title:
Adjoint "quarks" on coarse anisotropic lattices: Implications for string
  breaking in full QCD

abstract:
  A detailed study is made of four dimensional SU(2) gauge theory with static
adjoint ``quarks'' in the context of string breaking. A tadpole-improved action
is used to do simulations on lattices with coarse spatial spacings $a_s$,
allowing the static potential to be probed at large separations at a
dramatically reduced computational cost. Highly anisotropic lattices are used,
with fine temporal spacings $a_t$, in order to assess the behavior of the
time-dependent effective potentials. The lattice spacings are determined from
the potentials for quarks in the fundamental representation. Simulations of the
Wilson loop in the adjoint representation are done, and the energies of
magnetic and electric ``gluelumps'' (adjoint quark-gluon bound states) are
calculated, which set the energy scale for string breaking. Correlators of
gauge-fixed static quark propagators, without a connecting string of spatial
links, are analyzed. Correlation functions of gluelump pairs are also
considered; similar correlators have recently been proposed for observing
string breaking in full QCD and other models. A thorough discussion of the
relevance of Wilson loops over other operators for studies of string breaking
is presented, using the simulation results presented here to support a number
of new arguments.


title:
One-Loop Self Energy and Renormalization of the Speed of Light for some
  Anisotropic Improved Quark Actions

abstract:
  One-loop corrections to the fermion rest mass M_1, wave function
renormalization Z_2 and speed of light renormalization C_0 are presented for
lattice actions that combine improved glue with clover or D234 quark actions
and keep the temporal and spatial lattice spacings, a_t and a_s, distinct. We
explore a range of values for the anisotropy parameter \chi = a_s/a_t and treat
both massive and massless fermions.


title: Strings and Branes in Nonabelian Gauge Theory

abstract:
  It is an old speculation that SU(N) gauge theory can alternatively be
formulated as a string theory. Recently this subject has been revived, in the
wake of the discovery of D-branes. In particular, it has been argued that at
least some conformally invariant cousins of the theory have such a string
representation. This is a pedagogical introduction to these developments for
non-string theorists. Some of the existing arguments are simplified.


title: Insight into the Scalar Mesons from a Lattice Calculation

abstract:
  We study the possibility that the light scalar mesons are (qbar qbar q q)
states rather than (qbar q). We perform a lattice QCD calculation of
pseudoscalar meson scattering amplitudes, ignoring quark loops and quark
annihilation, and find indications that for sufficiently heavy quarks there is
a stable four-quark bound state with J^{PC}=0^{++} and non-exotic flavor
quantum numbers.


title: Regularization and Anomalies in Gauge Theory

abstract:
  Some of the basic issues related to the regularization and anomalies in gauge
theory are reviewed, with particular emphasis on the recent development in
lattice gauge theory. The generalized Pauli-Villars regularization is discussed
from a view point of the covariant regularization of currents, and the
construction of a regularized effective action in terms of covariant currents
is compared with the lattice formulation of chiral Abelian theory.


title: Global Anomalies in chiral gauge theories on the lattice

abstract:
  We discuss the issue of global anomalies in chiral gauge theories on the
lattice. In Luscher's approach, these obstructions make it impossible to define
consistently a fermionic measure for the path integral. We show that an SU(2)
theory has such a global anomaly if the Weyl fermion is in the fundamental
representation. The anomaly in higher representations is also discussed. We
finally show that this obstruction is the lattice analogue of the SU(2) anomaly
first discovered by Witten.


title: Chiral condensate in the quenched Schwinger model

abstract:
  A numerical investigation of the quenched Schwinger model on the lattice
using the overlap Dirac operator points to a divergent chiral condensate.


title:
Topology in 2D CP**(N-1) models on the lattice: a critical comparison of
  different cooling techniques

abstract:
  Two-dimensional CP**(N-1) models are used to compare the behavior of
different cooling techniques on the lattice. Cooling is one of the most
frequently used tools to study on the lattice the topological properties of the
vacuum of a field theory. We show that different cooling methods behave in an
equivalent way. To see this we apply the cooling methods on classical
instantonic configurations and on configurations of the thermal equilibrium
ensemble. We also calculate the topological susceptibility by using the cooling
technique.


title: Towards a Many-Body Treatment of Hamiltonian Lattice SU(N) Gauge Theory

abstract:
  We develop a consistent approach to Hamiltonian lattice gauge theory, using
the maximal-tree gauge. The various constraints are discussed and implemented.
An independent and complete set of variables for the colourless sector is
determined. A general scheme to construct the eigenstates of the electric
energy operator using a symbolic method is described. It is shown how the
one-plaquette problem can be mapped onto a N-fermion problem. Explicit
solutions for U(1), SU(2), SU(3), SU(4), and SU(5) lattice gauge theory are
shown.


title: Topological Charge of Lattice Abelian Gauge Theory

abstract:
  Configuration space of abelian gauge theory on a periodic lattice becomes
topologically disconnected by excising exceptional gauge field configurations.
It is possible to define a U(1) bundle from the nonexceptional link variables
by a smooth interpolation of the transition functions. The lattice analogue of
Chern character obtained by a cohomological technique based on the
noncommutative differential calculus is shown to give a topological charge
related to the topological winding number of the U(1) bundle.


