title: On the perfect lattice actions of abelian-projected SU(2) QCD

abstract:
  We study the perfect lattice actions of abelian-projected SU(2) gluodynamics.
Using the BKT and duality transformations on the lattice, an effective string
model is derived from the direction-dependent quadratic monopole action,
obtained numerically from SU(2) gluodynamics in maximally abelian gauge. The
string tension and the restoration of continuum rotational invariance are
investigated using strong coupling expansion of lattice string model
analytically. We also found that the block spin transformation can be performed
analytically for the quadratic monopole action.


title:
IR-Divergence and Anomalous Temperature Dependence of the Condensate in
  the Quenched Schwinger Model

abstract:
  The Schwinger model is used to study the artifacts of quenching in a
controlled way. The model is solved on a finite-temperature cylinder of
circumference $\beta=1/T$ with bag-inspired local boundary conditions at the
two ends $x^1=0$ and $x^1=L$ which break the $\gamma_5$-invariance and thus
play the role of a small quark mass. The quenched chiral condensate is found to
diverge exponentially as $L\to\infty$, and to diverge (rather than melt as for
$N_{\rm f}\geq1$) if the high-temperature limit $\beta\to0$ is taken at finite
box-length $L$. We comment on the generalization of our results to the massive
quenched theory, arguing that the condensate is finite as $L\to\infty$ and
proportional to $1/m$ up to logarithms.


title:
Perturbative renormalization factors of three- and four-quark operators
  for domain-wall QCD

abstract:
  Renormalization factors for three- and four-quark operators, which appear in
the low energy effective Lagrangian of the proton decay and the weak
interactions, are perturbatively calculated in domain-wall QCD. We find that
the operators are multiplicatively renormalizable up to one-loop level without
mixing with any other operators that have different chiral structures. As an
application, we evaluate a renormalization factor for $B_K$ at the parameters
where previous simulations have been performed, and find one-loop corrections
to $B_K$ are 1-5% in these cases.


title:
Analytical studies for the critical line and critical endpoint of the
  electroweak phase transition

abstract:
  We outline two approaches for studying the electroweak phase transition in
the framework of the four-dimensional SU(2) Higgs model on a lattice. The first
one is based on a combination of variational estimates for the free energy and
a solution of the resulting gap equations by means of dynamical linked cluster
expansions. In the second approach we first indicate the derivation of an
effective scalar field theory upon integration over the gauge fields. The phase
structure of the resulting scalar theory is then investigated by means of
generalized linked cluster expansions. We present results for the critical line
and the critical endpoint.


title: Central Dominance and the Confinement Mechanism in Gluodynamics

abstract:
  New topological objects, which we call center monopoles, naturally arise in
the Maximal Center Projection of SU(3) gluodynamics. The condensate of the
center monopoles is the order parameter of the theory.


title: Measuring Diquark Condensation in Lattice Simulations of Dense Matter

abstract:
  We discuss general aspects of the possibility of Bose condensation of diquark
pairs in systems of dense matter. Lattice field theory simulations are
presented for model four-fermion theories which are expected to manifest the
phenomenon, and results from measurements of both diquark two-point and
one-point functions presented. Whilst initial results are promising, there
remain systematic effects needing to be understood.


title: Two Colours QCD at Nonzero Chemical Potential

abstract:
  We identify the Goldstone modes appropriate to the low and high density
phases of SU(2) lattice gauge theory with staggered fermions. We present hybrid
Monte Carlo simulation results for susceptibilities on a 6^4 lattice at
beta=1.5, m=0.05. We specify how to implement a diquark source term in a
lattice simulation and present first measurements of the lattice diquark
condensate as a function of the diquark source.


title: Various Representations of Infrared Effective Lattice SU(2) Gluodynamics

abstract:
  We study various representations of infrared effective theory of SU(2)
gluodynamics starting from the Abelian monopole action derived recently by
numerical calculations in the Maximal Abelian projection. In particular we
derive the string model and the dual Abelian-Higgs (dual Ginzburg-Landau) model
which corresponds to infrared SU(2) gluodynamics. It occurs that the classical
string tension in the string model is of the same order as the string tension
in quantum SU(2) gluodynamics.


title: The Three Dimensional Thirring Model for N_f=4 and N_f=6

abstract:
  We present Monte Carlo simulation results for the three dimensional Thirring
model for numbers of fermion flavors N_f=4 and 6. For N_f=4 we find a second
order chiral symmetry breaking transition at strong coupling, corresponding to
an ultra-violet fixed point of the renormalisation group defining a non-trivial
continuum limit. The critical exponents extracted from a fit to a model
equation of state are distinct from those found for N_f=2. For N_f=6, in
contrast, we present evidence for tunnelling between chirally symmetric and
broken vacua at strong coupling, implying that the phase transition is first
order and no continuum limit exists. The implications for the phase diagram of
the model in the plane of coupling strength and N_f are briefly discussed.


title: Loop Representations of the Quark Determinant in Lattice QCD

abstract:
  The modelling of the ultraviolet contributions to the quark determinant in
lattice QCD in terms of a small number of Wilson loops is examined. Complete
Dirac spectra are obtained for sizeable ensembles of SU(3) gauge fields at
$\beta$=5.7 on 6$^4$, 8$^4$, and 10$^4$ lattices allowing for the first time a
detailed study of the volume dependence of the effective loop action generating
the quark determinant. The connection to the hopping parameter expansion is
examined in the heavy quark limit. We compare the efficiency and accuracy of
various methods- specifically, Lanczos versus stochastic approaches- for
extracting the quark determinant on an ensemble of configurations.


title: Calculation of the strange quark mass using domain wall fermions

abstract:
  We present a first calculation of the strange quark mass using domain wall
fermions. This paper contains an overview of the domain wall discretization and
a pedagogical presentation of the perturbative calculation necessary for
computing the mass renormalization. We combine the latter with numerical
simulations to estimate the strange quark mass. Our final result in the
quenched approximation is 95(26) MeV in the ${\bar{MS}}$ scheme at a scale of 2
GeV. We find that domain wall fermions have a small perturbative mass
renormalization, similar to Wilson quarks, and exhibit good scaling behavior.


title:
Catalysis of chiral symmetry breaking by external magnetic fields in
  three-dimensional lattice QED

abstract:
  The enhancement of the fermionic condensate due to the presence of both
homogeneous and non-homogeneous external magnetic fields is studied for
three-dimensional QED.


title:
Comparative Study of full QCD Hadron Spectrum and Static Quark Potential
  with Improved Actions

abstract:
  We investigate effects of action improvement on the light hadron spectrum and
the static quark potential in two-flavor QCD for $a^{-1} \approx 1$ GeV and
$m_{PS}/m_V = 0.7-0.9$. We compare a renormalization group improved action with
the plaquette action for gluons, and the SW-clover action with the Wilson
action for quarks. We find a significant improvement in the hadron spectrum by
improving the quark action, while the gluon improvement is crucial for a
rotationally invariant static potential. We also explore the region of light
quark masses corresponding to $m_{PS}/m_V \geq 0.4$ on a 2.7 fm lattice using
the improved gauge and quark action. A flattening of the potential is not
observed up to 2 fm.


title: The Scaling of Exact and Approximate Ginsparg-Wilson Fermions

abstract:
  We construct a number of lattice fermions, which fulfill the Ginsparg-Wilson
relation either exactly or approximately, and test them in the framework of the
2-flavor Schwinger model. We start from explicit approximations within a short
range, and study this formulation, as well as its correction to an exact
Ginsparg-Wilson fermion by the ``overlap formula''. Then we suggest a new
method to realize this correction perturbatively, without using the tedious
square root operator. In this way we combine many favorable properties: good
chiral behavior, small mass renormalization, excellent scaling and rotational
invariance, as well as a relatively modest computational effort, which makes
such formulations most attractive for QCD.


title: Further lattice evidence for a large re-scaling of the Higgs condensate

abstract:
  Using a high-statistics lattice simulation of the Ising limit of $(\lambda
\Phi^4)_4$ theory, we have measured the susceptibility and propagator in the
broken phase. We confirm our earlier finding of a discrepancy between the field
re-scaling implied by the propagator data and that implied by the
susceptibility. The discrepancy becomes {\it worse} as one goes closer to the
continuum limit; thus, it cannot be explained by residual perturbative effects.
The data are consistent with an unconventional description of symmetry breaking
and ``triviality'' in which the re-scaling factor for the finite-momentum
fluctuations tends to unity, but the re-scaling factor for the condensate
becomes larger and larger as one approaches the continuum limit. In the
Standard Model this changes the interpretation of the Fermi-constant scale and
its relation to the Higgs mass.


title:
Small eigenvalues of the staggered Dirac operator in the adjoint
  representation and Random Matrix Theory

abstract:
  The low-lying spectrum of the Dirac operator is predicted to be universal,
within three classes, depending on symmetry properties specified according to
random matrix theory. The three universal classes are the orthogonal, unitary
and symplectic ensemble. Lattice gauge theory with staggered fermions has
verified two of the cases so far, unitary and symplectic, with staggered
fermions in the fundamental representation of SU(3) and SU(2). We verify the
missing case here, namely orthogonal, with staggered fermions in the adjoint
representation of SU(N_c), N_c=2, 3.


title:
Low energy effective action of domain-wall fermion and the
  Ginsparg-Wilson relation

abstract:
  We derive the effective action of the light fermion field of the domain-wall
fermion, which is referred as $q(x)$ by Furman and Shamir. The inverse of the
effective Dirac operator turns out to be identical to the inverse of the
truncated overlap Dirac operator, except a local contact term which would give
the chiral symmetry breaking in the Ginsparg-Wilson relation. This result
allows us to relate the light fermion field and the fermion field described by
the truncated overlap Dirac operator and to understand the chiral property of
the light fermion through the exact chiral symmetry based on the
Ginsparg-Wilson relation.


title:
Infrared behavior of the gluon propagator in lattice Landau gauge: the
  three-dimensional case

abstract:
  We evaluate numerically the three-momentum-space gluon propagator in the
lattice Landau gauge, for three-dimensional pure-SU(2) lattice gauge theory
with periodic boundary conditions. Simulations are done for nine different
values of the coupling $\beta$, from $\beta = 0$ (strong coupling) to $\beta =
6.0$ (in the scaling region), and for lattice sizes up to $V = 64^3$. In the
limit of large lattice volume we observe, in all cases, a gluon propagator
decreasing for momenta smaller than a constant value $p_{dec}$. From our data
we estimate $p_{dec} \approx 350$ MeV. The result of a gluon propagator
decreasing in the infrared limit has a straightforward interpretation as
resulting from the proximity of the so-called first Gribov horizon in the
infrared directions.


