title: Inherently Global Nature of Topological Charge Fluctuations in QCD

abstract:
  We have recently presented evidence that in configurations dominating the
regularized pure-glue QCD path integral, the topological charge density
constructed from overlap Dirac operator organizes into an ordered space-time
structure. It was pointed out that, among other properties, this structure
exhibits two important features: it is low-dimensional and geometrically
global, i.e. consisting of connected sign-coherent regions with local
dimensions 1<= d < 4, and spreading over arbitrarily large space--time
distances. Here we show that the space-time structure that is responsible for
the origin of topological susceptibility indeed exhibits global behavior. In
particular, we show numerically that topological fluctuations are not saturated
by localized concentrations of most intense topological charge density. To the
contrary, the susceptibility saturates only after the space-time regions with
most intense fields are included, such that geometrically global structure is
already formed. We demonstrate this result both at the fundamental level (full
topological density) and at low energy (effective density). The drastic
mismatch between the point of fluctuation saturation (~ 50% of space-time at
low energy) and that of global structure formation (<4% of space-time at low
energy) indicates that the ordered space-time structure in topological charge
is inherently global and that topological charge fluctuations in QCD cannot be
understood in terms of individual localized pieces. Description in terms of
global brane-like objects should be sought instead.


title: Lattice QCD-2+1

abstract:
  We consider a 2+1-dimensional SU(N) lattice gauge theory in an axial gauge
with the link field U in the 1-direction set to one. The term in the
Hamiltonian containing the square of the electric field in the 1-direction is
non-local. Despite this non-locality, we show that weak-coupling perturbation
theory in this term gives a finite vacuum-energy density to second order, and
suggest that this property holds to all orders. Heavy quarks are confined, the
spectrum is gapped, and the space-like Wilson loop has area decay.


title: Comparing the Nambu-Goto string with LGT results

abstract:
  We discuss a way to evaluate the full prediction for the interquark potential
which is expected from the effective Nambu-Goto string model. We check the
correctness of the prescription reproducing the results obtained with the zeta
function regularization for the first two perturbative orders. We compare the
predictions with existing Monte Carlo data for the (2+1) dimensional Z(2),
SU(2) and SU(3) gauge theories: in the low temperature regime, we find good
agreement for large enough interquark distances, but an increasing mismatch
between theoretical predictions and numerical results is observed as shorter
and shorter distances are investigated. On the contrary, at high temperatures
(approaching the deconfinement transition from below) a remarkable agreement
between Monte Carlo data and the expectations from the Nambu-Goto effective
string is observed for a wide range of interquark distances.


title: Extrapolation of lattice QCD results beyond the power-counting regime

abstract:
  Resummation of the chiral expansion is necessary to make accurate contact
with current lattice simulation results of full QCD. Resummation techniques
including relativistic formulations of chiral effective field theory and
finite-range regularization (FRR) techniques are reviewed, with an emphasis on
using lattice simulation results to constrain the parameters of the chiral
expansion. We illustrate how the chiral extrapolation problem has been solved
and use FRR techniques to identify the power-counting regime (PCR) of chiral
perturbation theory. To fourth-order in the expansion at the 1% tolerance
level, we find 0 \le m_pi \le 0.18 GeV for the PCR, extending only a small
distance beyond the physical pion mass.


title: Generalized parton distributions and transversity from full lattice QCD

abstract:
  We present here the latest results from the QCDSF collaboration for moments
of generalized parton distributions and transversity in two-flavour QCD,
including a preliminary analysis of the pion mass dependence.


title:
Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical
  Potential

abstract:
  We present results of a simulation of 2-flavor QCD on a 4x16^3 lattice using
p4-improved staggered fermions with bare quark mass m/T=0.4. Derivatives of the
thermodynamic grand canonical partition function Z(V,T,mu_u,mu_d) with respect
to chemical potentials mu_(u,d) for different quark flavors are calculated up
to sixth order, enabling estimates of the pressure and the quark number density
as well as the chiral condensate and various susceptibilities as functions of
mu_q = (mu_u + mu_d)/2 via Taylor series expansion. Furthermore, we analyze
baryon as well as isospin fluctuations and discuss the relation between the
radius of convergence of the Taylor series and the chiral critical point in the
QCD phase diagram. We argue that bulk thermodynamic observables do not, at
present, provide direct evidence for the existence of a chiral critical point
in the QCD phase diagram. Results are compared to high temperature perturbation
theory as well as a hadron resonance gas model.


title:
Large N QCD on the lattice -- A review of recent results in the
  fermionic sector

abstract:
  It is possible to numerically solve QCD in the planar limit using standard
numerical techniques on existing computer clusters. The basic ideas behind the
computational strategy an recent numerical results in the fermionic sector of
large N QCD are reviewed.


title:
Simulations of Lattice Fermions with Chiral Symmetry in Quantum
  Chromodynamics

abstract:
  This thesis is dedicated to explore the feasibility of numerical calculations
in the $\epsilon$--regime of QCD for the extraction of physical information. We
apply two formulations of the Ginsparg-Wilson fermions the Neuberger operator
and the hypercube overlap operator to compute the observables of interest. As a
main result we present the comparison of the distributions of the leading
individual eigenvalues of the Neuberger operator in QCD and the analytical
predictions of chiral random matrix theory. We observe a good agreement as long
as each side of the physical volume exceeds about $L\approx 1.12\fm$. It turns
out that this bound for $L$ is generic and sets the size of the physical volume
where the axial correlator behaves according to chiral perturbation theory.
This allows us to compute a value for the pion decay constant $F_{\pi}$. As an
alternative procedure we only consider the contribution from the zero modes.
Here we are able to obtain an estimate for $F_{\pi}$ and $\alpha$. As a
theoretical development the L\"uscher topology conserving gauge action is
investigated. This enables us to sample the observables of interest in the
$\epsilon$--regime without recomputing the index. We can report that a
promising gauge action has been identified.


title: Finite Volume Dependence of Hadron Properties and Lattice QCD

abstract:
  Because the time needed for a simulation in lattice QCD varies at a rate
exceeding the fourth power of the lattice size, it is important to understand
how small one can make a lattice without altering the physics beyond
recognition. It is common to use a rule of thumb that the pion mass times the
lattice size should be greater than (ideally much greater than) four (i.e.,
$m_\pi L \gg 4$). By considering a relatively simple chiral quark model we are
led to suggest that a more realistic constraint would be $m_\pi (L - 2R) \gg
4$, where $R$ is the radius of the confinement region, which for these purposes
could be taken to be around 0.8-1.0 fm. Within the model we demonstrate that
violating the second condition can lead to unphysical behaviour of hadronic
properties as a function of pion mass. In particular, the axial charge of the
nucleon is found to decrease quite rapidly as the chiral limit is approached.


title: Properties of the deconfining phase transition in SU(N) gauge theories

abstract:
  We extend our earlier investigation of the finite temperature deconfinement
transition in SU(N) gauge theories, with the emphasis on what happens as N->oo.
We calculate the latent heat in the continuum limit, and find the expected
quadratic in N behaviour at large N. We confirm that the phase transition,
which is second order for SU(2) and weakly first order for SU(3), becomes
robustly first order for N>3 and strengthens as N increases. As an aside, we
explain why the SU(2) specific heat shows no sign of any peak as T is varied
across what is supposedly a second order phase transition. We calculate the
effective string tension and electric gluon masses at T=Tc confirming the
discontinuous nature of the transition for N>2. We explicitly show that the
large-N `spatial' string tension does not vary with T for T<Tc and that it is
discontinuous at T=Tc. For T>Tc it increases as T-squared to a good
approximation, and the k-string tension ratios closely satisfy Casimir Scaling.
Within very small errors, we find a single Tc at which all the k-strings
deconfine, i.e. a step-by-step breaking of the relevant centre symmetry does
not occur. We calculate the interface tension but are unable to distinguish
between linear or quadratic in N variations, each of which can lead to a
striking but different N=oo deconfinement scenario. We remark on the location
of the bulk phase transition, which bounds the range of our large-N
calculations on the strong coupling side, and within whose hysteresis some of
our larger-N calculations are performed.


title:
Systematic uncertainties in the precise determination of the strangeness
  magnetic moment of the nucleon

abstract:
  Systematic uncertainties in the recent precise determination of the
strangeness magnetic moment of the nucleon are identified and quantified. In
summary, G_M^s = -0.046 \pm 0.019 \mu_N.


title: Phenomenology using lattice QCD

abstract:
  This talk provides a brief summary of the status of lattice QCD calculations
of the light quark masses and the kaon bag parameter B_K. Precise estimates of
these four fundamental parameters of the standard model, i.e., m_u, m_d, m_s
and the CP violating parameter eta, help constrain grand unified models and
could provide a window to new physics.


title: Standard Model with the additional $Z_6$ symmetry on the lattice

abstract:
  An additional $Z_6$ symmetry hidden in the fermion and Higgs sectors of the
Standard Model has been found recently\cite{BVZ2003}. A lattice regularization
of the Standard Model was constructed that possesses this symmetry. In
\cite{BVZ2004} we have reported our results on the numerical simulation of the
Electroweak sector of the model. In this paper we report our results on the
numerical simulation of the full ($SU(3)\otimes SU(2) \otimes U(1)$) model. The
phase diagram of the model has been investigated using static quark and lepton
potentials. Various types of monopoles have been constructed. Their densities
appear to be sensitive to the phase transition lines. Differences between the
realizations of the Standard Model which do or do not possess the mentioned
$Z_6$ symmetry, are discussed.


title: Numerical Methods for the QCD Overlap Operator IV: Hybrid Monte Carlo

abstract:
  The extreme computational costs of calculating the sign of the Wilson matrix
within the overlap operator have so far prevented four dimensional dynamical
overlap simulations on realistic lattice sizes, because the computational power
required to invert the overlap operator, the time consuming part of the Hybrid
Monte Carlo algorithm, is too high. In this series of papers we introduced the
optimal approximation of the sign function and have been developing
preconditioning and relaxation techniques which reduce the time needed for the
inversion of the overlap operator by over a factor of four, bringing the
simulation of dynamical overlap fermions on medium-size lattices within the
range of Teraflop-computers.
  In this paper we adapt the HMC algorithm to overlap fermions. We approximate
the matrix sign function using the Zolotarev rational approximation, treating
the smallest eigenvalues of the Wilson operator exactly within the fermionic
force. We then derive the fermionic force for the overlap operator, elaborating
on the problem of Dirac delta-function terms from zero crossings of eigenvalues
of the Wilson operator. The crossing scheme proposed shows energy violations
which are better than O($\Delta\tau^2$) and thus are comparable with the
violations of the standard leapfrog algorithm over the course of a trajectory.
We explicitly prove that our algorithm satisfies reversibility and area
conservation. Finally, we test our algorithm on small $4^4$, $6^4$, and $8^4$
lattices at large masses.