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

abstract:
  In the previous paper we developed a strong-coupling expansion for the
lattice QCD with the overlap fermions and showed that L\"usher's "extended"
chiral symmetry is spontaneously broken in some parameter region of the overlap
fermions. In this paper, we obtain a low-energy effective action and show that
there exist quasi-Nambu-Goldsone bosons which are identified as the pions. The
pion field is a {\em nonlocal} composite field of quark and anti-quark even at
the strong-coupling limit because of the nonlocality of the overlap fermion
formalism and L\"usher's chiral symmetry. The pions become massless in the
limit of the vanishing bare-quark mass as it is desired.


title: Cost of Generalised HMC Algorithms for Free Field Theory

abstract:
  We study analytically the computational cost of the Generalised Hybrid Monte
Carlo (GHMC) algorithm for free field theory. We calculate the autocorrelation
functions of operators quadratic in the fields, and optimise the GHMC momentum
mixing angle, the trajectory length, and the integration stepsize. We show that
long trajectories are optimal for GHMC, and that standard HMC is much more
efficient than algorithms based on the Second Order Langevin (L2MC) or Kramers
Equation. We show that contrary to naive expectations HMC and L2MC have the
same volume dependence, but their dynamical critical exponents are z=1 and
z=3/2 respectively.


title: Review of Unquenched Results

abstract:
  One of the major frontiers of lattice field theory is the inclusion of light
fermions in simulations, particularly in pursuit of accurate, first principles
predictions from lattice QCD. With dedicated Teraflops-scale computers
currently simulating QCD, another step towards precision full QCD simulations
is underway. In addition to ongoing staggered and Wilson fermion simulations,
first results from full QCD with domain wall fermions are available. After some
discussion of work toward better algorithms, simulations completed to date will
be discussed.


title: The 1 Teraflops QCDSP computer

abstract:
  The QCDSP computer (Quantum Chromodynamics on Digital Signal Processors) is
an inexpensive, massively parallel computer intended primarily for simulations
in lattice gauge theory. Currently, two large QCDSP machines are in full-time
use: an 8,192 processor, 0.4 Teraflops machine at Columbia University and an
12,288 processor, 0.6 Teraflops machine at the RIKEN-BNL Research Center at
Brookhaven National Laboratory. We describe the design process, architecture,
software and current physics projects of these computers.


title:
The derivation of the dual superconductor theory from the Maximal Center
  projected SU(3) - gluodynamics

abstract:
  We consider the Center projected SU(3) gluodynamics and rewrite it as a dual
superconductor theory. The center monopole field plays the role of Higgs field
in the dual superconductor theory.
  The center monopole creation operator is constructed.


title:
Green's Function Monte Carlo study of correlation functions in the
  (2+1)D U(1) lattice gauge theory

abstract:
  A ``forward walking'' Quantum Monte Carlo (QMC) algorithm has been developed
to calculate correlation functions for the Hamiltonian lattice formulation of
U(1) Yang-Mills theory in (2+1) dimensions. It is shown that Wilson loops can
be calculated with high accuracy. Creutz ratios are used to determine the
string tension, which agrees with results from other approaches. Timelike
correlations are used to estimate the mass gaps, which agree with series
expansion results in the strong coupling regime.


title: New approximate solutions of the Ginsparg-Wilson equation - tests in 2-d

abstract:
  A new method for finding approximate solutions of the Ginsparg-Wilson
equation is tested in 2-d. The Dirac operator is first constructed and then
used in a dynamical simulation of the 2-flavor Schwinger model. We find a very
small mass of the pi-particle implying almost chirally symmetric fermions. The
generalization of our method to 4-d is straightforward.


title: The Pressure in 2, 2+1 and 3 Flavour QCD

abstract:
  We calculate the pressure in QCD with two and three light quarks on a lattice
of size 16^3x4 using tree level improved gauge and fermion actions. We argue
that for temperatures T > 2T_c systematic effects due to the finite lattice
cut-off and non-vanishing quark masses are below 15% in this calculation and
give an estimate for the continuum extrapolated pressure in QCD with massless
quarks. We find that the flavour dependence of the pressure is dominated by
that of the Stefan-Boltzmann constant. Furthermore we perform a calculation of
the pressure using 2 light (m_u,d/T=0.4) and one heavier quark (m_s/T = 1). In
this case the pressure is reduced relative to that of three flavour QCD. This
effect is stronger than expected from the mass dependence of an ideal Fermi
gas.


title: Computation of the Vortex Free Energy in SU(2) Gauge Theory

abstract:
  We present the first measurement of the vortex free-energy order parameter at
weak coupling for SU(2) in simulations employing multihistogram methods. The
result shows that the excitation probability for a sufficiently thick vortex in
the vacuum tends to unity. This is rigorously known to provide a necessary and
sufficient condition for maintaining confinement at weak coupling in SU(N)
gauge theories.


title: On the topological structure of the QCD vacuum

abstract:
  A review of results from lattice studies using improved and scale controlled
cooling methods is presented and their significance is discussed. The
improvement of the action ensures stable instanton solutions of physical sizes.
The scale controlled cooling can be generally used as a gauge invariant low
pass filter to extract the physics from noisy MC configurations; in particular
it preserves instanton-antiinstanton pairs selected according to their
interaction. We apply these methods to analyze various features of the
topological structure of the Yang-Mills vacuum in a scaling invariant way.


title: A Quantum Perfect Lattice Action for Monopoles and Strings

abstract:
  A quantum perfect lattice action in four dimensions can be derived
analytically as a renormalized trajectory when we perform a block spin
transformation of monopole currents in a simple but non-trivial case of
quadratic monopole interactions. The spectrum of the lattice theory is
identical to that of the continuum theory. The perfect monopole action is
transformed exactly into a lattice action of a string model. A perfect operator
evaluating a static potential between electric charges is also derived
explicitly. If the monopole interactions are weak as in the case of infrared
SU(2) QCD, the string interactions become strong. The static potential and the
string tension is estimated analytically by the use of the strong coupling
expansion and the continuum rotational invariance is restored completely.