title: Gauge fixing and gluon propagator in lambda-gauges

abstract:
  We discuss critical slowing-down of several gauge-fixing algorithms for the
so-called lambda-gauges in the SU(2) case at zero temperature. For these gauges
we also evaluate the gluon propagator using different definitions of the
lattice gluon field, corresponding to discretization errors of different
orders.


title: A non-perturbative calculation of the mass of the Bc

abstract:
  We present a calculation of the mass of the 1S0 pseudoscalar anti-b c (Bc)
state using a non-perturbative measurement from quenched lattice QCD. We find
M_Bc = 6.386(9)(98)(15) GeV where the first error is statistical, the second
systematic due to the quark mass ambiguities and quenching and the third the
systematic error due to the estimation of mass of the eta_b.


title:
A Monte Carlo study of leading order scaling corrections of phi^4 theory
  on a three dimensional lattice

abstract:
  We present a Monte Carlo study of the one-component $\phi^4$ model on the
cubic lattice in three dimensions. Leading order scaling corrections are
studied using the finite size scaling method. We compute the corrections to
scaling exponent $\omega$ with high precision. We determine the value of the
coupling $\lambda$ at which leading order corrections to scaling vanish. Using
this result we obtain estimates for critical exponents that are more precise
than those obtained with field theoretic methods.


title:
Confinement in the Deconfined Phase: A numerical study with a cluster
  algorithm

abstract:
  We have previously found analytically a very unusual and unexpected form of
confinement in SU(3) Yang-Mills theory. This confinement occurs in the
deconfined phase of the theory. The free energy of a single static test quark
diverges, even though it is contained in deconfined bulk phase and there is no
QCD string present. This phenomenon occurs in cylindrical volumes with a
certain choice of spatial boundary conditions. We examine numerically an
effective model for the Yang-Mills theory and, using a cluster algorithm, we
observe this unusual confinement. We also find a new way to determine the
interface tension of domain walls separating distinct bulk phases.


title: End states, ladder compounds, and domain wall fermions

abstract:
  A magnetic field applied to a cross linked ladder compound can generate
isolated electronic states bound to the ends of the chain. After exploring the
interference phenomena responsible, I discuss a connection to the domain wall
approach to chiral fermions in lattice gauge theory. The robust nature of the
states under small variations of the bond strengths is tied to chiral symmetry
and the multiplicative renormalization of fermion masses.


title: Leutwyler-Smilga sum rules for Ginsparg-Wilson lattice fermions

abstract:
  We argue that lattice QCD with Ginsparg-Wilson fermions satisfies the
Leutwyler-Smilga sum rules for the eigenvalues of the chiral Dirac operator.
The result is obtained in the one flavor case, by rephrasing Leutwyler and
Smilga's original analysis for the finite volume partition function. This is a
further evidence that Ginsparg-Wilson fermions, even if breaking explicitly the
chirality on the lattice in accordance to the Nielsen-Ninomiya theorem, mimic
the main features of the continuum theory related to chiral symmetry.


title:
Non-Perturbative Renormalization of Lattice Four-Fermion Operators
  without Power Subtractions

abstract:
  A general non-perturbative analysis of the renormalization properties of
$\Delta I=3/2$ four-fermion operators in the framework of lattice
regularization with Wilson fermions is presented. We discuss the
non-perturbative determination of the operator renormalization constants in the
lattice Regularization Independent (RI or MOM) scheme. We also discuss the
determination of the finite lattice subtraction coefficients from Ward
Identities. We prove that, at large external virtualities, the determination of
the lattice mixing coefficients, obtained using the RI renormalization scheme,
is equivalent to that based on Ward Identities, in the continuum and chiral
limits. As a feasibility study of our method, we compute the mixing matrix at
several renormalization scales, for three values of the lattice coupling
$\beta$, using the Wilson and tree-level improved SW-Clover actions.


title: Monopole clusters, Z(2) vortices and confinement in SU(2)

abstract:
  We extend our previous study of magnetic monopole currents in the maximally
Abelian gauge [hep-lat/9712003] to larger lattices at small lattice spacings
(20^4 at beta = 2.5 and 32^4 at beta = 2.5115). We confirm that at these weak
couplings there continues to be one monopole cluster that is very much longer
than the rest and that the string tension, K, is entirely due to it. The
remaining clusters are compact objects whose population as a function of radius
follows a power law that deviates from the scale invariant form, but much too
weakly to suggest a link with the analytically calculable size distribution of
small instantons. We also search for traces of Z(2) vortices in the Abelian
projected fields; either as closed loops of `magnetic' flux or through
appropriate correlations amongst the monopoles. We find, by direct calculation,
that there is no confining condensate of such flux loops. We also find, through
the calculation of doubly charged Wilson loops within the monopole fields, that
there is no suppression of the q=2 effective string tension out to at distances
of at least r ~ 1.6/sqrt{K}, suggesting that if there are any vortices they are
not encoded in the monopole fields.


title:
Insight into the Role of Instantons and their Zero Modes from Lattice
  QCD

abstract:
  Evidence from lattice QCD calculations is presented showing that instantons
and their associated zero modes play a major role in the physics of light
hadrons and the propagation of light quarks in the QCD vacuum.


title:
Chiral Symmetry Restoration and Realisation of the Goldstone Mechanism
  in the U(1) Gross-Neveu Model at Non-Zero Chemical Potential

abstract:
  We simulate the Gross-Neveu model in 2+1 dimensions at nonzero baryon density
(chemical potential mu =/= 0). It is possible to formulate this model with a
real action and therefore to perform standard hybrid Monte Carlo simulations
with mu =/= 0 in the functional measure. We compare the physical observables
from these simulations with simulations using the Glasgow method where the
value of mu in the functional measure is fixed at a value mu_upd. We find that
the observables are sensitive to the choice of mu_upd. We consider the
implications of our findings for Glasgow method QCD simulations at mu =/= 0. We
demonstrate that the realisation of the Goldstone mechanism in the Gross-Neveu
model is fundamentally different from that in QCD. We find that this difference
explains why there is an unphysical transition in QCD simulations at mu =/= 0
associated with the pion mass scale whereas the transition in the Gross-Neveu
model occurs at a larger mass scale and is therefore consistent with
theoretical predictions. We note classes of theories which are exceptions to
the Vafa-Witten theorem which permit the possibility of formation of baryon
number violating diquark condensates.


title:
Symmetries and spectrum of SU(2) Lattice Gauge Theory at finite chemical
  potential

abstract:
  We study SU(2) Lattice Gauge Theory with dynamical fermions at non-zero
chemical potential $\mu$. The symmetries special to SU(2) for staggered
fermions on the lattice are discussed explicitly and their relevance to
spectroscopy and condensates at non-zero chemical potential are considered.
Using the molecular dynamics algorithm on small lattices we find qualitative
changes in the theory's spectroscopy at small and large values of $\mu$. This
preliminary study should lay the groundwork for future large scale simulations.


title: Performance of lattice QCD programs on CP-PACS

abstract:
  The CP-PACS is a massively parallel MIMD computer with the theoretical peak
speed of 614 GFLOPS which has been developed for computational physics
applications at the University of Tsukuba, Japan. We report on the performance
of the CP-PACS computer measured during recent production runs using our
Quantum Chromodynamics code for the simulation of quarks and gluons in particle
physics. With the full 2048 processing nodes, our code shows a sustained speed
of 237.5 GFLOPS for the heat-bath update of gluon variables, 264.6 GFLOPS for
the over-relaxation update, and 325.3 GFLOPS for quark matrix inversion with an
even-odd preconditioned minimal residual algorithm.


title: A lattice NRQCD calculation of the $B^0-\bar{B}^0$ mixing parameter B_B

abstract:
  We present a lattice calculation of the B meson B-parameter B_B using the
NRQCD action. The heavy quark mass dependence is explicitly studied over a mass
range between m_b and 4m_b with the $O(1/m_Q)$ and $O(1/m_Q^2)$ actions. We
find that the ratios of lattice matrix elements $<O_N^{lat}>/<A_0^{lat}>^2$ and
$<O_S^{lat}>/<A_0^{lat}>^2$, which contribute to B_B through mixing, have
significant $1/m_Q$ dependence while that of the leading operator
$<O_L^{lat}>/<A_0^{lat}>^2$ has little $1/m_Q$ effect. The combined result for
B_B(m_b) has small but non-zero mass dependence, and the B_B(m_b) becomes
smaller by 10% with the 1/m_Q correction compared to the static result. Our
result in the quenched approximation at \beta=5.9 is B_{B_d}(5 GeV) =
0.75(3)(12), where the first error is statistical and the second is a
systematic uncertainty.


title: The axial anomaly in lattice QED. A universal point of view

abstract:
  We give a perturbative proof that U(1) lattice gauge theories generate the
axial anomaly in the continuum limit under very general conditions on the
lattice Dirac operator. These conditions are locality, gauge covariance and the
absense of species doubling. They hold for Wilson fermions as well as for
realizations of the Dirac operator that satisfy the Ginsparg-Wilson relation.
The proof is based on the lattice power counting theorem.


title: Finite Density Fat QCD

abstract:
  Lattice formulation of Finite Baryon Density QCD is problematic from computer
simulation point of view; it is well known that for light quark masses the
reconstructed partition function fails to be positive in a wide region of
parameter space. For large bare quark masses, instead, it is possible to obtain
more sensible results; problems are still present but restricted to a small
region. We present evidence for a saturation transition independent from the
gauge coupling $\beta$ and for a transition line that, starting from the
temperature critical point at $\mu=0$, moves towards smaller $\beta$ with
increasing $\mu$ as expected from simplified phenomenological arguments.


title: Probing the non-perturbative dynamics of SU(2) vacuum

abstract:
  The vacuum dynamics of SU(2) lattice gauge theory is studied by means of a
gauge-invariant effective action defined using the lattice Schr\"odinger
functional. Numerical simulations are performed both at zero and finite
temperature. The vacuum is probed using an external constant Abelian
chromomagnetic field. The results suggest that at zero temperature the external
field is screened in the continuum limit. On the other hand at finite
temperature it seems that confinement is restored by increasing the strength of
the applied field.


title: Simple Observables from Fat Link Fermion Actions

abstract:
  A comparison is made of the (quenched) light hadron spectrum and of simple
matrix elements for a hypercubic fermion action (based on a fixed point action)
and the clover action, both using fat links, at a lattice spacing a= 0.18 fm.
Renormalization constants for the naive and improved vector current and the
naive axial current are computed using Ward identities. The renormalization
factors are very close to unity, and the spectroscopy of light hadrons and the
pseudoscalar and vector decay constants agree well with simulations at smaller
lattice spacings (and with experiment).