title: Heavy Quark Potentials and Quarkonia Binding

abstract:
  I review recent progress in studying in-medium modification of inter-quark
forces at finite temperature in lattice QCD. Some applications to the problem
of quarkonium binding in potential models is also discussed.


title:
The compact Q=2 Abelian Higgs model in the London limit: vortex-monopole
  chains and the photon propagator

abstract:
  The confining and topological properties of the compact Abelian Higgs model
with doubly-charged Higgs field in three space-time dimensions are studied. We
consider the London limit of the model. We show that the monopoles are forming
chain-like structures (kept together by ANO vortices) the presence of which is
essential for getting simultaneously permanent confinement of singly-charged
particles and breaking of the string spanned between doubly-charged particles.
In the confinement phase the chains are forming percolating clusters while in
the deconfinement (Higgs) phase the chains are of finite size. The described
picture is in close analogy with the synthesis of the Abelian monopole and the
center vortex pictures in confining non--Abelian gauge models. The screening
properties of the vacuum are studied by means of the photon propagator in the
Landau gauge.


title:
Relating Chiral Perturbation Theory and QCD Simulations with Overlap
  Hypercube Fermions

abstract:
  We present simulation results for lattice QCD with light pions. For the quark
fields we apply chirally symmetric lattice Dirac operators, in particular the
overlap hypercube operator, along with the standard overlap operator for
comparison. This allows us to simulate at very low pion masses. The results are
related to Random Matrix Theory and to Chiral Perturbation Theory in order to
extract information about the pion decay constant, the scalar condensate and
the topological susceptibility.


title: Static quark anti-quark free and internal energy in 2-flavor QCD

abstract:
  We study the change in free and internal energy due to the presence of a
heavy quark anti-quark pair in a thermal heat bath in QCD with 2-flavors of
staggered quarks at finite temperature. We discuss string breaking below as
well as screening above the transition. Similarities and differences to the
quenched case are discussed.


title: Running coupling of 2-flavor QCD at zero and finite temperature

abstract:
  We present lattice studies of the running coupling in 2-flavor QCD. The
coupling at zero temperature (T=0) is extracted from Wilson loops while the
coupling at finite temperature ($T\neq0$) is determined from Polyakov loop
correlation functions.


title:
Effective Actions for the SU(2) Confinement-Deconfinement Phase
  Transition

abstract:
  We compare different Polyakov loop actions yielding effective descriptions of
finite-temperature SU(2) Yang-Mills theory on the lattice. The actions are
motivated by a simultaneous strong-coupling and character expansion obeying
center symmetry and include both Ising and Ginzburg-Landau type models. To keep
things simple we limit ourselves to nearest-neighbor interactions. Some
truncations involving the most relevant characters are studied within a novel
mean-field approximation. Using inverse Monte-Carlo techniques based on exact
geometrical Schwinger-Dyson equations we determine the effective couplings of
the Polyakov loop actions. Monte-Carlo simulations of these actions reveal that
the mean-field analysis is a fairly good guide to the physics involved. Our
Polyakov loop actions reproduce standard Yang-Mills observables well up to
limitations due to the nearest-neighbor approximation.


title: Deconfinement and Quarkonium Suppression

abstract:
  Modifications in the production pattern of heavy quark bound states have long
been considered to provide sensitive signatures for the thermal properties of
dense matter created in heavy ion collisions. The original concept of Matsui
and Satz for quarkonium suppression as signature for deconfinement in heavy ion
collisions has been challenged recently through lattice studies of spectral
functions, which indicate the persistence of heavy quark bound states at
temperatures well above the transition, as well as through the refined analysis
of hadronization and recombination models, which take into account the thermal
evolution of the medium generated in a heavy ion collision. We will review here
recent developments on these topics.


title:
Operator product expansion and quark condensate from Lattice QCD in
  coordinate space

abstract:
  We present a Lattice QCD determination of the chiral quark condensate based
on a new method. We extract the quark condensate from the operator product
expansion of the quark propagator at short euclidean distances, where it
represents the leading contribution in the chiral limit. From this study we
obtain <\bar q q>^ms(2 GeV)=-(265+-5+-22 MeV)^3$, in good agreement with
determinations of this quantity based on different approaches. The simulation
is performed by using the O(a)-improved Wilson action at beta=6.45 on a volume
32^3\times70 in the quenched approximation.


title:
Quarkonium correlators and spectral functions at zero and finite
  temperature from Fermilab action

abstract:
  We study charmonium and bottomonium systems at zero and finite temperatures
using Lattice QCD with Fermilab action on anisotropic lattices.


title:
Non-perturbative improvement of the axial current for dynamical Wilson
  fermions

abstract:
  A non-perturbative determination of the axial current improvement coefficient
cA is performed with two flavors of dynamical improved Wilson fermions and
plaquette gauge action. The improvement condition is formulated with
Schroedinger functional boundary conditions and enforced at constant physical
volume. Large sensitivity is obtained by using two different pseudo-scalar
states in the PCAC relation. We estimate the resulting correction to F_PS at
beta=5.2 to be around 10%.


title: Remnant index theorem and low-lying eigenmodes for twisted mass fermions

abstract:
  We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators
with a twisted mass term. The twist term expels the eigenvalues from a strip in
the complex plane and all eigenmodes obtain a non-vanishing matrix element with
gamma-5. For a twisted Ginsparg-Wilson operator the spectrum is located on two
arcs in the complex plane. Modes due to non-trivial topological charge of the
underlying gauge field have their eigenvalues at the edges of these arcs and
obey a remnant index theorem. For configurations in the confined phase we find
that the twist mainly affects the zero modes, while the bulk of the spectrum is
essentially unchanged.


title: Accurate Determinations of $\alpha_s$ from Realistic Lattice QCD

abstract:
  We obtain a new value for the QCD coupling constant by combining lattice QCD
simulations with experimental data for hadron masses. Our lattice analysis is
the first to: 1) include vacuum polarization effects from all three light-quark
flavors (using MILC configurations); 2) include third-order terms in
perturbation theory; 3) systematically estimate fourth and higher-order terms;
4) use an unambiguous lattice spacing; and 5) use an $\order(a^2)$-accurate QCD
action. We use 28~different (but related) short-distance quantities to obtain
$\alpha_{\bar{\mathrm{MS}}}^{(5)}(M_Z) = 0.1170(12)$.


title: Heat Bath Efficiency with Metropolis-Type Updating

abstract:
  We illustrate for 4D SU(2) and U(1) lattice gauge theory that sampling with a
biased Metropolis scheme is essentially equivalent to using the heat bath
algorithm. Only, the biased Metropolis method can also be applied when an
efficient heat bath algorithm does not exist.


title: Spectrum of quenched twisted mass lattice QCD at maximal twist

abstract:
  Hadron masses are computed from quenched twisted mass lattice QCD for a
degenerate doublet of up and down quarks with the twist angle set to pi/2,
since this maximally twisted theory is expected to be free of linear
discretization errors. Two separate definitions of the twist angle are used,
and the hadron masses for these two cases are compared. The flavor breaking,
that can arise due to twisting, is discussed in the context of mass splittings
within the Delta(1232) multiplet.


title: Search for the pentaquark resonance signature in lattice QCD

abstract:
  Claims concerning the possible discovery of the \Theta^+ pentaquark, with
minimal quark content uudd\bar{s}, have motivated our comprehensive study into
possible pentaquark states using lattice QCD. We review various pentaquark
interpolating fields in the literature and create a new candidate ideal for
lattice QCD simulations. Using these interpolating fields we attempt to isolate
a signal for a five-quark resonance. Calculations are performed using improved
actions on a large 20^3 x 40 lattice in the quenched approximation. The
standard lattice resonance signal of increasing attraction between baryon
constituents for increasing quark mass is not observed for spin-1/2 pentaquark
states. We conclude that evidence supporting the existence of a spin-1/2
pentaquark resonance does not exist in quenched QCD.


title:
Chiral Perturbation Theory for Staggered Sea Quarks and Ginsparg-Wilson
  Valence Quarks

abstract:
  We study lattice QCD with staggered sea and Ginsparg-Wilson valence quarks.
The Symanzik effective action for this mixed lattice theory, including the
lattice spacing contributions of O(a^2), is derived. Using this effective
theory we construct the leading order chiral Lagrangian. The masses and decay
constants of pseudoscalars containing two Ginsparg-Wilson valence quarks are
computed at one loop order.


title:
Phase diagram of QCD with four quark flavors at finite temperature and
  baryon density

abstract:
  We analyze the phase diagram of QCD with four staggered flavors in the (mu,
T) plane using a method recently proposed by us. We explore the region T > 0.7
Tc and mu <1.4 Tc, where Tc is the transition temperature at zero baryon
density, and find a first order transition line. Our results are quantitatively
compatible with those obtained with the imaginary chemical potential approach
and the double reweighting method, in the region where these approaches are
reliable, T > 0.9 Tc and mu < Tc. But, in addition, our method allows us to
extend the transition line to lower temperatures and higher chemical
potentials.


title: Warped Domain Wall Fermions

abstract:
  We consider Kaplan's domain wall fermions in the presence of an Anti-de
Sitter (AdS) background in the extra dimension. Just as in the flat space case,
in a completely vector-like gauge theory defined after discretizing this extra
dimension, the spectrum contains a very light charged fermion whose chiral
components are localized at the ends of the extra dimensional interval. The
component on the IR boundary of the AdS space can be given a large mass by
coupling it to a neutral fermion via the Higgs mechanism. In this theory, gauge
invariance can be restored either by taking the limit of infinite proper length
of the extra dimension or by reducing the AdS curvature radius towards zero. In
the latter case, the Kaluza-Klein modes stay heavy and the resulting classical
theory approaches a chiral gauge theory, as we verify numerically. Potential
difficulties for this approach could arise from the coupling of the
longitudinal mode of the light gauge boson, which has to be treated
non-perturbatively.


title: A comprehensive search for the \Theta^+ pentaquark on the lattice

abstract:
  We study spin 1/2 isoscalar and isovector, even and odd parity candidates for
the $\Theta^+(1540)$ pentaquark particle using large scale lattice QCD
simulations. Previous lattice works led to inconclusive results because so far
it has not been possible to unambiguously identify the known scattering
spectrum and tell whether additionally a genuine pentaquark state also exists.
Here we carry out this analysis using several possible wave functions
(operators). Linear combinations of those have a good chance of spanning both
the scattering and pentaquark states. Our operator basis is the largest in the
literature, and it also includes spatially non-trivial ones with unit orbital
angular momentum. The cross correlator we compute is 14$\times$14 with 60
non-vanishing elements. We can clearly distinguish the lowest scattering
state(s) in both parity channels up to above the expected location of the
pentaquark, but we find no trace of the latter. Based on that we conclude that
there are most probably no pentaquark bound states at our quark masses,
corresponding to $m_\pi$=400--630 MeV. However, we cannot rule out the
existence of a pentaquark state at the physical quark mass corresponding to
$m_\pi$=135 MeV or pentaquarks with a more exotic wave function.