title: NNLO Unquenched Calculation of the b Quark Mass

abstract:
  By combining the first unquenched lattice computation of the B-meson binding
energy and the two-loop contribution to the lattice HQET residual mass, we
determine the (\bar{{MS}}) (b)-quark mass, (\bar{m}_{b}(\bar{m}_{b})). The
inclusion of the two-loop corrections is essential to extract
(\bar{m}_{b}(\bar{m}_{b})) with a precision of ({\cal
O}(\Lambda^{2}_{QCD}/m_{b})), which is the uncertainty due to the renormalon
singularities in the perturbative series of the residual mass. Our best
estimate is (\bar{m}_{b}(\bar{m}_{b}) = (4.26 \pm 0.09) {\rm GeV}), where we
have combined the different errors in quadrature. A detailed discussion of the
systematic errors contributing to the final number is presented. Our results
have been obtained on a sample of (60) lattices of size (24^{3}\times 40) at
(\beta =5.6), using the Wilson action for light quarks and the lattice HQET for
the (b) quark, at two values of the sea quark masses. The quark propagators
have been computed using the unquenched links generated by the T(\chi)L
Collaboration.


title:
Application of heavy-quark effective theory to lattice QCD: I. Power
  Corrections

abstract:
  Heavy-quark effective theory (HQET) is applied to lattice QCD with Wilson
fermions at fixed lattice spacing a. This description is possible because
heavy-quark symmetries are respected. It is desirable because the ultraviolet
cutoff $1/a$ in current numerical work and the heavy-quark mass $m_Q$ are
comparable. Effects of both short distances, a and $1/m_Q$, are captured fully
into coefficient functions, which multiply the operators of the usual HQET.
Standard tools of HQET are used to develop heavy-quark expansions of lattice
observables and, thus, to propagate heavy-quark discretization errors. Three
explicit examples are given: namely, the mass, decay constant, and semileptonic
form factors of heavy-light mesons.


title: Anomaly Cancellation Condition in Lattice Gauge Theory

abstract:
  We study the gauge anomaly ${\cal A}$ defined on a 4-dimensional infinite
lattice while keeping the lattice spacing finite. We assume that (I) ${\cal A}$
depends smoothly and locally on the gauge potential, (II) ${\cal A}$ reproduces
the gauge anomaly in the continuum theory in the classical continuum limit, and
(III) U(1) gauge anomalies have a topological property. It is then shown that
the gauge anomaly ${\cal A}$ can always be removed by local counterterms to all
orders in powers of the gauge potential, leaving possible breakings
proportional to the anomaly in the continuum theory. This follows from an
analysis of nontrivial local solutions to the Wess-Zumino consistency condition
in lattice gauge theory. Our result is applicable to the lattice chiral gauge
theory based on the Ginsparg-Wilson Dirac operator, when the gauge field is
sufficiently weak $\|U(n,\mu)-1\|<\epsilon'$, where $U(n,\mu)$ is the link
variable and $\epsilon'$ a certain small positive constant.


title:
One-loop renormalization of fermionic currents with the overlap-Dirac
  operator

abstract:
  We compute the one-loop lattice renormalization of the two-quark operators
$\bar{\psi} \Gamma \psi$, where $\Gamma$ denotes the generic Dirac matrix, for
the lattice formulation of QCD using the overlap-Dirac operator.
  We also study the renormalization of quark bilinears which are more extended
and have better chiral properties.
  Finally, we present improved estimates of these renormalization constants,
coming from cactus resummation and from mean field perturbation theory.


title: Lattice monopole action in pure SU(3) QCD

abstract:
  We obtain an almost perfect monopole action numerically after abelian
projection in pure SU(3) lattice QCD. Performing block-spin transformations on
the dual lattice, the action fixed depends only on a physical scale b. Monopole
condensation occurs for large b region. The numerical results show that
two-point monopole interactions are dominant for large b. We next perform the
block-spin transformation analytically in a simplified case of two-point
monopole interactions with a Wilson loop on the fine lattice. The perfect
operator evaluating the static quark potential on the coarse b-lattice are
derived. The monopole partition function can be transformed into that of the
string model. The static potential and the string tension are estimated in the
string model framework. The rotational invariance of the static potential is
recovered, but the string tension is a little larger than the physical one.


title: Quasi-asymptotic freedom in the two dimensional O(3) model

abstract:
  The behaviour of the renormalized spin 2-point function in the O(3) and
dodecahedron spin model are investigated numerically. The Monte Carlo data show
excellent agreement between the two models. The short distance behavior comes
very close to standard theoretical expectations, yet it differs significantly
from it. A possible explanation of this situation is offered.


title: Quenched QCD near the chiral limit

abstract:
  A numerical study of quenched QCD for light quarks is presented using O(a)
improved fermions. Particular attention is paid to the possible existence and
determination of quenched chiral logarithms. A `safe' region to use for chiral
extrapolations appears to be at and above the strange quark mass.


title:
Reply to A. Patrascioiu's and E. Seiler's Comment on our paper
  "Percolation properties of the 2D Heisenberg model"

abstract: Reply to comment appeared on hep-lat/9912014.


title: Recursive sampling simulations of 3D gravity coupled to scalar fermions

abstract:
  We study numerically the phase structure of a model of 3D gravity interacting
with scalar fermions. We measure the 3D counterpart of the "string"
susceptibility exponent as a function of the inverse Newton coupling $\alpha$.
We show that there are two phases separated by a critical point around
$\alpha_c \simeq 2$. The numerical results support the hypothesis that the
phase structures of 3D and 2D simplicial gravity are qualitatively similar, the
inverse Newton coupling in 3D playing the role of the central charge of matter
in 2D.