title: Controlling One-Dimensional Langevin Dynamics on the Lattice

abstract:
  Stochastic evolutions of classical field theories have recently become
popular in the study of problems such as determination of the rates of
topological transitions and the statistical mechanics of nonlinear coherent
structures. To obtain high precision results from numerical calculations, a
careful accounting of spacetime discreteness effects is essential, as well as
the development of schemes to systematically improve convergence to the
continuum. With a kink-bearing $\phi^4$ field theory as the application arena,
we present such an analysis for a 1+1-dimensional Langevin system. Analytical
predictions and results from high resolution numerical solutions are found to
be in excellent agreement.

categories: hep-lat cond-mat hep-ph nlin.PS patt-sol


title:
Translational Anomaly in Chiral Gauge Theories on a Torus and the
  Overlap Formalism

abstract:
  We point out that a fermion determinant of a chiral gauge theory on a 2D
torus has a phase ambiguity proportional to the Polyakov loops along the
boundaries, which can be reproduced by the overlap formalism. We show that the
requirement on the fermion determinant that a singularity in the gauge field
can be absorbed by a change of the boundary condition for the fermions, is not
compatible with translational invariance in general. As a consequence, the
gauge anomaly for singular gauge transformations discovered by
Narayanan-Neuberger actually exists in any 2D U(1) chiral gauge theory unless
the theory is vector-like. We argue that the gauge anomaly is peculiar to the
overlap formalism with the Wigner-Brillouin phase choice and that it is not
necessarily a property required in the continuum. We also generalize our
results to any even dimension.


title: A Study of Gluon Propagator on Coarse Lattice

abstract:
  We study gluon propagator in Landau gauge with lattice QCD, where we use an
improved lattice action. The calculation of gluon propagator is performed on
lattices with the lattice spacing from 0.40 fm to 0.24 fm and with the lattice
volume from $(2.40 fm)^4$ to $(4.0 fm)^4$. We try to fit our results by two
different ways, in the first one we interpret the calculated gluon propagators
as a function of the continuum momentum, while in the second we interpret the
propagators as a function of the lattice momentum. In the both we use models
which are the same in continuum limit. A qualitative agreement between two
fittings is found.


title:
Critical specific heats of the N-vector spin models on the sc and the
  bcc lattices

abstract:
  We have computed through order $\beta^{21}$ the high-temperature expansions
for the nearest-neighbor spin correlation function $G(N,\beta)$ of the
classical N-vector model, with general N, on the simple-cubic and on the
body-centered-cubic lattices.
  For this model, also known in quantum field theory as the lattice O(N)
nonlinear sigma model, we have presented in previous papers extended expansions
of the susceptibility, of its second field derivative and of the second moment
of the correlation function.
  Here we study the internal specific energy and the specific heat
$C(N,\beta)$, obtaining new estimates of the critical parameters and therefore
a more accurate direct test of the hyperscaling relation $d \nu(N)=2 -
\alpha(N)$ on a range of values of the spin dimensionality N, including N=0
[the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY
model], N=3 [the classical Heisenberg model]. By the newly extended series, we
also compute the universal combination of critical amplitudes usually denoted
by $R^+_{\xi}(N)$, in fair agreement with renormalization group estimates.


title: Non-perturbative states in the 3D phi^4 theory

abstract:
  We show that the spectrum of the three dimensional phi^4 theory in the broken
symmetry phase contains non-perturbative states. We determine the spectrum
using a new variational technique based on the introduction of operators
corresponding to different length scales. The presence of non-perturbative
states accounts for the discrepancy between Monte Carlo and perturbative
results for the universal ratio xi/xi_2nd. We introduce and study some
universal amplitude ratios related to the overlap of the spin operator with the
states of the spectrum. The analysis is performed for the phi^4 theory
regularized on a lattice and for the Ising model. This is a nice verification
of the fact that universality reaches far beyond critical exponents. Finally,
we show that the spectrum of the model, including non-perturbative states,
accurately matches the glueball spectrum in the Z(2) gauge model, which is
related to the Ising model through a duality transformation.


title:
Renormalization group invariant average momentum of non-singlet parton
  densities

abstract:
  We compute, within the Schr\"odinger functional scheme, a renormalization
group invariant renormalization constant for the first moment of the
non-singlet parton distribution function. The matching of the results of our
non-perturbative calculation with the ones from hadronic matrix elements allows
us to obtain eventually a renormalization group invariant average momentum of
non-singlet parton densities, which can be translated into a preferred scheme
at a specific scale.


title: The confining string and its breaking in QCD

abstract:
  We point out that the world sheet swept by the confining string in presence
of dynamical quarks can belong to two different phases, depending on the number
of charge species and the quark masses. When it lies in the normal phase (as
opposed to the tearing one) the string breaking is invisible in the Wilson
loop, while is manifest in operators composed of disjoint sources, as observed
in many numerical experiments. We work out an explicit formula for the
correlator of Polyakov loops at finite temperature, which is then compared with
recent lattice data, both in the quenched case and in presence of dynamical
quarks. The analysis in the quenched case shows that the free bosonic string
model describes accurately the data for distances larger than ~ 0.75 fm. In the
unquenched case we derive predictions on the dependence of the static potential
on the temperature which are compatible with the lattice data.


title: Monte Carlo simulation of SU(2) Yang-Mills theory with light gluinos

abstract:
  In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with light
dynamical gluinos the low energy features of the dynamics as confinement and
bound state mass spectrum are investigated. The motivation is supersymmetry at
vanishing gluino mass. The performance of the applied two-step multi-bosonic
dynamical fermion algorithm is discussed.


title: Gribov copies and gauge variant correlators in U(1) lattice gauge theory

abstract:
  We discuss the influence of Dirac sheets and zero-momentum modes on the gauge
variant photon correlators $\Gamma(\tau;\vp)$ with $\vp\ne 0$ and $\vp =0$ in
the pure gauge U(1) theory. A special attention has been paid to the $\beta$-
and volume-dependence of this influence. Numerical simulations are performed on
$12\times 6^3$ and $24\times 12^3$ lattices at different $y\beta$'s in the
Coulomb phase.


title:
Scaling investigation of renormalized correlation functions in O(a)
  improved quenched lattice QCD

abstract:
  We present a scaling investigation of some correlation functions in $\Or(a)$
improved quenched lattice QCD. In particular, as one observable the
renormalized PCAC quark mass is considered. Others are constructed such that
they become the vector meson mass and the pseudoscalar meson decay constant
when the volume is large. For the present discussion we remain in intermediate
volume, $(0.75^3\times1.5) {fm}^4$ with Schr\"odinger functional boundary
conditions. By fixing the `pion mass' and the spatial lattice size in units of
the hadronic scale $r_0$, we simulated four lattices with resolutions ranging
from 0.1 fm to 0.05 fm and performed the extrapolation to the continuum limit.
The maximal scaling violation found in the improved theory is a $\sim$ 6 %
effect at $a\simeq 0.1 fm$.


title: The heavy quarkonium spectrum from quenched lattice QCD

abstract:
  We present results of simulations of the quenched quarkonium spectrum at two
values of the lattice spacing and for quark masses around $m_c$ using the
tadpole improved clover action. Attention is focussed on the lowest lying S and
P states, and the triplet fine structure is obtained for the first time using a
relativistic action.


title:
Large-q expansion of the energy and magnetization cumulants for the
  two-dimensional q-state Potts model

abstract:
  We have calculated the large-q expansion for the energy cumulants and the
magnetization cumulants at the phase transition point in the two-dimensional
q-state Potts model to the 21st or 23rd order in $1/\sqrt{q}$ using the finite
lattice method. The obtained series allow us to give very precise estimates of
the cumulants for $q>4$ on the first order transition point. The result
confirms us the correctness of the conjecture by Bhattacharya et al. on the
asymptotic behavior not only of the energy cumulants but also of the
magnetization cumulants for $q \to 4_+$.


title: Representations of Fermionic Correlators at Finite Temperatures

abstract:
  The symmetry group of the staggered Fermion transfer matrix in a spatial
direction is constructed at finite temperature. Hadron-like operators carrying
irreducible representations of this group are written down from the breaking of
the zero temperature group. Analysis of the correlators in a free fermion
theory suggests new measurements which can test current interpretations.


title: Periodic vacuum and particles in two dimensions

abstract:
  Different dynamical symmetry breaking patterns are explored for the two
dimensional phi4 model with higher order derivative terms. The one-loop saddle
point expansion predicts a rather involved phase structure and a new Gaussian
critical line. This vacuum structure is corroborated by the Monte Carlo method,
as well. Analogies with the structure of solids, the density wave phases and
the effects of the quenched impurities are mentioned. The unitarity of the time
evolution operator in real time is established by means of the reflection
positivity.


title: The lattice Schwinger model as a discrete sum of filled Wilson loops

abstract:
  Using techniques from hopping expansion we identically map the lattice
Schwinger model with Wilson fermions to a model of oriented loops on the
lattice. This is done by first computing the explicit form of the fermion
determinant in the external field. Subsequent integration of the gauge fields
renders a sum over all loop configurations with simple Gaussian weights
depending on the number of plaquettes enclosed by the loops. In our new
representation vacuum expectation values of local fermionic operators (scalars,
vectors) can be computed by simply counting the loop flow through the sites
(links) supporting the scalars (vectors). The strong coupling limit, possible
applications of our methods to 4-D models and the introduction of a chemical
potential are discussed.