title: A lattice study of the pentaquark states

abstract:
  We present a study of the pentaquark system in quenched lattice QCD using
diquark-diquark and kaon-nucleon local and smeared interpolating fields. We
examine the volume dependence of the spectral weights of local correlators on
lattices of size $16^3\times 32$, $24^3\times32$ and $32^3\times 64$ at
$\beta=6.0$. We find that a reliable evaluation of the volume dependence of the
spectral weights requires accurate determination of the correlators at large
time separations. Our main result from the spectral weight analysis in the
pentaquark system is that within our variational basis and statistics we can
not exclude a pentaquark resonance. However our data also do not allow a clear
identification of a pentaquark state since only the spectral weights of the
lowest state can be determined to sufficient accuracy to test for volume
dependence. In the negative parity channel the mass extracted for this state is
very close to the KN threshold whereas in the positive parity channel is about
60% above.


title: Finite volume effects for meson masses and decay constants

abstract:
  We present a detailed numerical study of finite volume effects for masses and
decay constants of the octet of pseudoscalar mesons. For this analysis we use
chiral perturbation theory and asymptotic formulae a la Luscher and propose an
extension of the latter beyond the leading exponential term. We argue that such
a formula, which is exact at the one-loop level, gives the numerically dominant
part at two loops and beyond. Finally, we discuss the possibility to determine
low energy constants from the finite volume dependence of masses and decay
constants.


title: The clash of positivities in topological density correlators

abstract:
  We discuss the apparent conflict between reflection positivity and positivity
of the topological susceptibility in two-dimensional nonlinear sigma models and
in four-dimensional gauge theories. We pay special attention to the fact that
this apparent conflict is already present on the lattice; its resolution puts
some nontrivial restrictions on the short-distance behavior of the lattice
correlator. It is found that these restrictions can be satisfied both in the
case of asymptotic freedom and the dissident scenario of a critical point at
finite coupling.


title: Finite-Size Effects in Lattice QCD with Dynamical Wilson Fermions

abstract:
  As computing resources are limited, choosing the parameters for a full
Lattice QCD simulation always amounts to a compromise between the competing
objectives of a lattice spacing as small, quarks as light, and a volume as
large as possible. Aiming to push unquenched simulations with the Wilson action
towards the computationally expensive regime of small quark masses we address
the question whether one can possibly save computing time by extrapolating
results from small lattices to the infinite volume, prior to the usual chiral
and continuum extrapolations. In the present work the systematic volume
dependence of simulated pion and nucleon masses is investigated and compared
with a long-standing analytic formula by Luescher and with results from Chiral
Perturbation Theory. We analyze data from Hybrid Monte Carlo simulations with
the standard (unimproved) two-flavor Wilson action at two different lattice
spacings of a=0.08fm and 0.13fm. The quark masses considered correspond to
approximately 85 and 50% (at the smaller a) and 36% (at the larger a) of the
strange quark mass. At each quark mass we study at least three different
lattices with L/a=10 to 24 sites in the spatial directions (L=0.85-2.08fm).


title:
Static quark anti-quark interactions in zero and finite temperature QCD.
  I. Heavy quark free energies, running coupling and quarkonium binding

abstract:
  We analyze heavy quark free energies in 2-flavor QCD at finite temperature
and the corresponding heavy quark potential at zero temperature. Static quark
anti-quark sources in color singlet, octet and color averaged channels are used
to probe thermal modifications of the medium. The temperature dependence of the
running coupling, $\alpha_{qq}(r,T)$, is analyzed at short and large distances
and is compared to zero temperature as well as quenched calculations. In parts
we also compare our results to recent findings in 3-flavor QCD. We find that
the characteristic length scale below which the running coupling shows almost
no temperature dependence is almost twice as large as the Debye screening
radius. Our analysis supports recent findings which suggest that $\chi_c$ and
$\psi\prime$ are suppressed already at the (pseudo-) critical temperature and
thus give a probe for quark gluon plasma production in heavy ion collision
experiments, while $J/\psi$ may survive the transition and will dissolve at
higher temperatures.


title: A gauge-invariant object in non-Abelian gauge theory

abstract:
  We propose a nonlocal definition of a gauge-invariant object in terms of the
Wilson loop operator in a non--Abelian gauge theory. The trajectory is a closed
curve defined by an (untraced) Wilson loop which takes its value in the center
of the color group. We show that definition shares basic features with the
gauge-dependent 't Hooft construction of Abelian monopoles in Yang-Mills
theories. The chromoelectric components of the gluon field have a hedgehog-like
behavior in the vicinity of the object. This feature is dual to the structure
of the 't Hooft-Polyakov monopoles which possesses a hedgehog in the magnetic
sector. A relation to color confinement and lattice implementation of the
proposed construction are discussed.


title: Search for the possible S=+1 Pentaquark states in Quenched Lattice QCD

abstract:
  We study spin $\frac12$ hadronic states in quenched lattice QCD to search for
a possible $S=+1$ pentaquark resonance. Simulations are carried out on
$8^3\times 24$, $10^3\times 24$, $12^3\times 24$ and $16^3\times 24$ lattices
at $\beta$=5.7 at the quenched level with the standard plaquette gauge action
and the Wilson quark action. We adopt a Dirichlet boundary condition in the
time direction for the quark to circumvent the possible contaminations due to
the (anti)periodic boundary condition for the quark field, which are peculiar
to the pentaquark. By diagonalizing the $2\times 2$ correlation matrices
constructed from two independent operators with the quantum numbers
$(I,J)=(0,\frac12)$, we successfully obtain the energies of the lowest state
and the 2nd-lowest state in this channel. The analysis of the volume dependence
of the energies and spectral weight factors indicates that a resonance state is
likely to exist slightly above the NK threshold in $(I,J^P)=(0,\frac12^-)$
channel.


title: Calorons in SU(3) lattice gauge theory

abstract:
  We examine the semiclassical content of SU(3) Yang Mills theory on the
lattice at finite temperature. Employing the cooling method, a set of classical
fields is generated from a Monte Carlo ensemble. Various operators are used to
inspect this set with respect to topological properties. We find pseudoparticle
fields, so-called caloron solutions, possessing the remarkable features of
(superpositions of) Kraan-van Baal solutions, i.e. extensions of
Harrington-Shepard calorons to generic values of the holonomy.


title: Casimir Scaling in SU(2) Lattice Gauge Theory

abstract:
  By employing the multilevel algorithm in numerical Monte Carlo simulations,
we evaluate the static potential in four dimensional SU(2) lattice gauge theory
with no dynamical fermions, for static sources in the j=1/2,1,3/2
representations. We find data supporting the Casimir scaling hypothesis. With
the same technique we show that the ratio of the logarithm of Wilson loops in
the j=2 and j=1/2 representations, as a function of the area of the loops, also
satisfies Casimir scaling.


title: Chiral Extrapolations and the Covariant Small Scale Expansion

abstract:
  We calculate the nucleon and the delta mass to fourth order in a covariant
formulation of the small scale expansion. We analyze lattice data from the MILC
collaboration and demonstrate that the available lattice data combined with our
knowledge of the physical values for the nucleon and delta masses lead to
consistent chiral extrapolation functions for both observables up to fairly
large pion masses. This holds in particular for very recent data on the delta
mass from the QCDSF collaboration. The resulting pion-nucleon sigma term is
sigma_{piN} = 48.9 MeV. This first quantitative analysis of the quark-mass
dependence of the structure of the Delta(1232) in full QCD within chiral
effective field theory suggests that (the real part of) the nucleon-delta
mass-splitting in the chiral limit, Delta_0 = 0.33 GeV, is slightly larger than
at the physical point. Further analysis of simultaneous fits to nucleon and
delta lattice data are needed for a precision determination of the properties
of the first excited state of the nucleon.


title:
<A^2> Condensate, Bianchi Identities and Chromomagnetic Fields
  Degeneracy in SU(2) YM Theory

abstract:
  We consider the non-Abelian Bianchi identities in SU(2) pure Yang-Mills
theory in D=3,4 focusing on the possibility of their violation and the
significance of the chromomagnetic fields degeneracy points. We show that the
recently proposed non-Abelian Stokes theorem allows to formulate the Bianchi
identities in terms of the physical fluxes and their relative color
orientations. Then the violation of Bianchi identities becomes a well defined
concept ultimately related to the degeneracy points. The locality and gauge
invariance of our approach allows to study the problem numerically. We present
evidences that in D=4 the suppression of the Bianchi identities violation is
likely to destroy confinement while the removal of the degeneracy points drives
the theory to the topologically non-trivial sector. However, confronting the
results obtained in three and four dimensions we argue that it is the mass
dimension two condensate <A^2_{min}> which probably explains our findings.


title: A numerical study of confinement in compact QED

abstract:
  Compact U(1) lattice gauge theory in four dimensions is studied by means of
an efficient algorithm which exploits the duality transformation properties of
the model. We focus our attention onto the confining regime, considering the
interquark potential and force, and the electric field induced by two
infinitely heavy sources. We consider both the zero and finite temperature
setting, and compare the theoretical predictions derived from the effective
string model and the dual superconductor scenario to the numerical results.


title: I=2 Pion Scattering Length from Two-Pion Wave Functions

abstract:
  We calculate the two-pion wave function in the ground state of the I=2
$S$-wave system and find the interaction range between two pions, which allows
us to examine the validity of the necessary condition for the finite-volume
method for the scattering length proposed by L\"uscher. We work in the quenched
approximation employing a renormalization group improved gauge action for
gluons and an improved Wilson action for quarks at $1/a=1.207(12) {\rm GeV}$ on
$16^3 \times 80$, $20^3 \times 80$ and $24^3 \times 80$ lattices. We conclude
that the necessary condition is satisfied within the statistical errors for the
lattice sizes $L\ge 24$ ($3.92 {\rm fm}$) when the quark mass is in the range
that corresponds to $m_\pi^2 = 0.273-0.736 {\rm GeV}^2$. We obtain the
scattering length with a smaller statistical error from the wave function than
from the two-pion time correlator.


title:
Excited Baryon Spectroscopy from Lattice QCD: Finite Size Effect and
  Hyperfine Mass Splitting

abstract:
  A study of the finite-size effect is carried out for spectra of both
ground-state and excited-state baryons in quenched lattice QCD using Wilson
fermions. Our simulations are performed at beta=6.2 with three different
spatial sizes, La~1.6, 2.2 and 3.2 fm. It is found that the physical lattice
size larger than 3 fm is required for delta states in all spin-parity
(J^{P}=1/2^{+/-}, 3/2^{+/-}) channels and also negative-parity nucleon state
(J^{P}=1/2^{-}) even in the rather heavy quark mass region. We also find a
peculiar behavior of the finite-size effect on the hyperfine mass splittings
between the nucleon and the delta in both parity channels.