title: The masses of the mesons and baryons. Part II. The Standing Wave Model

abstract:
  In order to explain the empirical integer multiple rule for the stable mesons
and baryons presented in the preceding paper we assume that the particles are
held together in a cubic nuclear lattice. This is a novel approach to the
particles, based on the fact that the range of the weak nuclear force is only a
thousandth of the diameter of the nucleon, and that the crystals are the
best-known macroscopic bodies held together by a microscopic force. We
investigate the standing waves in a cubic nuclear lattice. From the frequency
distribution of the waves follows that the masses of the $\gamma$-branch
particles are integer multiples of $m(\pi^0)$. We show that each particle has
automatically an antiparticle. Assuming that the energy of the oscillations is
determined by Planck's formula for the energy of a linear oscillator, it turns
out that the $\pi^0$ meson and the other members of the $\gamma$-branch are
like cubic black bodies filled with plane, standing electromagnetic waves. Our
standing wave model explains the integer multiple rule of the masses of the
neutral mesons and baryons of the $\gamma$-branch and uses nothing else but
photons. Our results justify the cubic lattice assumption.


title: P-vortices, nexuses and effects of gauge copies

abstract:
  We perform the careful study of the gauge copies problem for the direct
center projection in SU(2) lattice gauge theory. Our results indicate that this
gauge is not appropriate for the investigation of the center vortices. We also
show that the point-like objects, nexuses, are important for the confinement
dynamics.


title:
Understanding stochastic perturbation theory: toy models and statistical
  analysis

abstract:
  The numerical stochastic perturbation method based on Parisi-Wu quantisation
is applied to a suite of simple models to test its validity at high orders.
Large deviations from normal distribution for the basic estimators are
systematically found in all cases (``Pepe effect''). As a consequence one
should be very careful in estimating statistical errors. We present some
results obtained on Weingarten's ``pathological'' model where reliable results
can be obtained by an application of the bootstrap method. We also present some
evidence that in the far less trivial application to Lattice Gauge Theory a
similar problem should not arise at moderately high loops (up to
O(\alpha^{10})).


title: Polarized structure functions from the lattice

abstract:
  We give a brief sketch of lattice structure function calculations and review
previous results for the axial coupling $g_A$. We outline a new technique for
treating fermions on the lattice that preserves chiral symmetry, domain wall
fermions. Finally, we give preliminary results for the nucleon spectrum using
this new technique. Remarkably, a large mass splitting between the $N$ and
$N^*$, roughly consistent with experiment, is produced in the calculation.
These results are encouraging for proposed calculations of nucleon structure
functions.


title: Infrared Behavior of the Gluon Propagator on a Large Volume Lattice

abstract:
  The first calculation of the gluon propagator using an order a^2 improved
action with the corresponding order a^2 improved Landau gauge fixing condition
is presented. The gluon propagator obtained from the improved action and
improved Landau gauge condition is compared with earlier unimproved results on
similar physical lattice volumes of 3.2^3 \times 6.4 fm^4. We find agreement
between the improved propagator calculated on a coarse lattice with lattice
spacing a = 0.35 fm and the unimproved propagator calculated on a fine lattice
with spacing a = 0.10 fm. This motivates us to calculate the gluon propagator
on a coarse large-volume lattice 5.6^3 \times 11.2 fm^4. The infrared behavior
of previous studies is confirmed in this work. The gluon propagator is enhanced
at intermediate momenta and suppressed at infrared momenta. Therefore the
observed infrared suppression of the Landau gauge gluon propagator is not a
finite volume effect.


title: CORE and the Haldane Conjecture

abstract:
  The Contractor Renormalization group formalism (CORE) is a real-space
renormalization group method which is the Hamiltonian analogue of the Wilson
exact renormalization group equations. In an earlier paper\cite{QGAF} I showed
that the Contractor Renormalization group (CORE) method could be used to map a
theory of free quarks, and quarks interacting with gluons, into a generalized
frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to
study these theories. Since generalizations of HAF's exhibit all sorts of
subtle behavior which, from a continuum point of view, are related to
topological properties of the theory, it is important to know that CORE can be
used to extract this physics. In this paper I show that despite the folklore
which asserts that all real-space renormalization group schemes are necessarily
inaccurate, simple Contractor Renormalization group (CORE) computations can
give highly accurate results even if one only keeps a small number of states
per block and a few terms in the cluster expansion. In addition I argue that
even very simple CORE computations give a much better qualitative understanding
of the physics than naive renormalization group methods. In particular I show
that the simplest CORE computation yields a first principles understanding of
how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1
HAF.


title: Isocliny in spinor space and Wilson fermions

abstract:
  We show that Clifford algebras are closely related to the study of isoclinic
subspaces of spinor spaces and, consequently, to the Hurwitz-Radon matrix
problem. Isocliny angles are introduced to parametrize gamma matrices, i.e.,
matrix representations of the generators of finite-dimensional Clifford
algebras C(m,n). Restricting the consideration to the Clifford algebra C(4,0),
this parametrization is then applied to the study of Dirac traces occurring in
Euclidean lattice quantum field theory within the hopping parameter expansion
for Wilson fermions.


title: Domain-Wall Induced Quark Masses in Topologically-Nontrivial Background

abstract:
  In the domain-wall formulation of chiral fermion, the finite separation
between domain-walls ($L_s$) induces an effective quark mass ($m_{\rm eff}$)
which complicates the chiral limit. In this work, we study the size of the
effective mass as the function of $L_s$ and the domain-wall height $m_0$ by
calculating the smallest eigenvalue of the hermitian domain-wall Dirac operator
in the topologically-nontrivial background fields. We find that, just like in
the free case, $m_{\rm eff}$ decreases exponentially in $L_s$ with a rate
depending on $m_0$. However, quantum fluctuations amplify the wall effects
significantly. Our numerical result is consistent with a previous study of the
effective mass from the Gell-Mann-Oakes-Renner relation.


title: The CP-PACS Project and Lattice QCD Results

abstract:
  The aim of the CP-PACS project was to develop a massively parallel computer
for performing numerical research in computational physics with primary
emphasis on lattice QCD. The CP-PACS computer with a peak speed of 614 GFLOPS
with 2048 processors was completed in September 1996, and has been in full
operation since October 1996. We present an overview of the CP-PACS project and
describe characteristics of the CP-PACS computer. The CP-PACS has been mainly
used for hadron spectroscopy studies in lattice QCD. Main results in lattice
QCD simulations are given.