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


title: Calorons on the lattice - a new perspective

abstract:
  We discuss the manifestation of instanton and monopole solutions on a
periodic lattice at finite temperature and their relation to the infinite
volume analytic caloron solutions with asymptotic non-trivial Polyakov loops.
As a tool we use improved cooling and twisted boundary conditions. Typically we
find 2Q lumps for topological charge Q. These lumps are BPS monopoles.


title: The Structure of Projected Center Vortices in Lattice Gauge Theory

abstract:
  We investigate the structure of center vortices in maximal center gauge of
SU(2) lattice gauge theory at zero and finite temperature. In center projection
the vortices (called P-vortices) form connected two dimensional surfaces on the
dual four-dimensional lattice. At zero temperature we find, in agreement with
the area law behaviour of Wilson loops, that most of the P-vortex plaquettes
are parts of a single huge vortex. Small P-vortices, and short-range
fluctuations of the large vortex surface, do not contribute to the string
tension. All of the huge vortices detected in several thousand field
configurations turn out to be unorientable. We determine the Euler
characteristic of these surfaces and find that they have a very irregular
structure with many handles. At finite temperature P-vortices exist also in the
deconfined phase. They form cylindric objects which extend in time direction.
After removal of unimportant short range fluctuations they consist only of
space-space plaquettes, which is in accordance with the perimeter law behaviour
of timelike Wilson loops, and the area law behaviour of spatial Wilson loops in
this phase.


title:
Dynamical lattice QCD thermodynamics and the U(1)_A symmetry with domain
  wall fermions

abstract:
  Results from numerical simulations of full, two flavor QCD thermodynamics at
N_t=4 with domain wall fermions are presented. For the first time a numerical
simulation of the full QCD phase transition displays a low temperature phase
with spontaneous chiral symmetry breaking but intact flavor symmetry and a high
temperature phase with the full $SU(2) \times SU(2)$ chiral flavor symmetry. It
is found that close to the transition in the high temperature phase the U(1)_A
axial symmetry is broken only by a small amount. This result is of particular
interest because of the connection between U(1)_A symmetry breaking and the
expected order of the transition.


title:
Lattice calculation of matrix elements relevant for Delta I=1/2 rule and
  epsilon-prime

abstract:
  We have gained enough statistical precision to distinguish signal from noise
in matrix elements of all operators relevant for the Delta I=1/2 rule in kaon
decays and for the direct CP violation parameter epsilon-prime. We confirm
significant enhancement of Delta I=1/2 transitions observed in experiments,
although a few large systematic uncertainties remain in our predictions:
higher-order chiral corrections and lattice spacing dependence. The estimate of
epsilon-prime parameter is further complicated by the problem of matching
lattice and continuum operators.


title: Hadron spectroscopy from lattice QCD

abstract:
  I present recent developments in the lattice QCD calculations of the light
hadron spectrum. Emphasis is placed on the limitation of the quenched
approximation in reproducing the observed spectrum and indications that the
discrepancy is reduced by introducing two flavors of light dynamical quarks.


title: Inverse Symmetry Breaking on the lattice: an accurate MC study

abstract:
  We present here a new MC study of ISB at finite temperature in a $Z_2\times
Z_2$ $\lambda\phi^4$ model in four dimensions. The results of our simulations,
even if not conclusive, are favourable to ISB. Detection of the effect required
measuring some critical couplings with six-digits precision, a level of
accuracy that could be achieved only by a careful use of FSS techniques. The
gap equations for the Debye masses, resulting from the resummation of the ring
diagrams, seem to provide a qualitatively correct description of the data,
while the simple one-loop formulae appear to be inadequate.


title: Z_2-Regge versus Standard Regge Calculus in two dimensions

abstract:
  We consider two versions of quantum Regge calculus. The Standard Regge
Calculus where the quadratic link lengths of the simplicial manifold vary
continuously and the Z_2-Regge Model where they are restricted to two possible
values. The goal is to determine whether the computationally more easily
accessible Z_2 model still retains the universal characteristics of standard
Regge theory in two dimensions. In order to compare observables such as average
curvature or Liouville field susceptibility, we use in both models the same
functional integration measure, which is chosen to render the Z_2-Regge Model
particularly simple. Expectation values are computed numerically and agree
qualitatively for positive bare couplings. The phase transition within the
Z_2-Regge Model is analyzed by mean-field theory.


title: Multi-bosonic algorithms for dynamical fermion simulations

abstract:
  Multi-bosonic fermion simulation algorithms are reviewed, with particular
emphasis on a recent application in SU(2) Yang-Mills theory with light gluinos.


title: The quenched limit of lattice QCD at non-zero baryon number

abstract:
  We discuss the thermodynamics of gluons in the background of static quark
sources. In order to do so we formulate the quenched limit of QCD at non-zero
baryon number. A first numerical analysis of this system shows that it
undergoes a smooth deconfining transition. We find evidence for a region of
coexisting phases that becomes broader with increasing baryon number density.
Although the action is in our formulation explicitly Z(3) symmetric the
Polyakov loop expectation value becomes non-zero already in the low temperature
phase. It indicates that the heavy quark potential stays finite at large
distances, ie. the string between static quarks breaks at non-zero baryon
number density already in the hadronic phase.


title: Deconfinement and Chiral Symmetry Restoration

abstract:
  We discuss the critical behaviour of strongly interacting matter close to the
QCD phase transition. Emphasis is put on a presentation of results from lattice
calculations that illustrate deconfining as well as chiral symmetry restoring
features of the phase transition. We show that both transitions coincide in QCD
while they fall apart in an SU(3) gauge theory coupled to adjoint fermions. We
also discuss some results on deconfinement in quenched QCD at non-zero baryon
number.


title: Variants of fattening and flavor symmetry restoration

abstract:
  We study the effects of different "fat link" actions for Kogut-Susskind
quarks on flavor symmetry breaking. Our method is mostly empirical - we compute
the pion spectrum with different valence quark actions on common sets of sample
lattices. Different actions are compared, as best we can, at equivalent
physical points. We find significant reductions in flavor symmetry breaking
relative to the conventional or to the "link plus staple" actions, with a
reasonable cost in computer time. We also develop and test a scheme for
approximate unitarization of the fat links. While our tests have concentrated
on the valence quark action, our results will be useful in designing
simulations with dynamical quarks.


title: A novel gauge invariant multi-state smearing technique

abstract:
  We present an investigation of a gauge invariant smearing technique that
allows the construction of smearing functions with arbitrary radial behaviour,
by foresaking the space filling nature of traditional smearing techniques. This
is applied to both heavy-heavy, heavy-light, and light-light systems with one
particular choice of radial ``wavefunction'' - the hydrogenic solutions - and
we find good stability for both fitted masses and amplitudes of the radially
excited states. The dependence of the amplitudes on the smearing radius is
demonstrated to be well understood, while near optimal smearing radii may be
found with extremely low statistics using a property of the smeared-local
correlator. The smearing technique is inexpensive since it is non-iterative,
achieves a good signal to noise ratio, and can be altered to use wavefunctions
from, say, potential models or the Bethe-Salpether equations in future
simulations.


title:
Scaling analysis of the magnetic monopole mass and condensate in the
  pure U(1) lattice gauge theory

abstract:
  We observe the power law scaling behavior of the monopole mass and condensate
in the pure compact U(1) gauge theory with the Villain action. In the Coulomb
phase the monopole mass scales with the exponent \nu_m=0.49(4). In the
confinement phase the behavior of the monopole condensate is described with
remarkable accuracy by the exponent \beta_{exp}=0.197(3). Possible implications
of these phenomena for a construction of a strongly coupled continuum U(1)
gauge theory are discussed.


title: The MultiBoson method

abstract:
  This review describes the multiboson algorithm for Monte Carlo simulations of
lattice QCD, including its static and dynamical aspects, and presents a
comparison with Hybrid Monte Carlo.


title:
Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice
  Regularization at Low Energies

abstract:
  The renormalized coupling $\gr$ defined through the connected 4-point
function at zero external momentum in the non-linear O(3) sigma-model in two
dimensions, is computed in the continuum form factor bootstrap approach with
estimated error $\sim 0.3%$. New high precision data are presented for $\gr$ in
the lattice regularized theory with standard action for nearly thermodynamic
lattices $L/\xi\sim 7$ and correlation lengths $\xi$ up to $\sim 122$ and with
the fixed point action for correlation lengths up to $\sim 12$. The agreement
between the form factor and lattice results is within $\sim 1%$. We also
recompute the phase shifts at low energy by measuring the two-particle energies
at finite volume, a task which was previously performed by L\"uscher and Wolff
using the standard action, but this time using the fixed point action.
Excellent agreement with the Zamolodchikov S-matrix is found.


title: Combinatorics of lattice paths with and without spikes

abstract:
  We derive a series of results on random walks on a d-dimensional hypercubic
lattice (lattice paths). We introduce the notions of terse and simple paths
corresponding to the path having no backtracking parts (spikes). These paths
label equivalence classes which allow a rearrangement of the sum over paths.
The basic combinatorial quantities of this construction are given. These
formulas are useful when performing strong coupling (hopping parameter)
expansions of lattice models. Some applications are described.


title:
Dual Higgs Mechanism based on the Dual Gauge Formalism in the Lattice
  QCD

abstract:
  We study the dual Higgs mechanism induced by monopole condensation based on
the dual gauge formalism in the maximally abelian (MA) gauge in the lattice
QCD. To examine ``monopole condensation'' in QCD, we study the monopole part or
the monopole-current system appearing in the MA gauge by extracting the dual
gluon field $B_\mu$. First, we investigate the inter-monopole potential using
the dual Wilson loop in the lattice QCD simulation. In the monopole part in the
MA gauge, the inter-monopole potential is found to be flat, and can be fitted
as the Yukawa potential in the infrared region. From more detailed analysis of
the inter-monopole potential considering the monopole size, we estimate the
effective dual-gluon mass $m_B \simeq 0.5$GeV and the effective monopole size
$R_{^{_{\rm M}}} \simeq 0.2$fm. Second, we study the dual gluon propagator
$G^D_{\mu\nu}(x-y) \equiv < B_\mu(x) B_\nu(y) >_{\rm MA}$ in the MA gauge, and
find that $G^D_{\mu\mu}$ behaves as the massive vector-boson propagator with
$m_B \simeq 0.4$ GeV in the infrared region. The effective-mass acquirement of
the dual gluon field $B_\mu$ at the long distance can be regarded as the
lattice QCD evidence of ``infrared monopole condensation'' in the MA gauge.


title: Confronting Instanton Perturbation Theory with QCD Lattice Results

abstract:
  We exploit a recent lattice investigation (UKQCD) on the topological
structure of the (quenched) QCD vacuum, in order to gain information on crucial
building blocks of instanton perturbation theory. A central motivation is to
further constrain our previous predictions of instanton-induced hard scattering
processes. First, we address the generic problem of extracting quantitative
information from cooled lattice data. We find a new scaling variable,
interpreted as a "cooling radius", which allows to combine lattice data for a
whole range of lattice spacings and cooling sweeps. This variable strongly
helps to extract information on the uncooled distributions of interest. After
performing the continuum extrapolation of the instanton size and
instanton-anti-instanton distance distributions, we find striking agreement
with the theoretical predictions from instanton-perturbation theory, for
instanton sizes below 0.5 fm and distances above 0.5 fm, respectively. These
results imply first direct support for the validity of the known valley
interaction between instantons and anti-instantons.


title: Hadron masses and matrix elements from the QCD Schr"odinger functional

abstract:
  We explain how masses and matrix elements can be computed in lattice QCD
using Schr"odinger functional boundary conditions. Numerical results in the
quenched approximation demonstrate that good precision can be achieved. For a
statistical sample of the same size, our hadron masses have a precision similar
to what is achieved with standard methods, but for the computation of matrix
elements such as the pseudoscalar decay constant the Schr"odinger functional
technique turns out to be much more efficient than the known alternatives.