title:
Entropy of spatial monopole currents in pure SU(2) QCD at finite
  temperature

abstract:
  We study properties of space-like monopole trajectories in the Maximal
Abelian gauge of quenched SU(2) QCD at the finite temperature. We concentrate
on infrared monopole clusters which are responsible for the confinement
properties of the theory. We determine numerically the effective action of the
monopoles projected onto the three-dimensional time-slice. Then we derive the
length distributions of the monopole loops and fix their entropy.


title: Measure of the path integral in lattice gauge theory

abstract:
  We show how to construct the measure of the path integral in lattice gauge
theory. This measure contains a factor beyond the standard Haar measure. Such
factor becomes relevant for the calculation of a single transition amplitude
(in contrast to the calculation of ratios of amplitudes). Single amplitudes are
required for computation of the partition function and the free energy. For
U(1) lattice gauge theory, we present a numerical simulation of the transition
amplitude comparing the path integral with the evolution in terms of the
Hamiltonian, showing good agreement.


title:
Infrared features of KS fermion and Wilson fermion in Lattice Landau
  Gauge QCD

abstract:
  The running coupling and the Kugo-Ojima parameter of unquenched lattice
Landau gauge are simulated and compared with the continuum theory. Presence of
infrared fixed point of $\alpha_0\sim 2-2.5$ irrespective of the fermion
actions (Wilson fermions and Kogut-Susskind(KS) fermions) in the continuum and
in the chiral limit is suggested. Although there exists dependence on the
polarization due to asymmetry of the lattice (time axis is longer than spacial
axes), the Kugo-Ojima parameter $c$ is consistent with 1. Presence of
$1+c_1/q^2$ correction factor in the running coupling depends on the lattice
size and the sea quark mass. In the large lattice size and small sea quark
mass, $c_1\sim 2.8$GeV is confirmed. The MILC configuration of $a=0.09$fm
suggests also presence of dimension 4 condensates with sign opposite to the
dimension 2 condensates. The gluon propagator, the ghost propagator and the
running coupling are compared with recent pQCD results including anomalous
dimension of fields up to the 4-loop level.


title: Two flavor QCD and Confinement

abstract:
  We argue that the order of the chiral transition for N_f=2 is a sensitive
probe of the QCD vacuum, in particular of the mechanism of color confinement. A
strategy is developed to investigate the order of the transition by use of
finite size scaling analysis. An in-depth numerical investigation is performed
with staggered fermions on lattices with N_t=4 and N_s=12,16,20,24,32 and quark
masses am_q ranging from 0.01335 to 0.307036. The specific heat and a number of
susceptibilities are measured and compared with the expectations of an O(4)
second order and of a first order phase transition. A second order transition
in the O(4) and O(2) universality classes are excluded. Substantial evidence
emerges for a first order transition. A detailed comparison with previous works
is performed.


title: Light quarks with twisted mass fermions

abstract:
  We investigate Wilson twisted mass fermions in the quenched approximation
using different definitions of the critical bare quark mass m_c to realize
maximal twist and, correspondingly, automatic O(a) improvement for physical
observables. A particular definition of m_c is given by extrapolating the value
of m_c obtained from the PCAC relation at non-vanishing bare twisted quark mass
mu to mu=0. Employing this improved definition of the critical mass the Wilson
twisted mass formulation provides the possibility to perform reliable
simulations down to very small quark masses with correspondingly small pion
masses of m_pi \simeq 250 MeV, while keeping the cutoff effects of O(a^2) under
control.


title:
Spin correlations and velocity-scaling in color-octet NRQCD matrix
  elements

abstract:
  We compute spin-dependent decay matrix elements for S-wave charmonium and
bottomonium in lattice nonrelativistic quantum chromodynamics (NRQCD).
Particular emphasis is placed upon the color-octet matrix elements, since the
corresponding production matrix elements are expected to appear in the dominant
contributions to the production cross sections at large transverse momenta. We
use three slightly different versions of the heavy-quark lattice Green's
functions in order to minimize the contributions that scale as powers of the
ultraviolet cutoff. The lattice matrix elements that we calculate obey the
hierarchy that is suggested by the velocity-scaling rules of NRQCD.


title: The quark mass dependence of the pion mass at infinite N

abstract:
  In planar QCD, in two space time dimensions, the meson eigenvalue equation
has a nonlocal structure interpretable as resulting from hidden degrees of
freedom. The nonlocality can be reconstructed from the functional form of the
pion mass dependence on quark mass within an expansion starting from a special
one dimensional Schroedinger problem. The one dimensional problem makes the
pion mass depend on the quark mass through a simple quadratic relation which is
shown to be compatible also with numerical data obtained in four dimensions.


title:
Reducing cutoff effects in maximally twisted lattice QCD close to the
  chiral limit

abstract:
  When analyzed in terms of the Symanzik expansion, lattice correlators of
multi-local (gauge-invariant) operators with non-trivial continuum limit
exhibit in maximally twisted lattice QCD ``infrared divergent'' cutoff effects
of the type a^{2k}/(m_\pi^2)^{h}, 2k\geq h\geq 1 (k,h integers), which tend to
become numerically large when the pion mass gets small. We prove that, if the
action is O(a) improved a` la Symanzik or, alternatively, the critical mass
counter-term is chosen in some ``optimal'' way, these lattice artifacts are
reduced to terms that are at worst of the order a^{2}(a^2/m_\pi^2)^{k-1}, k\geq
1. This implies that the continuum extrapolation of lattice results is smooth
at least down to values of the quark mass, m_q, satisfying the order of
magnitude inequality m_q >a^2\Lambda^3_{\rm QCD}.


title: Color confinement and dual superconductivity of the vacuum. IV

abstract:
  A scaling analysis is made of the order parameter describing monopole
condensation at the deconfining transition of N_f=2 QCD around the chiral
point. In accordance with scaling properties of the specific heat, studied in a
previous paper, scaling is consistent with a first order transition. The status
of dual superconductivity of the vacuum as a mechanism of color confinement is
reviewed.


title: Lattice formulation of ${\cal N}=4$ super Yang-Mills theory

abstract:
  We construct a lattice action for ${\cal N}=4$ super Yang-Mills theory in
four dimensions which is local, gauge invariant, free of spectrum doubling and
possesses a single exact supersymmetry. Our construction starts from the
observation that the fermions of the continuum theory can be mapped into the
component fields of a single real anticommuting Kahler-Dirac field. The
original supersymmetry algebra then implies the existence of a nilpotent scalar
supercharge $Q$ and a corresponding set of bosonic superpartners. Using this
field content we write down a $Q$-exact action and show that, with an
appropriate change of variables, it reduces to a well-known twist of ${\cal
N}=4$ super Yang-Mills theory due to Marcus. Using the discretization
prescription developed in an earlier paper on the ${\cal N}=2$ theory in two
dimensions we are able to translate this geometrical action to the lattice.


title:
Localization properties of lattice fermions with plaquette and improved
  gauge actions

abstract:
  We determine the location $\lambda_c$ of the mobility edge in the spectrum of
the hermitian Wilson operator in pure-gauge ensembles with plaquette, Iwasaki,
and DBW2 gauge actions. The results allow mapping a portion of the (quenched)
Aoki phase diagram. We use Green function techniques to study the localized and
extended modes. Where $\lambda_c>0$ we characterize the localized modes in
terms of an average support length and an average localization length, the
latter determined from the asymptotic decay rate of the mode density. We argue
that, since the overlap operator is commonly constructed from the Wilson
operator, its range is set by the value of $\lambda_c^{-1}$ for the Wilson
operator. It follows from our numerical results that overlap simulations
carried out with a cutoff of 1 GeV, even with improved gauge actions, could be
afflicted by unphysical degrees of freedom as light as 250 MeV.


title:
Monte Carlo study of glueball masses in the Hamiltonian limit of SU(3)
  lattice gauge theory

abstract:
  Using Standard Euclidean Monte Carlo techniques, we discuss in detail the
extraction of the glueball masses of 4-dimensional SU(3) lattice gauge theory
in the Hamiltonian limit, where the temporal lattice spacing is zero. By taking
into account the renormalization of both the anisotropy and the Euclidean
coupling, we calculate the string tension and masses of the scalar, axial
vector and tensor states using standard Wilson action on increasingly
anisotropic lattices, and make an extrapolation to the Hamiltonian limit. The
results are compared with estimates from various other Hamiltonian and
Euclidean studies. We find that more accurate determination of the glueball
masses and the mass ratios has been achieved and the results are a significant
improvement upon previous Hamiltonian estimates. The continuum predictions are
then found by extrapolation of results obtained from smallest values of spatial
lattice spacing. For the lightest scalar, tensor and axial vector states we
obtain masses of $m_{0^{++}}=1654 \pm 83$ MeV, $m_{2^{++}}=2272\pm 115$ MeV and
$m_{1^{+-}}=2940\pm 165$ MeV, respectively. These are consistent with the
estimates obtained in the previous studies in the Euclidean limit. The
consistency is a clear evidence of universality between Euclidean and
Hamiltonian formulations. From the accuracy of our estimates, we conclude that
the standard Euclidean Monte Carlo method is a reliable technique for obtaining
results in the Hamiltonian version of the theory, just as in Euclidean case.


title:
A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories
  with Sixteen Supercharges

abstract:
  We formulate supersymmetric Euclidean spacetime Ad* lattices whose classical
continuum limits are U(N) supersymmetric Yang-Mills theories with sixteen
supercharges in d=1,2,3 and 4 dimensions. This family includes the especially
interesting N=4 supersymmetry in four dimensions, as well as a Euclidean path
integral formulation of Matrix Theory on a one dimensional lattice.


title: Precision Lattice Computations in the Heavy Quark Sector

abstract:
  The phenomenology of the pseudo scalar mesons D_s and B_s and of the vector
mesons D_s* and B_s* was investigated in simulations of quenched lattice QCD.
The work is particularly focused on the continuum limit and the minimisation of
all systematic errors within the quenched approximation. The decay constants
F_Ds and F_Ds* and the difference in the masses between the D_s and the D_s*
were determined from the direct computer simulation of lattice QCD in large
physical volume (L ~ 1.5 fm). As an aside, the renormalisation group invariant
charm quark mass M_c could be obtained from the simulation results. For the
B_s- and the B_s*-meson, an interpolation in the meson mass to its physical
point was carried out for the decay constant and the mass splitting in the
continuum limit. The functional form of the interpolation to the static limit
was guided by the prediction of the Heavy Quark Effective Theory (HQET). A set
of conversion functions between HQET and QCD were derived and evaluated
numerically with input from perturbation theory.