title:
Mixing of B mesons and Decay Constants with the Non-Perturbatively
  Improved Action

abstract:
  Several quantities relevant to phenomenological studies of the mixing of
neutral B mesons are computed on the lattice. Our main results are: f_{Bd}
sqrt(B_{Bd})=206(28)(7) MeV, f_{Bs} sqrt(B_{Bs})/f_{Bd}sqrt(B_{Bd})=1.16(7). We
also obtain the related quantities f_{Bs}sqrt(B{Bs})=237(18)(8) MeV, f_{Bd}=
174(22)(+7-0)(-4-0) MeV, f_{Bs}= 204(15)(+7-0)(+3-0) MeV,
f_{Bs}/f_{Bd}=1.17(4)(+0-1), f_{Bd}/f_{Ds}=0.74(5). After combining our results
with the experimental world average (Delta m_d), we predict (Delta
m_s)=15.8(2.1)(3.3) ps^{-1}. We have also computed the relevant parameters for
mixing of neutral D mesons which may be useful in some extensions of the
Standard Model. All the quantities were obtained from a quenched simulation
with a non-perturbatively improved Clover action at beta=6.2, corresponding to
a lattice spacing 1/a=2.7(1) GeV, on a sample of 200 gauge-field
configurations. A discussion of the main systematic errors is also presented.


title: Chiral gauged fermions on a lattice

abstract:
  The chiral fermion model with local multifermion interactions proposed in
Nucl. Phys. B486 (1997) 282 and Phys. Rev. D61 (2000) 054502 processes an exact
SU_L(2) chiral gauge symmetry and SU_L(2) by U_R(1) chiral flavour symmetry on
a lattice and a plausible scaling region for the target chiral gauge theory in
the continuum limit. Following the previous analysis of massive and massless
fermion spectra in the scaling region, we compute the coupling vertices between
gauge field and fermions by the strong multifermion coupling expansion and
analytical continuation of these vertex functions in the energy-momentum space.
We show a peculiar scenario that a massless fermion is SU_L(2)-chirally gauged
in the low energy and 15 non-degenerate massive Dirac fermions are
SU_L(2)-vectorially gauged at the lattice scale O(1/a). The Ward identities
associated to the chiral gauge symmetry are realized by both the massless
chiral fermion and massive Dirac fermions. These Ward identities protect the
perturbative calculations in the small gauge coupling from hard gauge-symmetry
breakings and lead to the normal gauge-invariant renormalization prescription.
The vacuum functional is perturbatively computed by a continuum regularization
scheme in 16 edges of Brillouin zones. We achieve the correct form of the gauge
anomaly and U_L(1) fermion-flavour singlet anomaly with the soft chiral
symmetry breaking scale that is much smaller than the lattice scale. The
residual breakings of chiral gauge symmetry after the gauge anomaly
cancellation are eliminated in the normal gauge-invarinant renormalization
prescription. We discuss the consistency of the scenario and the reasons for it
to work for perturbative and non-perturbative gauge field.


title:
Monopole classical solutions and the vacuum structure in lattice gauge
  theories

abstract:
  Classical solutions corresponding to monopole-antimonopole pairs are found in
3d and 4d SU(2) and U(1) lattice gauge theories. The stability of these
solutions in different theories is studied.


title: The static quark potential in three flavor QCD

abstract:
  We study the effects of dynamical quarks on the static quark potential at
distances shorter than those where string breaking is expected. Quenched
calculations and calculations with three flavors of dynamical quarks are done
on sets of lattices with the lattice spacings matched within about one percent.
The effect of the sea quarks on the shape of the potential is clearly visible.
We investigate the consequences of these effects in a very crude model, namely
solving Schroedinger's equation in the resulting potential.


title: Improved Gauge Actions on Anisotropic Lattices I

abstract:
  On anisotropic lattices with the anisotropy $\xi=a_\sigma/a_\tau$ the
following basic parameters are calculated by perturbative method: (1) the
renormalization of the gauge coupling in spatial and temporal directions,
$g_\sigma$ and $g_\tau$, (2) the $\Lambda$ parameter, (3) the ratio of the
renormalized and bare anisotropy $\eta=\xi/\xi_B$ and (4) the derivatives of
the coupling constants with respect to $\xi$, $\partial g_\sigma^{-2}/\partial
\xi$ and $\partial g_\tau^{-2}/\partial \xi$. We employ the improved gauge
actions which consist of plaquette and six-link rectangular loops, $c_0 P(1
\times 1)_{\mu \nu} + c_1 P(1 \times 2)_{\mu \nu}$. This class of actions
covers Symanzik, Iwasaki and DBW2 actions. The ratio $\eta$ shows an impressive
behavior as a function of $c_{1}$, i.e.,$\eta>1$ for the standard Wilson and
Symanzik actions, while $\eta<1$ for Iwasaki and DBW2 actions. This is
confirmed non-perturbatively by numerical simulations in weak coupling regions.
The derivatives $\partial g^{-2}_{\tau}/\partial \xi$ and $\partial
g^{-2}_{\sigma}/\partial \xi$ also changes sign as $-c_{1}$ increases. For
Iwasaki and DBW2 actions they become opposite sign to those for standard and
Symanzik actions. However, their sum is independent of the type of actions due
to Karsch's sum rule.


title: Supersymmetric Yang-Mills Theories from Domain Wall Fermions

abstract:
  We present work in progress on employing domain wall fermions to simulate N=1
supersymmetric Yang-Mills theories on the lattice in d=4 and d=3 dimensions.
The geometrical nature of domain wall fermions gives simple insights into how
to construct these theories. We also discuss the obstacles associated with
simulating the N=2 theory in d=4.