title: Lorentz gauge and Gribov ambiguity in the compact lattice U(1) theory

abstract:
  The Gribov ambiguity problem is studied for compact U(1) lattice theory
within the Lorentz gauge. In the Coulomb phase, it is shown that apart from
double Dirac sheets all gauge (i.e. Gribov) copies originate mainly from the
zero-momentum modes of the gauge fields. The removal of the zero-momentum modes
turns out to be necessary for reaching the absolute maximum of the gauge
functional $F(\theta)$. A new gauge fixing procedure - zero-momentum Lorentz
gauge - is proposed.


title: Non-Universal Quantities from Dual RG Transformations

abstract:
  Using a simplified version of the RG transformation of Dyson's hierarchical
model, we show that one can calculate all the non-universal quantities entering
into the scaling laws by combining an expansion about the high-temperature
fixed point with a dual expansion about the critical point. The magnetic
susceptibility is expressed in terms of two dual quantities transforming
covariantly under the RG transformation and has a smooth limit in the
high-temperature limit. Using the analogy with hamiltonian systems, the
simplified example discussed here is similar to the anharmonic oscillator,
while more realistic examples can be tought of as coupled oscillators allowing
resonance phenomena.

categories: hep-lat chao-dyn cond-mat.stat-mech hep-th math-ph math.MP nlin.CD


title:
CP-PACS results for light hadron spectrum in quenched and two-flavor
  full QCD

abstract:
  We present a summary of our results for the light hadron spectrum in quenched
lattice QCD and preliminary ones in two-flavor full QCD. For the quenched
hadron spectrum we find that the mass formulae predicted by quenched chiral
perturbation theory(QChPT) give a good description of our results. Employing
the QChPT mass formulae for chiral extrapolations we conclude that the mass
spectrum in the continuum limit deviates unambiguously and systematically from
experiment. For our two-flavor full QCD results we focus on the dynamical quark
effects on the light hadron spectrum.


title:
Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation
  transition

abstract:
  By fixing lattice Yang-Mills configurations to the maximal center gauge and
subsequently applying the technique of center projection, one can identify
center vortices in these configurations. Recently, center vortices have been
shown to determine the string tension between static quarks at finite
temperatures (center dominance); also, they correctly reproduce the deconfining
transition to a phase with vanishing string tension. After verifying center
dominance also for the so-called spatial string tension, the present analysis
focuses on the global topology of vortex networks. General arguments are given
supporting the notion that the deconfinement transition in the center vortex
picture takes the guise of a percolation transition. This transition is
detected in Monte Carlo experiments by concentrating on various slices through
the closed vortex surfaces; these slices, representing loops in lattice
universes reduced by one dimension, clearly exhibit the expected transition
from a percolating to a non-percolating, deconfined, phase. The latter phase
contains a large proportion of vortex loops winding around the lattice in the
Euclidean time direction. At the same time, an intuitive picture clarifying the
persistence of the spatial string tension in the deconfined phase emerges.


title: Lattice Fields and Extra Dimensions

abstract:
  Lattice gauge theory is now well into its third decade as a major subfield of
theoretical particle physics. I open these lattice sessions with a brief review
of the motivations for this formulation of quantum field theory. I then comment
on the recent drive of lattice theorists to include a fictitious ``fifth''
dimension to treat issues of chiral symmetry and anomalies.


title: Phase diagram and Debye mass in thermally reduced QCD

abstract:
  At temperatures well above the transition, QCD admits a thermally reduced
version in 3D, which reproduces the long distance physics. We analyze the phase
diagram, point out the relevance of Z(3) symmetry in the location of the
transition and suggest a way out to reconcile this with the data. Related to
this symmetry is the existence of an observable, the Z(N) wall, or rather its
3D version, and discuss some of its advantages over other observables.


title:
Relation $Tr \gamma_{5}= 0$ and the index theorem in lattice gauge
  theory

abstract:
  The relation $Tr \gamma_{5}= 0$ implies the contribution to the trace from
unphysical (would-be) species doublers in lattice gauge theory. This statement
is also true for the Pauli-Villars regularization in continuum theory. If one
insists on $Tr \gamma_{5}= 0$, one thus inevitably includes unphysical states
in the Hilbert space. If one truncates the trace to the contribution from
physical species only, one obtains $\tilde{T}r \gamma_{5} = n_{+} - n_{-}$
which is equal to the Pontryagin index. A smooth continuum limit of $\tilde{T}r
\gamma_{5} = Tr \gamma_{5}(1-(a/2)D) = n_{+} - n_{-}$ for the Dirac operator
$D$ satisfying the Ginsparg-Wilson relation leads to the natural treatment of
chiral anomaly in continuum path integral. In contrast, the continuum limit of
$Tr \gamma_{5}= 0$ is not defined consistently. It is shown that the
non-decoupling of heavy fermions in the anomaly calculation is crucial to
understand the consistency of the customary lattice calculation of anomaly
where $Tr \gamma_{5}= 0$ is used. We also comment on a closely related
phenomenon in the analysis of the photon phase operator where the notion of
index and the modification of index by a finite cut-off play a crucial role.


title:
Chiral symmetry restoration in the three-dimensional four-fermion model
  at non-zero temperature and density

abstract:
  The three-dimensional four-fermion model with a Z_2 chiral symmetry and N=4
fermion species in the system is investigated numerically at non-zero
temparature and chemical potential. The phase diagram in the (chemical
potential, temperature) plane is mapped out quantitatively. A detailed finite
size scaling analysis shows that the zero temperature and non-zero chemical
potential chiral phase transition is first order, whereas the non-zero
temperature and non-zero chemical potential transition remains second order
down to very low temperatures. Quantitative results for the location of the end
of the first order line are given. The simulations at T=0 provided no evidence
for a nuclear liquid-gas transition.


title: Weyl fermions on the lattice and the non-abelian gauge anomaly

abstract:
  Starting from the Ginsparg-Wilson relation, a general construction of chiral
gauge theories on the lattice is described. Local and global anomalies are
easily discussed in this framework and a closed expression for the effective
action can be obtained. Particular attention is paid to the non-abelian gauge
anomaly, which is shown to be related to a local topological field on the
lattice representing the Chern character in 4+2 dimensions.


title: Monopole characteristics in various Abelian gauges

abstract:
  Renormalization group (RG) smoothing is employed on the lattice to
investigate and to compare the monopole structure of the SU(2) vacuum as seen
in different gauges (maximally Abelian (MAG), Polyakov loop (PG) and Laplacian
gauge (LG)). Physically relevant types of monopoles (LG and MAG) are
distinguished by their behavior near the deconfining phase transition. For the
LG, Abelian projection reproduces well the gauge independent monopole structure
encoded in an auxiliary Higgs field. Density and localization properties of
monopoles, their non-Abelian action and topological charge are studied. Results
are presented confirming the Abelian dominance with respect to the
non-perturbative static potential for all gauges considered.


title: Non-perturbative Renormalization Constants using Ward Identities

abstract:
  We extend the application of axial Ward identities to calculate $b_A, b_P$
and $b_T$, coefficients that give the mass dependence of the renormalization
constants of the corresponding bilinear operators in the quenched theory. The
extension relies on using operators with non-degenerate quark masses. It allows
a complete determination of the O(a) improvement coefficients for bilinears in
the quenched approximation using Ward Identities alone. Only the scale
dependent normalization constants $Z_P^0$ (or $Z_S^0$) and $Z_T$ are
undetermined. We present results of a pilot numerical study using hadronic
correlators.


title: Quenched Light Hadron Spectrum

abstract:
  We present results of a large-scale simulation for the flavor non-singlet
light hadron spectrum in quenched lattice QCD with the Wilson quark action.
Hadron masses are calculated at four values of lattice spacing in the range $a
\approx$ 0.1 - 0.05 fm on lattices with a physical extent of 3 fm at five quark
masses corresponding to $m_\pi/m_\rho \approx 0.75$ - 0.4. The calculated
spectrum in the continuum limit shows a systematic deviation from experiment,
though the magnitude of deviation is contained within 11%. Results for decay
constants and light quark masses are also reported.


title: Latest results from lattice QCD for exotic hybrid mesons

abstract:
  I review the results from lattice gauge theory for the masses of exotic
hybrid mesons.


title:
Vacuum structure of gauge theory on lattice with two parallel plaquette
  action

abstract:
  We perform Monte Carlo simulations of a lattice gauge system with an action
which contains two parallel plaquettes. The action is defined as a product of
gauge group variables over two parallel plaquettes belonging to a given
three-dimensional cube. The peculiar property of this system is that it has
strong degeneracy of the vacuum state inherited from corresponding gonihedric
$Z_2$ gauge spin system. These vacuua are well separated and can not be
connected by a gauge transformation. We measure different observables in these
vacuua and compare their properties.


title:
Mass spectrum and elastic scattering in the massive SU(2)_f Schwinger
  model on the lattice

abstract:
  We calculate numerically scattering phases for elastic meson-meson scattering
processes in the strongly coupled massive Schwinger-model with an SU(2) flavour
symmetry. These calculations are based on Luescher's method in which finite
size effects in two-particle energies are exploited. The results from
Monte-Carlo simulations with staggered fermions for the lightest meson ("pion")
are in good agreement with the analytical strong-coupling prediction.
Furthermore, the mass spectrum of low-lying mesonic states is investigated
numerically. We find a surprisingly rich spectrum in the mass region [m_\pi,4
m_\pi].


title:
Pion mass and the PCAC relation in the overlap fermion formalism: Gauged
  Gross-Neveu model on a lattice

abstract:
  We investigate chiral properties of the overlap lattice fermion by using
solvable model in two dimensions, the gauged Gross-Neveu model. In this model,
the chiral symmetry is spontaneously broken in the presence of small but finite
fermion mass. We calculate the quasi-Nambu-Goldstone(NG) boson mass as a
function of the bare fermion mass and two parameters in the overlap formula. We
find that the quasi-NG boson mass has desired properties as a result of the
extended chiral symmetry found by L\"uscher. We also examine the PCAC relation
and find that it is satisfied in the continuum limit. Comparison between the
overlap and Wilson lattice fermions is made.


title:
Determination of Anisotropy Coefficients for SU(3) Gauge Actions from
  the Integral and Matching Methods

abstract:
  We use two non-perturbative methods to obtain the anisotropy derivatives of
the coupling constants (the anisotropy coefficients) of SU(3) lattice gauge
theory. These coefficients appear in the derivative formulae for the energy
density and the pressure. We calculate them for the standard Wilson and two
improved actions, the 2x2 and the Square Symanzik action. Both methods lead for
all investigated actions to compatible results which are clearly different from
their known asymptotic perturbative limits. With increasing beta the limits are
however approached in all cases. Our findings strongly support the equivalence
of the integral and derivative methods for the calculation of energy density
and pressure.