title: Monte Carlo overrelaxation for SU(N) gauge theories

abstract:
  The standard approach to Monte Carlo simulations of SU(N) Yang-Mills theories
updates successive SU(2) subgroups of each SU(N) link. We follow up on an old
proposal of Creutz, to perform overrelaxation in the full SU(N) group instead,
and show that it is more efficient.


title: Nucleon and Delta masses in twisted mass chiral perturbation theory

abstract:
  We calculate the masses of the nucleons and deltas in twisted mass heavy
baryon chiral perturbation theory. We work to quadratic order in a power
counting scheme in which we treat the lattice spacing and the quark masses to
be of the same order. We give expressions for the mass and the mass splitting
of the nucleons and deltas both in and away from the isospin limit. We give an
argument using the chiral Lagrangian treatment that, in the strong isospin
limit, the nucleons remain degenerate and the delta multiplet breaks into two
degenerate pairs to all orders in chiral perturbation theory. We show that the
mass splitting between the degenerate pairs of the deltas first appears at
quadratic order in in the lattice spacing. We discuss the subtleties in the
effective chiral theory that arise from the inclusion of isospin breaking.


title: Flavor Twisted Boundary Conditions and the Nucleon Axial Current

abstract:
  With twisted boundary conditions on the quark fields, we study nucleon matrix
elements of the axial current utilizing twisted heavy baryon chiral
perturbation theory. One can explore the momentum transfer dependence of the
axial form factors more easily than by using ordinary lattice quantized momenta
alone. As examples, we derive expressions for the nucleon axial radius and
pseudoscalar form factor.


title:
Finite dt dependence of the Binder cumulants for 3-flavor QCD at finite
  temperature and isospin density

abstract:
  We simulate 3-flavour lattice QCD at small isospin chemical potential $\mu_I$
and finite temperature $T$. At $\mu_I=0$ there is a critical mass $m_c$ where
the finite-temperature transition changes from first order to a crossover. We
measure the $\mu_I$ dependence of the transition $\beta$ ($\beta_c$) for $m$
close to $m_c$. $\beta_c$ and hence $T_c$ decrease slowly with increasing
$\mu_I$. $\beta_c$ at finite $\mu_I$ is in good agreement $\beta_c$ at finite
$\mu$ (quark-number chemical potential). We use fourth-order Binder cumulants
to determine the nature of this transition and to search for a critical
endpoint. We measure the $dt$ dependence of these cumulants and extrapolate to
$dt=0$. ($dt$ is the `time' increment used in the hybrid molecular-dynamics
simulations.) Preliminary measurements of these Binder cumulants show little
$\mu_I$ dependence. (Simulations at imaginary $\mu$ indicate that the $\mu$
dependence of the Binder cumulants is also weak.) This contrasts to the $\mu_I$
dependence we observed at fixed $dt$.


title: CP and T violation in non-perturbative chiral gauge theories

abstract:
  We give a completely general derivation revealing the precise origin and the
quantitative effects of CP and T violations in chiral gauge theories on the
lattice.


title:
The Negativity of the Overlap-Based Topological Charge Density
  Correlator in Pure-Glue QCD and the Non-Integrable Nature of its Contact Part

abstract:
  We calculate the lattice two-point function of topological charge density in
pure-glue QCD using the discretization of the operator based on the overlap
Dirac matrix. Utilizing data at three lattice spacings it is shown that the
continuum limit of the correlator complies with the requirement of
non-positivity at non-zero distances. For our choice of the overlap operator
and the Iwasaki gauge action we find that the size of the positive core is ~2a
(with a being the lattice spacing) sufficiently close to the continuum limit.
This result confirms that the overlap-based topological charge density is a
valid local operator over realistic backgrounds contributing to the QCD path
integral, and is important for the consistency of recent results indicating the
existence of a low-dimensional global brane-like topological structure in the
QCD vacuum. We also confirm the divergent short-distance behavior of the
correlator, and the non-integrable nature of the associated contact part.


title: An estimate of the chiral condensate from unquenched lattice QCD

abstract:
  Using the parameters in the chiral Lagrangian obtained by MILC from their
unquenched lattice QCD calculations with 2+1 flavours of sea quarks, I estimate
<psi_bar psi> (2 GeV)/n_f = -(259 \pm 27 MeV)**3 in the MS_bar scheme. I
compare this value to other determinations.


title: Absence of evidence for pentaquarks on the lattice

abstract:
  We study the question of whether or not QCD predicts a pentaquark state. We
use the improved, fixed point lattice QCD action which has very little
sensitivity to the lattice spacing and also allows us to reach light quark
masses. The analysis was performed on a single volume of size $(1.8 {\rm
fm})^3\times 3.6 {\rm fm}$ with lattice spacing of $a=0.102$ fm. We use the
correlation matrix method to identify the ground and excited states in the
isospin 0, negative parity channel. In the quenched approximation where
dynamical quark effects are omitted, we do not find any evidence for a
pentaquark resonance in QCD.


title: Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum

abstract:
  As a probe of the Yang-Mills vacuum, we study numerically the eigenmode
spectrum of the covariant lattice Laplacian operator. We find that the
eigenmodes at the low and high ends of the spectrum are localized in finite
regions whose volume is insensitive to the lattice volume. We also find that
the vacuum is seen very differently by localized modes of the covariant
Laplacian in different representations of the gauge group. In the fundamental
representation, the data suggests that the localization volume is finite in
physical units set by the string tension, and localization disappears when
center vortices are removed. In the adjoint and j=3/2 representations the low
and high-lying modes are far more localized, and the localization volume
appears to scale to zero, in physical units, in the continuum limit. The
adjoint Laplacian is insensitive to vortex removal, but we find that
exponential localization is absent for adjoint eigenmodes in the Higgs phase of
a gauge-Higgs theory. Localization is also absent in the spectrum of the
Coulomb gauge Faddeev-Popov operator, as required in Coulomb gauge confinement
scenarios.


title: More on the finite size mass shift formula for stable particles

abstract:
  The next to leading order (NLO) contribution of the generalized finite size
mass shift formula for an interacting two stable particle system in a periodic
$L^{3}$ box is discriminated with maintaining its model independent structure
and validity to all orders in perturbation theory. The influence of the NLO
contribution is examined for the nucleon mass shift in the realistic
nucleon-pion system.


title: Exact lattice Ward-Takahashi identity for the N=1 Wess-Zumino model

abstract:
  We consider a lattice formulation of the four dimensional N=1 Wess-Zumino
model that uses the Ginsparg-Wilson relation. This formulation has an exact
supersymmetry on the lattice. We show that the corresponding Ward-Takahashi
identity is satisfied, both at fixed lattice spacing and in the continuum
limit. The calculation is performed in lattice perturbation theory up to order
$g^2$ in the coupling constant. We also show that this Ward-Takahashi identity
determines the finite part of the scalar and fermion renormalization wave
functions which automatically leads to restoration of supersymmetry in the
continuum limit. In particular, these wave functions coincide in this limit.


title: QCD at non-zero temperature and density from the lattice

abstract:
  The study of systems as diverse as the cores of neutron stars and heavy-ion
collision experiments requires the understanding of the phase structure of QCD
at non-zero temperature, T, and chemical potential, mu_q. We review some of the
difficulties of performing lattice simulations of QCD with non-zero mu_q, and
outline the re-weighting method used to overcome this problem. This method is
used to determine the critical endpoint of QCD in the (mu_q,T) plane. We study
the pressure and quark number susceptibility at small mu_q.


title: Divergent chiral condensate in the quenched Schwinger model

abstract:
  We calculate numerically the eigenvalue distribution of the overlap Dirac
operator in the quenched Schwinger model on a lattice. The distribution does
not fit any of the three universality classes of spontaneous chiral symmetry
breaking, and its strong volume dependence indicates that the chiral condensate
in the quenched theory is an ill-defined and divergent quantity. When we
reweight configurations with the Dirac determinant to study the theory with
N_f=1, we obtain a distribution of eigenvalues that is well-behaved and
consistent with the theory of explicit symmetry breaking due to the anomaly.


title: The role of the double pole in lattice QCD with mixed actions

abstract:
  We investigate effects resulting from the use of different discretizations
for the valence and the sea quarks in lattice QCD, considering Wilson and/or
Ginsparg-Wilson fermions. We assume that such effects appear through scaling
violations that can be studied using effective lagrangian techniques. We show
that a double pole is present in flavor-neutral Goldstone meson
propagators,even if the charged Goldstone mesons made out of valence quarks and
those made out of sea quarks have equal masses. We then consider some
observables known to be anomalously sensitive to the presence of a double pole.
For these observables, we find that the double-pole enhanced scaling violations
may turn out to be rather small in practice.


title: Asymptotics of the Infrared

abstract:
  We follow recent formulations of dimensionally reduced loop operators for
quantum field theories and exact representations of probabilistic lattice
dynamics to identify a new scheme for the evaluation of partition function
zeroes, allowing for the explicit analysis of quantum critical phenomena. This
new approach gives partition function zeroes from a factored quantum loop
operator basis and, as we show, constitutes an effective mapping of the
renormalization group $\beta$-function onto the noncommuting local operator
basis of a countably finite Hilbert space. The Vafa-Witten theorem for
CP-violation and related complex action problems of Euclidean Field theories
are discussed, following recent treatments, and are shown to be natural
consequences of the analyticity of the limiting distribution of these zeroes,
and properties of vacuum regimes governed by a dominant quantum fluctuation in
the vicinity of a renormalization group equation fixed point in the infrared.


title: Spin 3/2 Pentaquark Resonance Signature in Lattice QCD

abstract:
  The possible discovery of the Theta+ pentaquark has motivated a number of
studies of its nature using lattice QCD. While all the analyses thus far have
focussed on spin-1/2 states, here we report the results of the first
exploratory study in quenched lattice QCD of pentaquarks with spin 3/2. For the
spin-3/2 interpolating field we use a product of the standard N and K*
operators. We do not find any evidence for the standard lattice resonance
signature of attraction (i.e., binding at quark masses near the physical
regime) in the J^P = 3/2- channel. Some evidence of binding is inferred in the
isoscalar 3/2+ channel at several quark masses, in accord with the standard
lattice resonance signature. This suggests that this is a good candidate for
the further study of pentaquarks on the lattice.


title: Compact Gauge Fields for Supersymmetric Lattices

abstract:
  We show that a large class of Euclidean extended supersymmetric lattice gauge
theories constructed in [hep-lat/0302017 - hep-lat/0503039] can be regarded as
compact formulations by using the polar decomposition of the complex link
fields. In particular, the gauge part of the supersymmetric lattice action is
the standard Wilson action. This formulation facilitates the construction of
gauge invariant operators.