title: Vortices in SO(3)xZ(2) simulations

abstract:
  We study the configuration space of the Tomboulis $SO(3) \times Z(2)$
formulation with periodic boundary conditions. The dynamical variables are
constrained by the required coincidence of Z(2) and SO(3) monopoles. We propose
an update algorithm that satisfies the constraints and is straightforward to
implement. We further prove that this it reaches all configurations. We show
how the boundary conditions put constraints on the configuration space.
  We measure gauge invariant vortex counters for "thin",
  "thick" and "hybrid" vortex sheets. For comparison we also measure projection
vortex counters defined in the maximal center gauge.


title: Noncompact chiral U(1) gauge theories on the lattice

abstract:
  A new, adiabatic phase choice is adopted for the overlap in the case of an
infinite volume, noncompact abelian chiral gauge theory. This gauge choice
obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in
addition, produces a Wess-Zumino functional that is linear in the gauge
variables on the lattice. As a result, there are no gauge violations on the
trivial orbit in all theories, consistent and covariant anomalies are simply
related and Berry's curvature now appears as a Schwinger term. The adiabatic
phase choice can be further improved to produce a perfect phase choice, with a
lattice Wess-Zumino functional that is just as simple as the one in continuum.
When perturbative anomalies cancel, gauge invariance in the fermionic sector is
fully restored. The lattice effective action describing an anomalous abelian
gauge theory has an explicit form, close to one analyzed in the past in a
perturbative continuum framework.


title: On the eta-invariant in the 4D chiral U(1) theory

abstract:
  In contrast to its counterpart in a vector theory, the effective action of a
chiral gauge theory may have a non-vanishing imaginary part. It consists of the
so-called Chern-Simons form, which encodes the anomaly and a gauge invariant
piece related to the eta-invariant of some extended Dirac operator. We
investigate the imaginary part of the effective action in the 4D chiral U(1)
theory within the continuum fermion approach. Perturbative analysis indicates
in general a non-vanishing imaginary part of the effective action. However,
after anomaly cancellation we find only a small value of the imaginary part for
the investigated configurations.


title:
Implementation of C* boundary conditions in the Hybrid Monte Carlo
  algorithm

abstract:
  In the study of QCD dynamics, C* boundary conditions are physically relevant
in certain cases. In this paper we study the implementation of these boundary
conditions in the lattice formulation of full QCD with staggered fermions. In
particular, we show that the usual even-odd partition trick to avoid the
redoubling of the fermion matrix is still valid in this case. We give an
explicit implementation of these boundary conditions for the Hybrid Monte Carlo
algorithm.


title:
Chiral symmetry restoration and axial vector renormalization for Wilson
  fermions

abstract:
  Lattice gauge theories with Wilson fermions break chiral symmetry. In the
U(1) axial vector current this manifests itself in the anomaly. On the other
hand it is generally expected that the axial vector flavour mixing current is
non-anomalous. We give a short, but strict proof of this to all orders of
perturbation theory, and show that chiral symmetry restauration implies a
unique multiplicative renormalization constant for the current. This constant
is determined entirely from an irrelevant operator in the Ward identity. The
basic ingredients going into the proof are the lattice Ward identity, charge
conjugation symmetry and the power counting theorem. We compute the
renormalization constant to one loop order. It is largely independent of the
particular lattice realization of the current.


title: High Temperature 3D QCD: Dimensional Reduction at Work

abstract:
  We investigate the three-dimensional SU(3) gauge theory at finite temperature
in the framework of dimensional reduction. The large scale properties of this
theory are expected to be conceptually more complicated than in four
dimensions. The dimensionally reduced action is computed in closed analytical
form. The resulting effective two-dimensional theory is studied numerically
both in the electric and magnetic sector. We find that dimensional reduction
works excellently down to temperatures of 1.5 times the deconfinement phase
transition temperature and even on rather short length scales. We obtain strong
evidence that for ${\rm QCD}_3$, even at high temperature the colour averaged
potential is represented by the exchange of a single state, at variance with
the usual Debye screening picture involving a pair of electric gluons.


title: A new approach to Ginsparg-Wilson fermions

abstract:
  We expand the most general lattice Dirac operator D in a basis of simple
operators. The Ginsparg-Wilson equation turns into a system of coupled
quadratic equations for the expansion coefficients. Our expansion of D allows
for a natural cutoff and the remaining quadratic equations can be solved
numerically. The procedure allows to find Dirac operators which obey the
Ginpsparg-Wilson equation with arbitrary precision.


title: Determinant of a new fermionic action on a lattice - (II)

abstract:
  We investigate the fermion determinant of a new action on a
$(1+D)$-dimensional lattice for SU(2) gauge groups. This action possesses the
discrete chiral symmetry and provides $2^D$-component fermions. We also comment
on the numerical results on fermion determinants in the $(1+D)$-dimensional
SU(3) gauge fields.


title: Perfect discretizations of differential operators

abstract:
  We investigate an approach for the numerical solution of differential
equations which is based on the perfect discretization of actions. Such perfect
discretizations show up at the fixed points of renormalization group
transformations. This technique of integrating out the high momentum degrees of
freedom with a path integral has been mainly used in lattice field theory,
therefore our study of its application to PDE's explores new possibilities. We
calculate the perfect discretized Laplace operator for several non-trivial
boundary conditions analytically and numerically. Then we construct a
parametrization of the perfect Laplace operator and we show that with this
parametrization discretization errors -- or computation time -- can be reduced
dramatically compared to the standard discretization.