title:
A lattice implementation of the eta-invariant and effective action for
  chiral fermions on the lattice

abstract:
  We consider a lattice implementation of the eta-invariant, using the complex
phase of the determinant of the simplified domain-wall fermion, which couples
to an interpolating five-dimensional gauge field. We clarify the relation to
the effective action for chiral Ginsparg-Wilson fermions. The integrability,
which holds true for anomaly-free theories in the classical continuum limit, is
not assured on the lattice with a finite spacing. A lattice expression for the
five-dimensional Chern-Simons term is obtained.


title: The non-perturbative QCD Debye mass from a Wilson line operator

abstract:
  According to a proposal by Arnold and Yaffe, the non-perturbative
g^2T-contribution to the Debye mass in the deconfined QCD plasma phase can be
determined from a single Wilson line operator in the three-dimensional pure
SU(3) gauge theory. We extend a previous SU(2) measurement of this quantity to
the physical SU(3) case. We find a numerical coefficient which is more accurate
and smaller than that obtained previously with another method, but still very
large compared with the naive expectation: the correction is larger than the
leading term up to T ~ 10^7 T_c, corresponding to g^2 ~ 0.4. At moderate
temperatures T ~ 2 T_c, a consistent picture emerges where the Debye mass is
m_D ~ 6T, the lightest gauge invariant screening mass in the system is ~ 3T,
and the purely magnetic operators couple dominantly to a scale ~ 6T. Electric
(~ gT) and magnetic (~ g^2T) scales are therefore strongly overlapping close to
the phase transition, and the colour-electric fields play an essential role in
the dynamics.


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

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


title: Discretisation Errors in Landau Gauge on the Lattice

abstract:
  Lattice discretisation errors in the Landau gauge condition are examined. An
improved gauge fixing algorithm in which ${\cal O}(a^2)$ errors are removed is
presented. ${\cal O}(a^2)$ improvement of the gauge fixing condition improves
comparison with continuum Landau gauge in two ways: 1) through the elimination
of ${\cal O}(a^2)$ errors and 2) through a secondary effect of reducing the
size of higher-order errors. These results emphasise the importance of
implementing an improved gauge fixing condition.


title: A dual view of the 3d Heisenberg model and the abelian projection

abstract:
  The Heisenberg model in 3d is studied from a dual point of view. It is shown
that it can have vortex configurations, carrying a conserved charge(U(1)
symmetry). Vortices condens in the disordered phase. A disorder parameter
$\leftangle\mu\rightangle$ is defined dual to the magnetization $\leftangle\vec
n\rightangle$, which signals condensation of vortices, i.e. spontaneous
breaking of the dual U(1) symmetry. This study sheds light on the procedure
known as abelian projection in non abelian gauge theories.


title: Thermodynamics with Dynamical Clover Fermions

abstract:
  We investigate the finite temperature behavior of nonperturbatively improved
clover fermions on lattices with temporal extent N_t=4 and 6. Unfortunately in
the gauge coupling range, where the clover coefficient has been determined
nonperturbatively, the finite temperature crossover/transition occurs at heavy
pseudoscalar masses and large pseudoscalar to vector meson mass ratios.
However, on an N_t=6 lattice the thermal crossover for the improved fermions is
much smoother than for unimproved Wilson fermions and no strange metastable
behavior is observed.


title: Vortex percolation and confinement

abstract:
  The vortex state which arises from a projection of SU(2) to $Z_2$ gauge
theory is studied at finite temperatures with a special emphasis on the
deconfinement phase transition.


title: Dirac operator normality and chiral properties on the lattice

abstract:
  Normality in connection with $\gamma_5$-hermiticity determines the basic
chiral properties and rules. The Ginsparg-Wilson (GW) relation is one of the
allowed constraints on the spectrum. Interrelations between features of the
spectrum, the sum rule for chiral differences of real modes and contributions
to the Ward identity are pointed out. The alternative chiral transformation of
L\"uscher gives the same Ward identity as the usual one, in the global and in
the local case. Imposing normality on a general function of the hermitean
Wilson-Dirac (HWD) operator, inevitably leads at the same time to the Neuberger
operator and to the GW relation. In this context also the case with zero
eigenvalues of the HWD operator is handled. The eigenvalue flows of the HWD
operator obey a differential equation the characteristic features of the
solutions of which are discussed.


title: The Phase Diagram of 2 flavour QCD with improved Actions

abstract:
  It has been proposed, that the chiral continuum limit of 2-flavour QCD with
Wilson fermions is brought about by a phase in which flavour and parity
symmetry are broken spontaneously at finite lattice spacing. At finite
temperature this phase should retract from the weak coupling limit to form 5
cusps. This scenario is studied with tree level Symanzik improved actions for
both gauge and fermion fields on lattices of size $8^3\times 4$ and $12^2\times
24\times 4$.


title:
Field Strength Correlators and Gluon Condensates at Finite Temperature
  from Renormalization Group Smoothing

abstract:
  We summarize recent attempts to extract characteristics of non-perturbative
vacuum structure from lattice measurements of the gauge invariant field
strength correlator. As an alternative to cooling, we propose to apply the
renormalization group (RG) smoothing method in lattice studies. For pure SU(2)
gauge theory we present magnetic and electric correlation lengths and
condensates related to various correlators over a temperature range of 0.7
T_{dec} < T < 1.9 T_{dec}


title: The quark-composites approach to QCD: The nucleon-pion interaction

abstract:
  We derive the pion-nucleon interaction in the framework of a new perturbative
approach to QCD, based on the use of quark composites as fundamental variables.
The composites with the quantum numbers of the nucleons are assumed as new
integration variables in the Berezin integral which defines the partition
function, while the composites with the quantum numbers of the chiral mesons
are replaced by auxiliary bosonic fields. The action is modified by the
addition of irrelevant operators which provide the kinetic terms for these
composites, and the quark action is treated as a perturbation. The resulting
expansion has the quark confinement built in. To first order we get the
pion-nucleon interaction of the Yukawa model.


title: Fermion decoupling and the axial anomaly on the lattice

abstract:
  By an explicit calculation of the continuum limit of the triangle graph
amplitude in lattice QED we show that in the axial Ward identity the ABJ
anomaly exactly cancels the pseudoscalar density term in the limit of infinite
fermion mass $m$. The result, a reflection of decoupling of the heavy fermion,
provides a convenient framework for computing the flavor-singlet or U(1) axial
anomaly in non-Abelian gauge theories on lattice. Our calculations on the
lattice are performed using Wilson fermions but the results are general.


title: Wilson Fermions on a Randomly Triangulated Manifold

abstract:
  A general method of constructing the Dirac operator for a randomly
triangulated manifold is proposed. The fermion field and the spin connection
live, respectively, on the nodes and on the links of the corresponding dual
graph. The construction is carried out explicitly in 2-d, on an arbitrary
orientable manifold without boundary. It can be easily converted into a
computer code. The equivalence, on a sphere, of Majorana fermions and Ising
spins in 2-d is rederived. The method can, in principle, be extended to higher
dimensions.


title: The Wrong Kind of Gravity

abstract:
  The KPZ formula shows that coupling central charge less than one spin models
to 2D quantum gravity dresses the conformal weights to get new critical
exponents, where the relation between the original and dressed weights depends
only on the central charge. At the discrete level the coupling to 2D gravity is
effected by putting the spin models on annealed ensembles of planar random
graphs or their dual triangulations, where the connectivity fluctuates on the
same time-scale as the spins.
  Since the sole determining factor in the dressing is the central charge, one
could contemplate putting a spin model on a quenched ensemble of 2D gravity
graphs with the ``wrong'' central charge. We might then expect to see the
critical exponents appropriate to the central charge used in generating the
graphs. In such cases the KPZ formula could be interpreted as giving a
continuous line of critical exponents which depend on this central charge. We
note that rational exponents other than the KPZ values can be generated using
this procedure for the Ising, tricritical Ising and 3-state Potts models.


title: A test of a new simulation algorithm for dynamical quarks

abstract:
  Some results of test runs on a $6^3\times 12$ lattice with Wilson quarks and
gauge group SU(2) for a previously proposed fermion algorithm by A. Slavnov are
presented.


title: Fermion-scalar interactions with domain wall fermions

abstract:
  Domain wall fermions are defined on a lattice with an extra direction the
size of which controls the chiral properties of the theory. When gauge fields
are coupled to domain wall fermions the extra direction is treated as an
internal flavor space. Here it is found that this is not the case for scalar
fields. Instead, the interaction takes place only along the link that connects
the boundaries of the extra direction. This reveals a richness in the way
different spin particles are coupled to domain wall fermions. As an
application, 4-Fermi models are studied using large N techniques and the
results are supported by numerical simulations with N=2. It is found that the
chiral properties of domain wall fermions in these models are good across a
large range of couplings and that a phase with parity-flavor broken symmetry
can develop for negative bare masses if the number of sites along the extra
direction is finite.


title: Finite temperature QCD in the quark-composites approach

abstract:
  We investigate QCD at finite temperature in the quark composites approach,
which is based on the use of quark composites with hadronic quantum numbers as
fundamental variables. We find that chiral symmetry restoration and quark
deconfinement are one and the same first order phase transition, whose critical
temperature, in a one loop approximation, is $T= 2\sqrt{\Omega}
\rho^{-2}m_{\pi}$, where $m_{\pi}$ is the pion mass, $\Omega=24$ the number of
up and down quark components, and $\rho$ a parameter of order 1 whose precise
value can be determined by the study of the pion-pion interaction.


title: Predictions of chiral random matrix theory and lattice QCD results

abstract:
  Chiral random matrix theory makes very detailed predictions for the spectral
correlations of the QCD Dirac operator, both in the bulk of the spectrum and
near zero virtuality. These predictions have been successfully tested in
lattice QCD simulations by several groups. Moreover, the domain of validity of
random matrix theory has been predicted theoretically and identified in lattice
data. In this talk, the current numerical evidence is reviewed.


title: Diquark Condensation in Dense Matter - A Lattice Perspective

abstract:
  We review efforts to study, using the methods of lattice field theory, the
phenomenon of diquark condensation via BCS pairing at a Fermi surface, which
has been proposed as a mechanism for color superconductivity in dense quark
matter. The particular models studied are the Gross-Neveu model and SU(2)
lattice gauge theory; in both cases evidence for superfluidity at high density
is presented. The behaviour expected for quarks in both fundamental and adjoint
representations of SU(2) is contrasted.


