessary to probe the confined phase. We
consider the relevance of our findings for confinement in other gauge groups
with trivial center.


title:
Evidence for the reality of singular configurations in SU(2) gauge
  theory

abstract:
  We consider the SU(2) lattice gauge model and investigate numerically the
continuum limit of the simple center vortices which are singular configurations
of the gauge fields. We found that the vortices remain alive in the continuum
theory. Also we investigate the Creutz ratio and found that for all $\beta$ it
vanishes for those field configurations which do not contain the simple center
vortices inside the considered Wilson loop. It leads us to the conclusion that
these singular field configurations play a real role in the continuum theory.


title: Griffiths Inequalities for some O(n) Classical Spin Models with $n\ge 3$

abstract:
  The first and second Griffiths inequalities are proved for some classical
O($n$)-invariant spin models (including Euclidean quantum field theories) for
any $n$. The proof assumes a certain condition on an integral transform of the
measure. Some examples are discussed.

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


title: Three-quark ground-state potential in the SU(3) lattice QCD

abstract:
  With the smearing technique, the three-quark (3Q) ground-state potential
$V_{\rm 3Q}$ is numerically extracted in the SU(3)$_c$ lattice QCD Monte Carlo
simulation with $12^3 \times 24$ and $\beta=5.7$ at the quenched level. With
accuracy better than a few %, $V_{\rm 3Q}$ is well described by a sum of a
constant $C_{\rm 3Q}$, the two-body Coulomb part $-A_{\rm 3Q}\sum_{i<j}
\frac1{|{\bf r}_i-{\bf r}_j|}$ and the three-body linear confinement part
$\sigma_{\rm 3Q} L_{\rm min}$, where $L_{\rm min}$ denotes the minimal length
of the color flux tube linking the three quarks. By comparing with the Q-$\bar
{\rm Q}$ potential, we find a universal feature of the string tension as
$\sigma_{\rm 3Q} \simeq \sigma_{\rm Q \bar Q}$ and the one-gluon-exchange
result for the Coulomb coefficient as $A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar
Q}$. All our results including the constant term are consistent with the
requirement on the diquark limit in the lattice regularization.


title:
Thermodynamical Observables in a Finite Temperature Window from the
  Monte Carlo Hamiltonian

abstract:
  The Monte Carlo (MC) Hamiltonian is a new stochastic method to solve
many-body problems. The MC Hamiltonian represents an effective Hamiltonian in a
finite energy window. We construct it from the classical action via Monte Carlo
with importance sampling. The MC Hamiltonian yields the energy spectrum and
corresponding wave functions in a low energy window. This allows to compute
thermodynamical observables in a low temperature window. We show the working of
the MC Hamiltonian by an example from lattice field theory (Klein-Gordon
model).


title: Moments of Isovector Quark Distributions from Lattice QCD

abstract:
  We present a complete analysis of the chiral extrapolation of lattice moments
of all twist-2 isovector quark distributions, including corrections from N pi
and Delta pi loops. Even though the Delta resonance formally gives rise to
higher order non-analytic structure, the coefficients of the higher order terms
for the helicity and transversity moments are large and cancel much of the
curvature generated by the wave function renormalization. The net effect is
that, whereas the unpolarized moments exhibit considerable curvature, the
polarized moments show little deviation from linearity as the chiral limit is
approached.


title: Heavy and Light Quarks with Lattice Chiral Fermions

abstract:
  The feasibility of using lattice chiral fermions which are free of $O(a)$
errors for both the heavy and light quarks is examined. The fact that the
effective quark propagators in these fermions have the same form as that in the
continuum with the quark mass being only an additive parameter to a chirally
symmetric antihermitian Dirac operator is highlighted. This implies that there
is no distinction between the heavy and light quarks and no mass dependent
tuning of the action or operators as long as the discretization error $O(m^2
a^2)$ is negligible. Using the overlap fermion, we find that the $O(m^2a^2)$
(and $O(ma^2)$) errors in the dispersion relations of the pseudoscalar and
vector mesons and the renormalization of the axial-vector current and scalar
density are small. This suggests that the applicable range of $ma$ may be
extended to $\sim 0.56$ with only 5% error, which is a factor of $\sim 2.4$
larger than that of the improved Wilson action. We show that the generalized
Gell-Mann-Oakes-Renner relation with unequal masses can be utilized to
determine the finite $ma$ errors in the renormalization of the matrix elements
for the heavy-light decay constants and semileptonic decay constants of the B/D
meson.


title: More about the axial anomaly on the lattice

abstract:
  We study the axial anomaly defined on a finite-size lattice by using a Dirac
operator which obeys the Ginsparg-Wilson relation. When the gauge group is
U(1), we show that the basic structure of axial anomaly on the infinite
lattice, which can be deduced by a cohomological analysis, persists even on
(sufficiently large) finite-size lattices. For non-abelian gauge groups, we
propose a conjecture on a possible form of axial anomaly on the infinite
lattice, which holds to all orders in perturbation theory. With this
conjecture, we show that a structure of the axial anomaly on finite-size
lattices is again basically identical to that on the infinite lattice. Our
analysis with the Ginsparg-Wilson Dirac operator indicates that, in appropriate
frameworks, the basic structure of axial anomaly is quite robust and it
persists even in a system with finite ultraviolet and infrared cutoffs.


title: On the topological content of SU(2) gauge fields below T_c

abstract:
  Finite temperature Euclidean SU(2) lattice gauge fields generated in the
confinement phase close to the deconfinement phase transition are subjected to
cooling. The aim is to identify long-living, almost-classical local excitations
which carry (generically non-integer) topological charge. Two kinds of spatial
boundary conditions (fixed holonomy and standard periodic boundary conditions)
are applied. For the lowest-action almost-classical configurations we find that
their relative probability semi-quantitatively agrees for both types of
boundary conditions. We find calorons with unit topological charge as well as
(anti-)selfdual lumps (BPS-monopoles or dyons) combined in pairs of non-integer
(equal or opposite sign) topological charge. For calorons and separated pairs
of equal-sign dyons obtained by cooling we have found that (i) the gluon field
is well-described by Kraan-van Baal solutions of the Euclidean Yang-Mills field
equations and (ii) the lowest Wilson-fermion modes are well-described by
analytic solutions of the corresponding Dirac equation. For metastable
configurations found at higher action, the multi-center structure can be
interpreted in terms of dyons and antidyons, using the gluonic and fermionic
indicators as in the dyon-pair case. Additionally, the Abelian monopole
structure and field strength correlators between the centers are useful to
analyse the configurations in terms of dyonic constituents. We argue that a
semi-classical approximation of the non-zero temperature path integral should
be built on superpositions of solutions with non-trivial holonomy.