title: Comment on hep-lat/9901005 v1-v3 by W. Bietenholz

abstract:
  I comment on the above paper(s) discussing the issue of non-ultralocality for
Ginsparg-Wilson fermionic actions. The purpose of this note is to point out
that the new claim in "v3" (Feb 24, 2000), alleging the proof for "all
Ginsparg-Wilson fermions", might not be substantiated. The remarkable evolution
of versions of this paper is put in context with the literature existing at the
time of their appearance.


title: Data storage issues in lattice QCD calculations

abstract:
  I describe some of the data management issues in lattice Quantum
Chromodynamics calculations. I focus on the experience of the UKQCD
collaboration. I describe an attempt to use a relational database to store part
of the data produced by a lattice QCD calculation.


title: Free energy of an SU(2) monopole-antimonopole pair

abstract:
  We present a high-statistic numerical study of the free energy of a
monopole-antimonopole pair in pure SU(2) theory. We find that the
monopole-antimonopole interaction potential exhibits a screened behavior, as
one would expect in presence of a monopole condensate. Screening occurs both in
the low-temperature, confining phase of the theory, and in the high-temperature
deconfined phase, with no evidence of a discontinuity of the screening mass
across the transition. The mass of the object responsible for the screening at
low temperature is approximately twice the established value for the lightest
glueball, indicating a prevalent coupling to glueball excitations. At high
temperature, the screening mass increases. We contrast the behavior of the
quantum system with that of the corresponding classical system, where the
monopole-antimonopole potential is of the Coulomb type.


title: S and P-wave heavy-light mesons in lattice NRQCD

abstract:
  The mass spectrum of S and P-wave mesons containing a single heavy quark is
computed in the quenched approximation, using NRQCD up to third order in the
inverse heavy quark mass expansion. Previous results found third order
contributions which are as large in magnitude as the total second order
contribution for the charmed S-wave spin splitting. The present work considers
variations such as anisotropic lattices, Landau link tadpole improvement, and a
highly-improved light quark action, and finds that the second order correction
to the charmed S-wave spin splitting is about 20% of the leading order
contribution, while the third order correction is about 20%(10%) for
D^*-D(D_s^*-D_s). Nonleading corrections are very small for the bottom meson
spectrum, and are statistically insignificant for the P-wave charmed masses.
The relative orderings among P-wave charmed and bottom mesons, and the sizes of
the mass splittings, are discussed in light of experimental data and existing
calculations.


title:
Static potentials and glueball masses from QCD simulations with Wilson
  sea quarks

abstract:
  We calculate glueball and torelon masses as well as the lowest lying hybrid
potential in addition to the static ground state potential in lattice
simulations of QCD with two flavours of dynamical Wilson fermions. The results
are obtained on lattices with $16^3\times 32$ and $24^3\times 40$ sites at
$\beta=5.6$, corresponding to a lattice spacing, $a^{-1}=2.65^{+5}_{-8}$ GeV,
as determined from the Sommer force radius, at physical sea quark mass. The
range spanned in the present study of five different quark masses is reflected
in the ratios, $0.83\geq m_{\pi}/m_{\rho}\geq 0.57$.


title: The construction of generalized Dirac operators on the lattice

abstract:
  We discuss the steps to construct Dirac operators which have arbitrary
fermion offsets, gauge paths, a general structure in Dirac space and satisfy
the basic symmetries (gauge symmetry, hermiticity condition, charge
conjugation, hypercubic rotations and reflections) on the lattice. We give an
extensive set of examples and offer help to add further structures.


title: Percolation and Magnetization in the Continuous Spin Ising Model

abstract:
  In the strong coupling limit the partition function of SU(2) gauge theory can
be reduced to that of the continuous spin Ising model with nearest neighbour
pair-interactions. The random cluster representation of the continuous spin
Ising model in two dimensions is derived through a Fortuin-Kasteleyn
transformation, and the properties of the corresponding cluster distribution
are analyzed. It is shown that for this model, the magnetic transition is
equivalent to the percolation transition of Fortuin-Kasteleyn clusters, using
local bond weights. These results are also illustrated by means of numerical
simulations.


title: Series expansions for lattice Green functions

abstract:
  Lattice Green functions appear in lattice gauge theories, in lattice models
of statistical physics and in random walks. Here, space coordinates are treated
as parameters and series expansions in the mass are obtained. The singular
points in arbitrary dimensions are found. For odd dimensions these are branch
points with half odd-integer exponents, while for even dimensions they are of
the logarithmic type. The differential equations for one, two and three
dimensions are derived, and the general form for arbitrary dimensions is
indicated. Explicit series expressions are found in one and two dimensions.
These series are hypergeometric functions. In three and higher dimensions the
series are more complicated. Finally an algorithmic method by Vohwinkel,
Luscher and Weisz is shown to generalize to arbitrary anisotropies and mass.


title: Wave functions for Hamiltonian Lattice Gauge Theory

abstract:
  We study four dimensional SU(2) lattice gauge theory in the Hamiltonian
formalism by Green's Function Monte Carlo methods. A trial ground state wave
function is introduced to improve the configuration sampling and we discuss the
interplay between its complexity and the simulation systematic errors. As a
case study, we compare the leading strong coupling approximation and an
improved 4 parameters wave function with 1X1 and 1X2 plaquette terms. Our
numerical results favors the second option.


title: Partially Quenched Chiral Perturbation Theory and the Replica Method

abstract:
  We describe a novel framework for partially quenched chiral perturbation
theory based on the replica method. The computational rules are exceedingly
simple. We illustrate these rules by computing the partially quenched chiral
condensate to one-loop order. By considering arbitrary chiral $k$-point
functions we show explicitly to one-loop order the equivalence between this
method and the one based on supersymmetry. It is possible to go smoothly from
the conventional replica method to a supersymmetric variant by choosing the
number of valence quarks to be negative.