title: Lattice QCD at non-zero baryon number

abstract:
  We discuss the quenched limit of lattice QCD at non-zero baryon number
density. We find evidence for a mixed phase that becomes broader with
increasing baryon number. Although the action is explicitly Z(3) symmetric the
Polyakov loop expectation value becomes non-zero already in the low temperature
phase. It indicates that the heavy quark potential stays finite at large
distances, i.e. the string between static quarks breaks at non-zero baryon
number density already in the hadronic phase. This behaviour is validated by
calculating the heavy quark potential using Polyakov loop correlations.


title: Partial Flavor Symmetry Restoration for Chiral Staggered Fermions

abstract:
  We study the leading discretization errors for staggered fermions by first
constructing the continuum effective Lagrangian including terms of O(a^2), and
then constructing the corresponding effective chiral Lagrangian. The terms of
O(a^2) in the continuum effective Lagrangian completely break the SU(4) flavor
symmetry down to the discrete subgroup respected by the lattice theory. We
find, however, that the O(a^2) terms in the potential of the chiral Lagrangian
maintain an SO(4) subgroup of SU(4). It follows that the leading discretization
errors in the pion masses are SO(4) symmetric, implying three degeneracies
within the seven lattice irreducible representations. These predictions hold
also for perturbatively improved versions of the action. These degeneracies are
observed, to a surprising degree of accuracy, in existing data. We argue that
the SO(4) symmetry does not extend to the masses and interactions of other
hadrons (vector mesons, baryons, etc), nor to higher order in a^2. We show how
it is possible that, for physical quark masses of O(a^2), the new SO(4)
symmetry can be spontaneously broken, leading to a staggered analogue of the
Aoki-phase of Wilson fermions. This does not, however, appear to happen for
presently studied versions of the staggered action.


title: Transfer matrices and lattice fermions at finite density

abstract:
  I discuss the connection between the Hamiltonian and path integral approaches
for fermionic fields. I show how the temporal Wilson projection operators
appear naturally in a lattice action. I also carefully treat the insertion of a
chemical potential term.


title: Low-temperature expansion in link formulation. II

abstract:
  We extend our previous analysis to arbitrary two dimensional SU(N) principal
chiral model in a link formulation. A general expression for the second order
coefficient of fixed distance correlation function is given in terms of Green
functions. This coefficient is calculated for distance 1 and is proven to be
path independent. We also study the weak coupling expansion of the free energy
of one dimensional SU(N) model and explain why it is non-uniform in the volume.
Further, we investigate the contribution of holonomy operators to the
low-temperature expansion in two dimensions. All our results agree with the
conventional expansion. Nevertheless, we give some example which indicates that
the expansion in the link formulation can also suffer from ambiguities
previously found in the conventional perturbation theory.


title: Percolation properties of the 2D Heisenberg model

abstract:
  We analyze the percolation properties of certain clusters defined on
configurations of the 2--dimensional Heisenberg model. We find that, given any
direction \vec{n} in O(3) space, the spins almost perpendicular to \vec{n} form
a percolating cluster. This result gives indications of how the model can avoid
a previously conjectured Kosterlitz-Thouless phase transition at finite
temperature T.


title:
General Physics Motivations for Numerical Simulations of Quantum Field
  Theory

abstract:
  In this introductory article a brief description of Quantum Field Theories
(QFT) is presented with emphasis on the distinction between strongly and weakly
coupled theories. A case is made for using numerical simulations to solve QCD,
the regnant theory describing the interactions between quarks and gluons. I
present an overview of what these calculations involve, why they are hard, and
why they are tailor made for parallel computers. Finally, I try to communicate
the excitement amongst the practitioners by giving examples of the quantities
we will be able to calculate to within a few percent accuracy in the next five
years.


title: Chiral Fermions on the Lattice

abstract:
  The Overlap-Dirac operator provides a lattice regularization of massless
vector gauge theories with an exact chiral symmetry. Practical implementations
of this operator and recent results in quenched QCD using this Overlap-Dirac
operator are reviewed.


title: On P-vortices and the Gribov problem

abstract:
  We study the possible connection between centre vortices and P-vortices in
SU(2) gauge theory. After briefly recalling some essential properties of centre
vortices we point out that there is no known a priori connection between the
gauge dependent P-vortices and the gauge invariant centre vortices. We then
show by Monte Carlo simulations that the `centre projected physics' strongly
depends on the gauge copy from which the maximal centre gauge fixing is
started. This reveals the presence of Gribov problems, and casts some doubts on
the physical meaning of P-vortices, and should be further investigated.


title:
Z_2 Monopoles, Vortices and the Universality of the SU(2) Deconfinement
  Transition

abstract:
  We investigate the effect of $Z_2$ magnetic monopoles and vortices on the
finite temperature deconfinement phase transition in the fundamental - adjoint
SU(2) lattice gauge theory. In the limit of complete suppression of the $Z_2$
monopoles, the mixed action for the SU(2) theory in its Villain form is shown
to be self-dual under the exchange of the fundamental and adjoint couplings. By
further suppressing the $Z_2$ vortices we show that the extended model reduces
to the Wilson action with a modified coupling. The universality of the SU(2)
deconfinement phase transition with the Ising model is therefore expected to
remain intact in the entire plane of the fundamental-adjoint couplings in the
continuum limit. The self-duality arguments related to the suppression of $Z_2$
monopoles are also applicable to the Villain form of mixed action for the SU(N)
theory with $Z_{N}$ magnetic monopoles.


title: A lattice model with a theta term in three dimensions

abstract:
  We study a three-dimensional abelian lattice model in which the analogue of a
theta term can be defined. This term is defined by introducing a neutral scalar
field and its effect is to couple magnetic monopoles to the scalar field and
vortices to the gauge field. An interesting feature of this model is the
presence of an exact duality symmetry that acts on a three parameter space. It
is shown that this model has an interesting phase structure for non-zero values
of theta. In addition to the usual confinement and vortex phases there are
phases in which loops with composite charges condense. The presence of novel
point like excitations also alters the physical properties of the system.


title: What We Do Understand of Colour Confinement

abstract:
  The status of our understanding of confinement is reviewed. The evidence from
lattice is that monopole condensation, or dual superconductivity, is at work.
Confinement is an order-disorder transition. Different monopole species look
equivalent, indicating that the symmetry of the disordered phase is more
interesting that we understand.


title: A Noisy Monte Carlo Algorithm

abstract:
  We propose a Monte Carlo algorithm to promote Kennedy and Kuti's linear
accept/reject algorithm which accommodates unbiased stochastic estimates of the
probability to an exact one. This is achieved by adopting the Metropolis
accept/reject steps for both the dynamical and noise configurations. We test it
on the five state model and obtain desirable results even for the case with
large noise. We also discuss its application to lattice QCD with stochastically
estimated fermion determinants.


title: Hadronic Spectral Functions in Lattice QCD

abstract:
  QCD spectral functions of hadrons in the pseudo-scalar and vector channels
are extracted from lattice Monte Carlo data of the imaginary time Green's
functions. The maximum entropy method works well for this purpose, and the
resonance and continuum structures in the spectra are obtained in addition to
the ground state peaks.


title:
Two dimensional CP^2 Model with \theta-term and Topological Charge
  Distributions

abstract:
  Topological charge distributions in 2 dimensional CP^2 model with theta-term
is calculated. In strong coupling regions, topological charge distribution is
approximately given by Gaussian form as a function of topological charge and
this behavior leads to the first order phase transition at \theta=\pi. In weak
coupling regions it shows non-Gaussian distribution and the first order phase
transition disappears. Free energy as a function of \theta shows "flattening"
behavior at theta=theta_f<pi, when we calculate the free energy directly from
topological charge distribution. Possible origin of this flattening phenomena
is prensented.


title: B meson leptonic decay constant with quenched lattice NRQCD

abstract:
  We present a lattice NRQCD study of the B meson decay constant in the
quenched approximation with emphasis given to the scaling behavior. The NRQCD
action and the heavy-light axial current we use include all terms of order 1/M
and the perturbative $O(\alpha_s a)$ and $O(\alpha_s/M)$ corrections. Using
simulations at three value of couplings $\beta$=5.7, 5.9 and 6.1 on lattices of
size $12^3\times 32, 16^3\times 48$ and $24^3\times 64$, we find no significant
$a$ dependence in $f_B$ if the $O(\alpha_s a)$ correction is included in the
axial current. We obtain $f_B = 167(7)(15)$ MeV, $f_{B_s}=
191(4)(17)(^{+4}_{-0})$ MeV and $f_{B_s}/f_B =1.15(3)(1)(^{+3}_{-0})$, with the
first error being statistical, the second systematic, and the third due to
uncertainty of strange quark mass, while quenching errors being not included.


title: On the I=2 channel pi-pi interaction in the chiral limit

abstract:
  An approximate local potential for the residual pi+ pi+ interaction is
computed. We use an O(a**2) improved action on a coarse 9x9x9x13 lattice with
approximately a=0.4fm. The results present a continuation of previous work:
Increasing the number of gauge configurations and quark propagators we attempt
extrapolation of the pi+ pi+ potential to the chiral limit.


title: Exploring the pi+ pi+ interaction in lattice QCD

abstract:
  An effective residual interaction for a meson-meson system is computed in
lattice QCD. We describe the theoretical framework and present its application
to the I=2 channel S-wave interaction of the pi pi system. Scattering phase
shifts are also computed and compared to experimental results.


title: Potential between adjoint sources in arbitrary representations

abstract:
  The potential between sources in arbitrary representations of the gauge group
is studied on an anisotropic lattice in a spherical model approximation. It is
shown analytically that for half-integer $j$ and $j'$ in the confinement phase
the potential rises linearly, whereas for integer $j$ and half-integer $j'$ it
rises infinitely which means a strong suppression of the combination of such
states . For integer $j$ and $j'$ the potential shows Debay screening and
Coulomb behavior in the deconfinement phase >. It is also shown, that
$<\chi^{(j)}> \backsim <\chi>^{2j}$ when $<\chi> \gtrsim1$ and is in agreement
with the mean field theory prediction, and $<\chi^{(j)}> \backsim <\chi>$ for
$<\chi> \lesssim1$ which agrees with MC experiment. String tension
model-computed for sources invariant under center group transformations
demonstrates Casimir scaling in the intermediate distance regime and turns into
zero at large distances.


title: Considerations on Neuberger's operator

abstract:
  We discuss new approaches to the numerical implementation of Neuberger's
operator for lattice fermions and the possible use of block spin
transformations.