title: Artefacts and <A2> power corrections : revisiting the MOM Z_psi and Z_V

abstract:
  We extract the power corrections due to the A^2 condensate in the overlap
quark propagator (vector part of the inverse propagator Z_psi). The results are
consistent with the previous gluon analysis. The role of artefacts is
extensively discussed.


title:
Low-lying mode contribution to the quenched meson correlators in the
  epsilon-regime

abstract:
  We present a quenched calculation of meson correlators with the overlap
fermion at very small masses 2.6--13 MeV. In this region the pion Compton
wavelength is larger than our lattice size L\simeq 1.23fm and the system is in
the so-called epsilon-regime of chiral perturbation theory. We found that the
scalar and pseudo-scalar correlators are precisely approximated by a few
hundred low-lying fermion eigenmodes in this regime, whereas axial-vector
correlator receives significant contributions from higher eigenmodes. We also
measure the disconnected pseudo-scalar correlator, which is well saturated with
the low-lying modes. Matching these lattice data with the one-loop expressions
for the correlators in quenched chiral perturbation theory, we evaluate the
decay constant F_pi and the chiral condensate Sigma as well as the parameters
m_0 and alpha, which describe the artifacts of the quenched approximation.


title:
Two Particle States and the $S$-matrix Elements in Multi-channel
  Scattering

abstract:
  Using a quantum mechanical model, the exact energy eigenstates for
two-particle two-channel scattering are studied in a cubic box with periodic
boundary conditions in all three directions. A relation between the exact
energy eigenvalue in the box and the two-channel $S$-matrix elements in the
continuum is obtained. This result can be viewed as a generalization of the
well-known L\"uscher's formula which establishes a similar relation in elastic
scattering.


title:
Spectral Analysis of Excited Nucleons in Lattice QCD with Maximum
  Entropy Method

abstract:
  We study the mass spectra of excited baryons with the use of the lattice QCD
simulations. We focus our attention on the problem of the level ordering
between the positive-parity excited state N'(1440) (the Roper resonance) and
the negative-parity excited state N^*(1535). Nearly perfect parity projection
is accomplished by combining the quark propagators with periodic and
anti-periodic boundary conditions in the temporal direction. Then we extract
the spectral functions from the lattice data by utilizing the maximum entropy
method. We observe that the masses of the N' and N^* states are close for wide
range of the quark masses (M_pi=0.61-1.22 GeV), which is in contrast to the
phenomenological prediction of the quark models. The role of the Wilson
doublers in the baryonic spectral functions is also studied.


title:
Another approach to local cohomology problem in abelian lattice gauge
  theories

abstract:
  A new technique is proposed to classify a topological field in abelian
lattice gauge theories. We perform the classification by regarding the
topological field as a local composite field of the gauge field tensor instead
of the vector potential associated to an admissible gauge field. Our method
reproduces the result obtained by the ordinary method in the infinite
four-dimensional lattice and can be extended to arbitrary higher dimensions. It
also works in the direct cohomological analysis on a finite lattice.


title: Chiral and Continuum Extrapolation of Partially-Quenched Lattice Results

abstract:
  The vector meson mass is extracted from a large sample of partially quenched,
two-flavor lattice QCD simulations. For the first time, discretisation,
finite-volume and partial quenching artefacts are treated in a unified
framework which is consistent with the low-energy behaviour of QCD. This
analysis incorporates the leading infrared behaviour dictated by chiral
effective field theory. As the two-pion decay channel cannot be described by a
low-energy expansion alone, a highly-constrained model for the decay channel of
the rho-meson is introduced. The latter is essential for extrapolating lattice
results from the quark-mass regime where the rho is observed to be a physical
bound state.


title: Masslessness of ghosts in equivariantly gauge-fixed Yang--Mills theories

abstract:
  We show that the one-loop ghost self-energy in an equivariantly gauge-fixed
Yang--Mills theory vanishes at zero momentum. A ghost mass is forbidden by
equivariant BRST symmetry, and our calculation confirms this explicitly. The
four-ghost self interaction which appears in the equivariantly gauge-fixed
Yang--Mills theory is needed in order to obtain this result.


title: Lattice simulations of QCD with $\mu_B\neq0$ versus phase quenched QCD

abstract:
  Previously published lattice results for QCD at $\mu_B\neq0$ are compared to
analytic predictions for phase quenched QCD. We observe that the strength of
the sign problem in QCD is linked directly to the position of the phase
transition line for pion condensation in phase quenched QCD and that the number
of terms needed in the Taylor expansion approach depends on the strength of the
sign problem. Together this emphasizes the physical importance of the sign
problem and helps to clarify the range over which the Taylor expansion approach
is practically applicable. Finally, we observe that the positions of the
endpoint of the first order chiral phase transition in the QCD phase diagram
found in two successive computations by Fodor and Katz are both close to the
position of the phase transition line for pion condensation in phase quenched
QCD.


title:
Non-perturbative renormalization of left-left four-fermion operators in
  quenched lattice QCD

abstract:
  We define a family of Schroedinger Functional renormalization schemes for the
four-quark multiplicatively renormalizable operators of the $\Delta F = 1$ and
$\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization
with quenched Wilson quarks, we compute non-perturbatively the renormalization
group running of these operators in the continuum limit in a large range of
renormalization scales. Continuum limit extrapolations are well controlled
thanks to the implementation of two fermionic actions (Wilson and Clover). The
ratio of the renormalization group invariant operator to its renormalized
counterpart at a low energy scale, as well as the renormalization constant at
this scale, is obtained for all schemes.


title:
A perturbative study of two four-quark operators in finite volume
  renormalization schemes

abstract:
  Starting from the QCD Schroedinger functional (SF), we define a family of
renormalization schemes for two four-quark operators, which are, in the chiral
limit, protected against mixing with other operators. With the appropriate
flavour assignments these operators can be interpreted as part of either the
$\Delta F=1$ or $\Delta F=2$ effective weak Hamiltonians. In view of lattice
QCD with Wilson-type quarks, we focus on the parity odd components of the
operators, since these are multiplicatively renormalized both on the lattice
and in continuum schemes. We consider 9 different SF schemes and relate them to
commonly used continuum schemes at one-loop order of perturbation theory. In
this way the two-loop anomalous dimensions in the SF schemes can be inferred.
As a by-product of our calculation we also obtain the one-loop cutoff effects
in the step-scaling functions of the respective renormalization constants, for
both O(a) improved and unimproved Wilson quarks. Our results will be needed in
a separate study of the non-perturbative scale evolution of these operators.


title: Perturbation theory for O(3) topological charge correlators

abstract:
  To check the consistency of positivity requirements for the two-point
correlation function of the topological charge density, which were identified
in a previous paper, we are computing perturbatively this two-point correlation
function in the two-dimensional O(3) model. We find that at the one-loop level
these requirements are fulfilled.


title: Parallel Programming with Matrix Distributed Processing

abstract:
  Matrix Distributed Processing (MDP) is a C++ library for fast development of
efficient parallel algorithms. It constitues the core of FermiQCD. MDP enables
programmers to focus on algorithms, while parallelization is dealt with
automatically and transparently. Here we present a brief overview of MDP and
examples of applications in Computer Science (Cellular Automata), Engineering
(PDE Solver) and Physics (Ising Model).


title:
Quenched Charmed Meson Spectra using Tadpole Improved Quark Action on
  Anisotropic Lattices

abstract:
  Charmed meson charmonium spectra are studied with improved quark actions on
anisotropic lattices. We measured the pseudo-scalar and vector meson dispersion
relations for 4 lowest lattice momentum modes with quark mass values ranging
from the strange quark to charm quark with 3 different values of gauge coupling
$\beta$ and 4 different values of bare speed of light $\nu$. With the bare
speed of light parameter $\nu$ tuned in a mass-dependent way, we study the mass
spectra of $D$, $D_s$, $\eta_c$,
  $D^{\ast}$, $D_s^{\ast}$ and $J/\psi$ mesons.
  The results extrapolated to the continuum limit are compared with the
experiment and qualitative agreement is found.


title: Color Dynamics in External Fields

abstract:
  We investigate the vacuum dynamics of U(1), SU(2), and SU(3) lattice gauge
theories in presence of external (chromo)magnetic fields, both in (3+1) and
(2+1) dimensions. We find that the critical coupling for the phase transition
in compact U(1) gauge theory is independent of the strength of an external
magnetic field. On the other hand we find that, both in (3+1) and (2+1)
dimensions, the deconfinement temperature for SU(2) and SU(3) gauge systems in
a constant abelian chromomagnetic field decreases when the strength of the
applied field increases. We conclude that the dependence of the deconfinement
temperature on the strength of an external constant chromomagnetic field is a
peculiar feature of non abelian gauge theories and could be useful to get
insight into color confinement.


title:
Scaling and Goldstone effects in a QCD with two flavours of adjoint
  quarks

abstract:
  We study QCD with two Dirac fermions in the adjoint representation at finite
temperature by Monte Carlo simulations.In such a theory the deconfinement and
chiral phase transitions occur at different temperatures. We locate the second
order chiral transition point at beta_c=5.624(2) and show that the scaling
behaviour of the chiral condensate in the vicinity of beta_c is in full
agreeement with that of the 3d O(2) universality class, and to a smaller extent
comparable to the 3d O(6) class. From the previously determined first order
deconfinement transition point beta_d=5.236(3) and the two-loop beta function
we find the ratio T_c/T_d = 7.8(2). In the region between the two phase
transitions we explicitly confirm the quark mass dependence of the chiral
condensate which is expected due to the existence of Goldstone modes like in 3d
O(N) spin models. At the deconfinement transition the condensate shows a gap,
and below beta_d, it is nearly mass-independent for fixed beta.


title: Gluon and Ghost Propagators in Landau Gauge on the Lattice

abstract:
  We study the ultraviolet behaviour of the ghost and gluon propagators in
quenched QCD using lattice simulations. Extrapolation of the lattice data
towards the continuum allows to use perturbation theory to extract
$\Lambda_{\text{QCD}}$ - the fundamental parameter of the pure gauge theory.
The values obtained from the ghost and gluon propagators are coherent. The
result for pure gauge SU(3) at three loops is $\Lambda_{\ms}\approx
320\text{MeV}$. However this value does depend strongly upon the order of
perturbation theory and upon the renormalisation description of the continuum
propagators. Moreover, this value has been obtained without taking into account
possible power corrections to the short-distance behaviour of correlation
functions.


title:
Pion mass dependence of the nucleon mass in the chiral quark soliton
  model

abstract:
  The dependence of the nucleon mass on the mass of the pion is studied in the
framework of the chiral quark-soliton model. A remarkable agreement is observed
with lattice data from recent full dynamical simulations. The possibility and
limitations to use the model results as a guideline for the chiral
extrapolation of lattice data are discussed.


title: Quantum chaos in QCD and hadrons

abstract:
  This article is the written version of a talk delivered at the Workshop on
Nonlinear Dynamics and Fundamental Interactions in Tashkent and starts with an
introduction into quantum chaos and its relationship to classical chaos. The
Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within
random-matrix theory. In accordance to the title, the presentation is twofold
and begins with research results on quantum chromodynamics and the quark-gluon
plasma. We conclude with recent research work on the spectroscopy of baryons.
Within the framework of a relativistic constituent quark model we investigate
the excitation spectra of the nucleon and the delta with regard to a possible
chaotic behavior for the cases when a hyperfine interaction of either
Goldstone-boson-exchange or one-gluon-exchange type is added to the confinement
interaction. Agreement with predictions from the experimental hadron spectrum
is established.


title: Observation of String Breaking in QCD

abstract:
  We numerically investigate the transition of the static quark-antiquark
string into a static-light meson-antimeson system. Improving noise reduction
techniques, we are able to resolve the signature of string breaking dynamics
for n_f=2 lattice QCD at zero temperature. This result can be related to
properties of quarkonium systems. We also study short-distance interactions
between two static-light mesons.


title: $B_s$-$\bar{B_s}$ mixing from lattice QCD

abstract:
  We study the $B^0_s-\bar{B^0_s}$ mixing amplitude in Standard Model by
computing the relevant hadronic matrix element in the static limit of lattice
HQET with the Neuberger light quark action. In the quenched approximation, and
after matching to the $\bar{\rm MS}$ scheme in QCD, we obtain
$\hat{B}^{\bar{\rm MS},{\rm NLO}}_{B_s}(m_b)=0.940(16)(22)$.


title: Quarks with Twisted Boundary Conditions in the Epsilon Regime

abstract:
  We study the effects of twisted boundary conditions on the quark fields in
the epsilon regime of chiral perturbation theory. We consider the
$SU(2)_L\times SU(2)_R$ chiral theory with non-degenerate quarks and the
$SU(3)_L\times SU(3)_R$ chiral theory with massless up and down quarks and
massive strange quarks. The partition function and condensate are derived for
each theory. Because flavor-neutral Goldstone bosons are unaffected by twisted
boundary conditions chiral symmetry is still restored in finite volumes. The
dependence of the condensate on the twisting parameters can be used to extract
the pion decay constant from simulations in the epsilon regime. The relative
contribution to the partition function from sectors of different topological
charge is numerically insensitive to twisted boundary conditions.


title:
Renormalisation of one-link quark operators for overlap fermions with
  L\"uscher-Weisz gauge action

abstract:
  We compute lattice renormalisation constants of one-link quark operators
({\it i.e.} operators with one covariant derivative) for overlap fermions and
L\"uscher-Weisz gauge action in one-loop perturbation theory. Among others,
such operators enter the calculation of moments of polarised and unpolarised
hadron structure functions. Results are given for \beta=8.45, \beta=8.0 and
mass parameter \rho=1.4, which are commonly used in numerical simulations. We
apply mean field (tadpole) improvement to our results.


title: Evidence for fine tuning of fermionic modes in lattice gluodynamics

abstract:
  We consider properties of zero and near-zero fermionic modes in lattice
gluodynamics. The modes are known to be sensitive to the topology of the
underlying gluonic fields in the quantum vacuum state of the gluodynamics. We
find evidence that these modes are fine tuned, that is exhibit sensitivity to
both physical (one can say, hadronic) scale and to the ultraviolet cutoff.
Namely, the density of the states is in physical units while the localization
volume of the modes tends to zero in physical units with the lattice spacing
tending to zero. We discuss briefly possible theoretical implications and also
include some general, review-type remarks.


title: Effect of low-lying fermion modes in the $\epsilon$-regime of QCD

abstract:
  We investigate the effects of low-lying fermion eigenmodes on the QCD
partition function in the $\epsilon$-regime. The fermion determinant is
approximated by a truncated product of low-lying eigenvalues of the
overlap-Dirac operator. With two flavors of dynamical quarks, we observe that
the lattice results for the lowest eigenvalue distribution, eigenvalue sum
rules and partition function reproduce the analytic predictions made by
Leutwyler and Smilga, which strongly depend on the topological charge of the
background gauge configuration. The value of chiral condensate extracted from
these measurements are consistent with each other. For one dynamical quark
flavor, on the other hand, we find an apparent disagreement among different
determinations of the chiral condensate, which may suggest the failure of the
$\epsilon$-expansion in the absence of massless Nambu-Goldstone boson.


title:
Exotic Particles and $w_\infty$-Algebras in Two- and High-Dimensional
  Spaces

abstract:
  We construct a set of noncommuting translation operators in two and
high-dimensional lattices. The algebras they close are $w_{\infty}$-algebras.
The construction is based on the introduction of noncommmuting elementary link
operators which link two neighborhood sites in the lattice. This kind of
operators preserve the braiding nature of exotic particles living basically in
two-dimensional space.


title:
Model independent approach to studies of the confining dual Abrikosov
  vortex in SU(2) lattice gauge theory

abstract:
  We address the problem of determining the type I, type II or borderline dual
superconductor behavior in maximal Abelian gauge SU(2) through the study of the
dual Abrikosov vortex. We find that significant electric currents in the
simulation data call into question the use of the dual Ginzburg Landau Higgs
model in interpreting the data. Further, two definitions of the penetration
depth parameter take two different values. The splitting of this parameter into
two is intricately connected to the existence of electric currents. It is
important in our approach that we employ definitions of flux and electric and
magnetic currents that respect Maxwell equations exactly for lattice averages
independent of lattice spacings. Applied to specific Wilson loop sizes, our
conclusions differ from those that use the dual GLH model.


title:
Testing and tuning symplectic integrators for Hybrid Monte Carlo
  algorithm in lattice QCD

abstract:
  We examine a new 2nd order integrator recently found by Omelyan et al. The
integration error of the new integrator measured in the root mean square of the
energy difference, $\bra\Delta H^2\ket^{1/2}$, is about 10 times smaller than
that of the standard 2nd order leapfrog (2LF) integrator. As a result, the step
size of the new integrator can be made about three times larger. Taking into
account a factor 2 increase in cost, the new integrator is about 50% more
efficient than the 2LF integrator. Integrating over positions first, then
momenta, is slightly more advantageous than the reverse. Further parameter
tuning is possible. We find that the optimal parameter for the new integrator
is slightly different from the value obtained by Omelyan et al., and depends on
the simulation parameters. This integrator could also be advantageous for the
Trotter-Suzuki decomposition in Quantum Monte Carlo.


title:
Phase structure of four flavor QCD in the T \mu plane from a new method
  for simulations of lattice gauge theories at non zero baryon density

abstract:
  We review a method for numerical simulations of lattice gauge theories at
non-zero baryonic chemical potential we recently proposed. We first report on a
test of the method using a solvable model and then present results for the
phase structure of four flavour QCD. For the first time the region of chemical
potential up to 1.4 T_C is explored, finding a first order transition line.


title: Neutron electric dipole moment from lattice QCD

abstract:
  We carry out a feasibility study for the lattice QCD calculation of the
neutron electric dipole moment (NEDM) in the presence of the $\theta$ term. We
develop the strategy to obtain the nucleon EDM from the CP-odd electromagnetic
form factor $F_3$ at small $\theta$, in which NEDM is given by $\lim_{q^2\to
0}\theta F_3(q^2)/(2m_N)$ where $q$ is the momentum transfer and $m_N$ is the
nucleon mass. We first derive a formula which relates $F_3$, a matrix element
of the electromagnetic current between nucleon states, with vacuum expectation
values of nucleons and/or the current. In the expansion of $\theta$, the
parity-odd part of the nucleon-current-nucleon three-point function contains
contributions not only from the parity-odd form factors but also from the
parity-even form factors multiplied by the parity-odd part of the nucleon
two-point function, and therefore the latter contribution must be subtracted to
extract $F_3$. We then perform an explicit lattice calculation employing the
domain-wall quark action with the RG improved gauge action in quenched QCD at
$a^{-1}\simeq 2$ GeV on a $16^3\times 32\times 16$ lattice. At the quark mass
$m_f a =0.03$, corresponding to $m_\pi/m_\rho \simeq 0.63$, we accumulate 730
configurations, which allow us to extract the parity-odd part in both two- and
three-point functions. Employing two different Dirac $\gamma$ matrix
projections, we show that a consistent value for $F_3$ cannot be obtained
without the subtraction described above. We obtain $F_3(q^2\simeq 0.58
\textrm{GeV}^2)/(2m_N) =$ $-$0.024(5) $e\cdot$fm for the neutron and
$F_3(q^2\simeq 0.58 \textrm{GeV}^2)/(2m_N) =$ 0.021(6) $e\cdot$fm for the
proton.


title: Practical all-to-all propagators for lattice QCD

abstract:
  A new method for computing all elements of the lattice quark propagator is
proposed. The method combines the spectral decomposition of the propagator,
computing the lowest eigenmodes exactly, with noisy estimators which are
'diluted', i.e. taken to have support only on a subset of time, space, spin or
colour. We find that the errors are dramatically reduced compared to
traditional noisy estimator techniques.


title: Nucleon structure functions with domain wall fermions

abstract:
  We present a quenched lattice QCD calculation of the first few moments of the
polarized and un-polarized structure functions of the nucleon. Our calculations
are done using domain wall fermions and the DBW2 gauge action with inverse
lattice spacing ~1.3GeV, physical volume approximatelly (2.4 fm)^3, and light
quark masses down to about 1/4 the strange quark mass. Values of the individual
moments are found to be significantly larger than experiment, as in past
lattice calculations, but interestingly the chiral symmetry of domain wall
fermions allows for a precise determination of the ratio of the flavor
non-singlet momentum fraction to the helicity distribution, which is in very
good agreement with experiment. We discuss the implications of this result.
Next, we show that the chiral symmetry of domain wall fermions is useful in
eliminating mixing of power divergent lower dimensional operators with twist-3
operators. Finally, we find the isovector tensor charge at renormalization
scale 2 GeV in the MS bar scheme to be 1.192(30), where the error is the
statistical error only.