title: Dual Higgs Theory for Color Confinement in Quantum Chromodynamics

abstract:
  Based on the dual superconductor picture, we study the confinement phenomena
systematically, using the lattice QCD, the monopole-current dynamics and the
dual Ginzburg-Landau (DGL) theory. (1) We study the origin of abelian dominance
for the confinement force in the maximally abelian (MA) gauge in terms of the
gluon-field properties using the lattice QCD. In the MA gauge, the off-diagonal
gluon amplitude is strongly suppressed, and the off-diagonal gluon phase tends
to be random, according to the weakness of the constraint from the QCD action.
Within the random-variable approximation for the off-diagonal gluon phase, we
show the perimeter law of the off-diagonal gluon contribution to the Wilson
loop, i.e. abelian dominance for the string tension, in the semi-analytical
manner. (2) We study the QCD-monopole structure in terms of the gluon field,
using the lattice QCD in the MA gauge. Around the monopole, both abelian and
off-diagonal parts of the QCD action become large, however, due to the
cancellation between them, monopoles can appear in QCD without large cost of
the QCD action. (3) We derive a simple relation between the confinement force
and the monopole density by idealizing the monopole contribution to the Wilson
loop. (4) We study the monopole current dynamics. (5) We consider the
derivation of the DGL theory from the monopole ensemble. (6) We study the QCD
phase transition at finite temperatures in the DGL theory. (7) We apply the DGL
theory for the hadron-bubble formation in early Universe and quark-gluon-plasma
formation process in the ultra-relativistic heavy-ion collision.


title: Deconfinement and non-zero baryon density

abstract:
  I discuss a few issues related with deconfinement at finite baryon density by
considering lattice results for two colors QCD and ``toy'' studies of three
colors QCD.


title: Fermion determinant and chiral anomaly on a finite lattice

abstract:
  The fermion determinant and the chiral anomaly of lattice Dirac operator D on
a finite lattice are investigated. The condition for D to reproduce correct
chiral anomaly at each site of a finite lattice for smooth background gauge
fields is that D possesses exact zero modes satisfying the Atiyah-Singer index
theorem. This is also the necessary condition for D to have correct fermion
determinant (ratio) which plays the important role of incorporating dynamical
fermions in the functional integral. We outline a scheme for dynamical fermion
simulation of lattice QCD with topologically proper D.


title: The Phase Diagram of the Three Dimensional Thirring Model

abstract:
  We present Monte Carlo simulation results for the three dimensional Thirring
model on moderate sized lattices using a hybrid molecular dynamics algorithm
which permits an odd or non-integer number Nf of fermion flavors. We find a
continuous chiral symmetry breaking transition for Nf approximately equal to 3
with critical exponents consistent with expectations from previous studies. For
Nf=5 the order of the transition is difficult to determine on the lattice sizes
explored. We present a phase diagram for the model in the (1/g^2,Nf) plane and
contrast our findings with expectations based on approximate solutions of the
continuum Schwinger-Dyson equations.


title: Alpha_S from Upsilon Spectroscopy with Dynamical Wilson Fermions

abstract:
  We estimate the QCD coupling constant from a lattice calculation of the
bottomonium spectrum. The second order perturbative expansion of the plaquette
expectation value is employed to determine alpha_S at a scale set by the 2S-1S
and 1P-1S level splittings. The latter are computed in NRQCD in a dynamical
gauge field background with two degenerate flavours of Wilson quarks at
intermediate masses and extrapolated to the chiral limit. Combining the N_f=2
result with the quenched result at equal lattice spacing we extrapolate to the
physical number of light flavours to find a value of alpha_{\bar MS}^{(5)}(m_Z)
= 0.1118(17). The error quoted covers both statistical and systematic
uncertainties in the scale determination. An additional 5% uncertainty comes
from the choice of the underlying sea quark formulation and from truncation
errors in perturbative expansions.


title:
Study of SU(3) vortex-like configurations with a new maximal center
  gauge fixing method

abstract:
  We present a new way of fixing the gauge to (direct) maximal center gauge in
SU(N) Yang-Mills theory and apply this method to SU(3) configurations which are
vortex-like. We study the structure of the Z_3 configurations obtained after
center-projecting the SU(3) ones.


title: Magnetic field on lattice U(1)-Higgs and SU(2)xU(1)-Higgs theories

abstract:
  External (hyper)magnetic field can modify the phase structure in U(1)
gauge+Higgs (Landau-Ginzburg) and SU(2)xU(1) gauge+Higgs (Standard Model)
theories. In this talk I discuss how the magnetic field can be implemented on
the lattice, and summarize the effects on symmetry breaking phase transitions.


title:
Four-loop free energy for the 2D O(n) nonlinear sigma-model with 0-loop
  and 1-loop Symanzik improved actions

abstract:
  We calculate up to four loops the free energy of the two-dimensional (2D)
O(n) nonlinear sigma-model regularized on the lattice with the 0-loop and
1-loop Symanzik improved actions. An effective coupling constant based on this
calculation is defined.


title: Precision computation of the strange quark's mass in quenched QCD

abstract:
  We determine the renormalization group invariant quark mass corresponding to
the sum of the strange and the average light quark mass in the quenched
approximation of QCD, using as essential input the mass of the K-mesons. In the
continuum limit we find $(M_s + M_{light})/F_K=0.874(29)$, which includes
systematic errors. Translating this non-perturbative result into the running
quark masses in the $\msbar$-scheme at $\mu=2 GeV$ and using the quark mass
ratios from chiral perturbation theory, we obtain $\mbar_s(2 GeV)=97(4) MeV$.
With the help of recent results by the CP-PACS Collaboration, we estimate that
a 10% higher value would be obtained if one replaced $F_K$ by the nucleon mass
to set the scale. This is a typical ambiguity in the quenched approximation.


title:
Four-loop contributions to long-distance quantities in the
  two-dimensional nonlinear sigma-model on a square lattice: revised numerical
  estimates

abstract:
  We give the correct analytic expression of a finite integral appearing in the
four-loop computation of the renormalization-group functions for the
two-dimensional nonlinear sigma-model on the square lattice with standard
action, explaining the origin of a numerical discrepancy. We revise the
numerical expressions of Caracciolo and Pelissetto for the perturbative
corrections of the susceptibility and of the correlation length. For the values
used in Monte Carlo simulations, N=3, 4, 8, the second perturbative correction
coefficient of the correlation length varies by 3%, 4%, 3% respectively. Other
quantities vary similarly.


title:
Non-commutative Differential Calculus and the Axial Anomaly in Abelian
  Lattice Gauge Theories

abstract:
  The axial anomaly in lattice gauge theories has a topological nature when the
Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial
anomaly in Abelian gauge theories on an infinite hypercubic lattice by
utilizing cohomological arguments. The crucial tool in our approach is the
non-commutative differential calculus~(NCDC) which makes the Leibniz rule of
exterior derivatives valid on the lattice. The topological nature of the
``Chern character'' on the lattice becomes manifest in the context of NCDC. Our
result provides an algebraic proof of L\"uscher's theorem for a
four-dimensional lattice and its generalization to arbitrary dimensions.


title: Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions

abstract:
  Axial anomaly of lattice abelian gauge theory in hyper-cubic regular lattice
in arbitrary even dimensions is investigated by applying the method of exterior
differential calculus. The topological invariance, gauge invariance and
locality of the axial anomaly determine the explicit form of the topological
part. The anomaly is obtained up to a multiplicative constant for finite
lattice spacing and can be interpreted as the Chern character of the abelian
lattice gauge theory.


title: Two dimensional lattice Gross--Neveu model with domain-wall fermions

abstract:
  We investigate the two dimensional lattice Gross--Neveu model in large flavor
number limit using the domain-wall fermion formulation, as a toy model of
lattice QCD. We study nonperturbative behaviorn of the restoration of chiral
symmetry of the domain-wall fermions as the extent of the extra dimension
$(N_s)$ is increased to infinity. We find the the parity broken phase (Aoki
phase) for finite $N_s$, and study the phase diagram, which is related to the
mechanism of the chiral restoration in $N_s\to\infty$ limit. The continuum
limit is taken and $O(a)$ scaling violation of observables vanishes in
$N_s\to\infty$ limit. We also examine the systematic dependencies of
observables to the parameters.


title: Probing the quark-gluon plasma with a new Fermionic correlator

abstract:
  We present the first measurement of a new correlation function of Fermion
bilinears in finite temperature QCD with and without dynamical quarks in a
quantum number channel in which non-trivial correlations are known to be
present for purely gluonic operators. We find that the Fermion correlator
vanishes for $T \ge 3T_c/2$, in agreement with the expectation for weakly
interacting quarks in a quark-gluon plasma.


title:
Exponential corrections to low-temperature expansion of 2D non-abelian
  models

abstract:
  The thermodynamic limit of certain exponential corrections to the weak
coupling expansion of two-dimensional models is investigated. The expectation
values of operators contributing to the first order coefficient of the
low-temperature expansion of the free energy are calculated for the order
O(e^{-\beta}). They are proven to diverge logarithmically with the volume for
non-abelian models.


title:
Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical
  Potential

abstract:
  In quantum chromodynamics (QCD) at nonzero chemical potential, the
eigenvalues of the Dirac operator are scattered in the complex plane. Can the
fluctuation properties of the Dirac spectrum be described by universal
predictions of non-Hermitian random matrix theory? We introduce an unfolding
procedure for complex eigenvalues and apply it to data from lattice QCD at
finite chemical potential $\mu$ to construct the nearest-neighbor spacing
distribution of adjacent eigenvalues in the complex plane. For intermediate
values of $\mu$, we find agreement with predictions of the Ginibre ensemble of
random matrix theory, both in the confinement and in the deconfinement phase.


title:
Meron-Cluster Simulation of a Chiral Phase Transition with Staggered
  Fermions

abstract:
  We examine a (3+1)-dimensional model of staggered lattice fermions with a
four-fermion interaction and Z(2) chiral symmetry using the Hamiltonian
formulation. This model cannot be simulated with standard fermion algorithms
because those suffer from a very severe sign problem. We use a new fermion
simulation technique - the meron-cluster algorithm - which solves the sign
problem and leads to high-precision numerical data. We investigate the finite
temperature chiral phase transition and verify that it is in the universality
class of the 3-d Ising model using finite-size scaling.


title: Monte Carlo simulation of systems with complex-valued measures

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


title: Screening Masses in SU(2) Pure Gauge Theory

abstract:
  We perform a systematic scaling study of screening masses in pure gauge SU(2)
theory at temperatures above the phase transition temperature. The major finite
volume effect is seen to be spatial deconfinement. We extract the screening
masses in the infinite volume and zero lattice spacing limit. We find that
these physical results can be deduced from runs on rather coarse lattices.
Dimensional reduction is clearly seen in the spectrum.