title:
Casimir scaling of domain wall tensions in the deconfined phase of D=3+1
  SU(N) gauge theories

abstract:
  We perform lattice calculations of the spatial 't Hooft k-string tensions in
the deconfined phase of SU(N) gauge theories for N=2,3,4,6. These equal (up to
a factor of T) the surface tensions of the domain walls between the
corresponding (Euclidean) deconfined phases. For T much larger than Tc our
results match on to the known perturbative result, which exhibits Casimir
Scaling, being proportional to k(N-k). At lower T the coupling becomes stronger
and, not surprisingly, our calculations show large deviations from the
perturbative T-dependence. Despite this we find that the behaviour proportional
to k(N-k) persists very accurately down to temperatures very close to Tc. Thus
the Casimir Scaling of the 't Hooft tension appears to be a `universal' feature
that is more general than its appearance in the low order high-T perturbative
calculation. We observe the `wetting' of these k-walls at T around Tc and the
(almost inevitable) `perfect wetting' of the k=N/2 domain wall. Our
calculations show that as T tends to Tc the magnitude of the spatial `t Hooft
string tension decreases rapidly. This suggests the existence of a (would-be)
't Hooft string condensation transition at some temperature which is close to
but below Tc. We speculate on the `dual' relationship between this and the
(would-be) confining string condensation at the Hagedorn temperature that is
close to but above Tc.


title:
Non-perturbative renormalization of the axial current with dynamical
  Wilson fermions

abstract:
  We present a new normalization condition for the axial current, derived from
the PCAC relation with non-vanishing quark mass. This condition is expected to
reduce mass effects in the chiral extrapolation of the results for the
normalization factor Z_A. The application to the two-flavor theory with
improved Wilson fermions shows that this expectation is indeed fulfilled. Using
the Schroedinger functional setup we calculate Z_A(g_0^2) as well as the vector
current normalization factor Z_V(g_0^2) for beta = 6/g_0^2 >= 5.2.


title: The \phi_3^4 lattice field theory viewed from the high-temperature side

abstract:
  We analyze high-temperature series expansions of the two-point and four-point
correlation-functions in the three-dimensional euclidean lattice scalar field
theory with quartic self-coupling, which have been recently extended through
twenty-fifth order for the simple-cubic and body-centered-cubic lattices. We
conclude that the length of the present series is sufficient for a fairly
accurate description of the critical behavior of the model and confirm the
validity of universality, scaling and hyperscaling. In the case of the
body-centered-cubic lattice, we determine the value of the quartic
self-coupling for which the leading corrections to scaling approximately vanish
and correspondingly the universal critical parameters can be determined with
high accuracy. In particular, for the susceptibility and the correlation-length
exponents we find \gamma=1.2373(2) and \nu=0.6301(2). For the four-point
renormalized coupling we find g=23.56(3). In the case of the simple-cubic
lattice our results are consistent with earlier estimates.


title: Investigations in 1+1 dimensional lattice $\phi^4$ theory

abstract:
  In this work we perform a detailed numerical analysis of (1+1) dimensional
lattice $\phi^4$ theory. We explore the phase diagram of the theory with two
different parameterizations. We find that symmetry breaking occurs only with a
negative mass-squared term in the Hamiltonian. The renormalized mass $m_R$ and
the field renormalization constant $Z$ are calculated from both coordinate
space and momentum space propagators in the broken symmetry phase. The critical
coupling for the phase transition and the critical exponents associated with
$m_R$, $Z$ and the order parameter are extracted using a finite size scaling
analysis of the data for several volumes. The scaling behavior of $Z$ has the
interesting consequence that $<\phi_R>$ does not scale in 1+1 dimensions. We
also calculate the renormalized coupling constant $ \lambda_R$ in the broken
symmetry phase. The ratio $ \lambda_R/m_R^2 $ does not scale and appears to
reach a value independent of the bare parameters in the critical region in the
infinite volume limit.


title: Topological charge in 1+1 dimensional lattice $\phi^4$ theory

abstract:
  We investigate the topological charge in 1+1 dimensional $\phi^4$ theory on a
lattice with Anti Periodic Boundary Condition (APBC) in the spatial direction.
We propose a simple order parameter for the lattice theory with APBC and we
demonstrate its effectiveness. Our study suggests that kink condensation is a
possible mechanism for the order-disorder phase transition in the 1+1
dimensional $\phi^4$ theory. With renormalizations performed on the lattice
with Periodic Boundary Condition (PBC), the topological charge in the
renormalized theory is given as the ratio of the order parameters in the
lattices with APBC and PBC. We present a comparison of topological charges in
the bare and the renormalized theory and demonstrate invariance of the charge
of the renormalized theory in the broken symmetry phase.


title:
Masses and Decay Constants of Pseudoscalar Mesons to Two Loops in
  Two-Flavor Partially Quenched Chiral Perturbation Theory

abstract:
  This paper presents a first study of the masses and decay constants of the
charged, or flavor-off-diagonal, pseudoscalar mesons to two loops for two
flavors of sea-quarks, in Partially Quenched Chiral Perturbation Theory
(PQ$\chi$PT). Explicit analytical expressions up to ${\cal O}(p^6)$ in the
momentum expansion are given. The calculations have been performed within the
supersymmetric formulation of PQ$\chi$PT. A numerical analysis is done to
indicate the size of the corrections.


title: Precision Lattice Calculation of SU(2) 't Hooft loops

abstract:
  The [dual] string tension of a spatial 't Hooft loop in the deconfined phase
of Yang-Mills theory can be formulated as the tension of an interface
separating different Z_N deconfined vacua. We review the 1-loop perturbative
calculation of this interface tension in the continuum and extend it to the
lattice. The lattice corrections are large. Taking these corrections into
account, we compare Monte Carlo measurements of the dual string tension with
perturbation theory, for SU(2). Agreement is observed at the 2% level, down to
temperatures O(10) T_c.


title: Updating algorithms with multi-step stochastic correction

abstract:
  Nested multi-step stochastic correction offers a possibility to improve
updating algorithms for numerical simulations of lattice gauge theories with
fermions. The corresponding generalisations of the two-step multi-boson (TSMB)
algorithm as well as some applications with hybrid Monte Carlo (HMC) algorithms
are considered.


title: Towards the infrared limit in SU(3) Landau gauge lattice gluodynamics

abstract:
  We study the behavior of the gluon and ghost dressing functions in SU(3)
Landau gauge at low momenta available on lattice sizes 12^4-32^4 at
$\beta$=5.8, 6.0 and 6.2. We demonstrate the ghost dressing function to be
systematically dependent on the choice of Gribov copies, while the influence on
the gluon dressing function is not resolvable. The running coupling given in
terms of these functions is found to be decreasing for momenta q<0.6 GeV. We
study also effects of the finite volume and of the lattice discretization.


title: On lattice actions for static quarks

abstract:
  We introduce new discretizations of the action for static quarks. They
achieve an exponential improvement (compared to the Eichten-Hill
regularization) on the signal to noise ratio in static-light correlation
functions. This is explicitly checked in a quenched simulation and it is
understood quantitatively in terms of the self energy of a static quark and the
lattice heavy quark potential at zero distance. We perform a set of scaling
tests in the Schroedinger functional and find scaling violations in the O(a)
improved theory to be rather small -- for one observable significantly smaller
than with the Eichten-Hill regularization. In addition we compute the
improvement coefficients of the static light axial current up to O(g_0^4)
corrections and the corresponding renormalization constants non-perturbatively.
The regularization dependent part of the renormalization of the b-quark mass in
static approximation is also determined.


title:
Matrix product representation of gauge invariant states in a Z_2 lattice
  gauge theory

abstract:
  The Gauss law needs to be imposed on quantum states to guarantee gauge
invariance when one studies gauge theory in hamiltonian formalism. In this
work, we propose an efficient variational method based on the matrix product
ansatz for a Z_2 lattice gauge theory on a spatial ladder chain. Gauge
invariant low-lying states are identified by evaluating expectation values of
the Gauss law operator after numerical diagonalization of the gauge
hamiltonian.


title: Cutoff Effects in O(N) Nonlinear Sigma Models

abstract:
  In the nonlinear O(N) sigma model at N=3 unexpected cutoff effects have been
found before with standard discretizations and lattice spacings. Here the
situation is analyzed further employing additional data for the step scaling
function of the finite volume massgap at N=3,4,8 and a large N-study of the
leading as well as next-to-leading terms in 1/N. The latter exact results are
demonstrated to follow Symanzik's form of the asymptotic cutoff dependence. At
the same time, when fuzzed with artificial statistical errors and then fitted
like the Monte Carlo results, a picture similar to N=3 emerges. We hence cannot
conclude a truly anomalous cutoff dependence but only relatively large cutoff
effects, where the logarithmic component is important. Their size shrinks at
larger N, but the structure remains similar. The large N results are
particularly interesting as we here have exact nonperturbative control over an
asymptotically free model both in the continuum limit and on the lattice.


title:
HMC algorithm with multiple time scale integration and mass
  preconditioning

abstract:
  We present a variant of the HMC algorithm with mass preconditioning
(Hasenbusch acceleration) and multiple time scale integration. We have tested
this variant for standard Wilson fermions at beta=5.6 and at pion masses
ranging from 380 MeV to 680 MeV. We show that in this situation its performance
is comparable to the recently proposed HMC variant with domain decomposition as
preconditioner. We give an update of the ``Berlin Wall'' figure, comparing the
performance of our variant of the HMC algorithm to other published performance
data. Advantages of the HMC algorithm with mass preconditioning and multiple
time scale integration are that it is straightforward to implement and can be
used in combination with a wide variety of lattice Dirac operators.


title: Lattice QCD at Finite Temperature

abstract:
  I review recent progress in lattice QCD at finite temperature. Results on the
transition temperature will be summarized. Recent progress in understanding
in-medium modifications of interquark forces and quarkonia spectral functions
at finite temperatures is discussed.


title: I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD

abstract:
  We compute the I=2 pi-pi scattering length at pion masses of m_pi ~ 294, 348
and 484 MeV in fully-dynamical lattice QCD using Luscher's finite-volume
method. The calculation is performed with domain-wall valence-quark propagators
on asqtad-improved MILC configurations with staggered sea quarks at a single
lattice spacing, b ~ 0.125 fm. Chiral perturbation theory is used to perform
the extrapolation of the scattering length from lattice quark masses down to
the physical value, and we find m_pi a_2 = -0.0426 +- 0.0006 +- 0.0003 +-
0.0018, in good agreement with experiment. The I=2 pi-pi scattering phase shift
is calculated to be delta = -43 +- 10 +- 5 degrees at |p| ~ 544 MeV for m_pi ~
484 MeV.


title:
Perturbative Study of the Supersymmetric Lattice Theory from Matrix
  Model

abstract:
  We study the lattice model for the supersymmetric Yang-Mills theory in two
dimensions proposed by Cohen, Kaplan, Katz, and Unsal. We re-examine the formal
proof for the absence of susy breaking counter terms as well as the stability
of the vacuum by an explicit perturbative calculation for the case of U(2)
gauge group. Introducing fermion masses and treating the bosonic zero momentum
mode nonperturbatively, we avoid the infra-red divergences in the perturbative
calculation. As a result, we find that there appear mass counter terms for
finite volume which vanish in the infinite volume limit so that the theory
needs no fine-tuning. We also find that the supersymmetry plays an important
role in stabilizing the lattice space-time by the deconstruction.