title:
Topologically Unquenched QCD: Prospects from an explorative study in
  2-flavour QED(2)

abstract:
  The concept of simulating a variant of QCD with sea quarks which interact
with the gluon configuration only via global gluonic quantities like $\int
F\tilde F dx$ and $\int FF dx$ is tested for the case of the massive 2-flavour
Schwinger model. It is found to amount to an importance sampling method which
generates -at essentially the costs of a quenched run- an ensemble in between a
full and a quenched one, thus providing a competitive alternative to the
quenched approximation.


title: Measuring the aspect ratio renormalization of anisotropic-lattice gluons

abstract:
  Using tadpole inproved actions we investigate the consistency between
different methods of measuring the aspect ratio renormalization of
anisotropic-lattice gluons for bare aspect ratios \chi_0=4,6,10 and inverse
lattice spacing in the range a_s^{-1}=660-840 MeV. The tadpole corrections to
the action, which are established self-consistently, are defined for two cases,
mean link tadpoles in Landau gauge and gauge invariant mean plaquette tadpoles.
Parameters in the latter case exhibited no dependence on the spatial lattice
size, L, while in the former, parameters showed only a weak dependence on L
easily extrapolated to L=\infty.
  The renormalized anisotropy \chi_R was measured using both the torelon
dispersion relation and the sideways potential method. We found good agreement
between these different approaches. Any discrepancy was at worst 3-4% which is
consistent with the effect of lattice artifacts that for the torelon we
estimate as O(\a_Sa_s^2/R^2) where R is the flux-tube radius.
  We also present some new data that suggests that rotational invariance is
established more accurately for the mean-link action than the plaquette action.


title: O(2) symmetry breaking vs. vortex loop percolation

abstract:
  We study with lattice Monte Carlo simulations the relation of global O(2)
symmetry breaking in three dimensions to the properties of a geometrically
defined vortex loop network. We find that different definitions of constructing
a network lead to different results even in the thermodynamic limit, and that
with typical definitions the percolation transition does not coincide with the
thermodynamic phase transition. These results show that geometrically defined
percolation observables need not display universal properties related to the
critical behaviour of the system, and do not in general survive in the field
theory limit.


title: Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature

abstract:
  We compute the low-lying spectrum of the staggered Dirac operator above and
below the finite temperature phase transition in both quenched QCD and in
dynamical four flavor QCD. In both cases we find, in the high temperature
phase, a density with close to square root behavior, $\rho(\lambda) \sim
(\lambda-\lambda_0)^{1/2}$. In the quenched simulations we find, in addition, a
volume independent tail of small eigenvalues extending down to zero. In the
dynamical simulations we also find a tail, decreasing with decreasing mass, at
the small end of the spectrum. However, the tail falls off quite quickly and
does not seem to extend to zero at these couplings. We find that the
distribution of the smallest Dirac operator eigenvalues provides an efficient
observable for an accurate determination of the location of the chiral phase
transition, as first suggested by Jackson and Verbaarschot.


title:
Meron-cluster algorithms and chiral symmetry breaking in a (2+1)-d
  staggered fermion model

abstract:
  The recently developed Meron-Cluster algorithm completely solves the
exponentially difficult sign problem for a number of models previously
inaccessible to numerical simulation. We use this algorithm in a high-precision
study of a model of N=1 flavor of staggered fermions in (2+1)-dimensions with a
four-fermion interaction. This model cannot be explored using standard
algorithms. We find that the Z(2) chiral symmetry of this model is
spontaneously broken at low temperatures and that the finite-temperature chiral
phase transition is in the universality class of the 2-d Ising model, as
expected.


title: Weak transition matrix elements from finite-volume correlation functions

abstract:
  The two-body decay rate of a weakly decaying particle (such as the kaon) is
shown to be proportional to the square of a well-defined transition matrix
element in finite volume. Contrary to the physical amplitude, the latter can be
extracted from finite-volume correlation functions in euclidean space without
analytic continuation. The K -> pi pi transitions and other non-leptonic decays
thus become accessible to established numerical techniques in lattice QCD.


title: New Domain-Wall Fermion Actions

abstract:
  In perturbation theory, the wave function of domain-wall quarks decreases
exponentially with the fifth coordinate. We show that, regardless of the
quark's own momentum, the fall-off rate of the one-loop wave function is equal
to the slowest rate encountered at tree-level for any lattice four-momentum. We
propose new domain-wall actions involving beyond-nearest neighbor couplings in
the four physical dimensions, for which the perturbative wave function
decreases much faster. It is hoped that the new actions may preserve the good
chiral properties of domain-wall fermions up to larger values of the lattice
spacing.


title:
Half-integer topological charges below and above the deconfinement
  transition?

abstract:
  For pure SU(2) lattice gauge theory at finite T, by the help of the cooling
method, we search for classical (approximate) solutions having non-trivial
holonomy at the spatial boundary. We identify various typical objects and
provide their relative frequency of occurence for the confinement and
deconfinement phases. Among the configurations obtained we see also the
dissociated BPS monopole pairs recently discussed by van Baal and
collaborators.


title:
One loop renormalisation of Lattice NRQCD currents for semileptonic
  $B\to D^{(\ast)}$ decays to order $\frac{\vec{p}}{M}$

abstract:
  We present the results of a perturbative calculation to match the axial and
vector currents for semileptonic $B\to D^{(\ast)}$ decays in lattice NRQCD to
the continuum \MSb scheme. The matching is performed to
$O(\alpha_s\frac{\vec{p}}{M})$ in Feynman gauge and in the on-shell
renormalisation scheme.
  The spatial and temporal components of the currents renormalise differently;
to this order the matching involves a straightforward renormalisation for the
$V_0$ and $A_k$ currents, and a rank two and four mixing matrix for the $A_0$
and $V_k$ currents respectively. The resultant one loop corrections are of
$O(5%)$, boding well for the accuracy of forthcoming simulations.


title: Lorentz gauge fixing and lattice QED

abstract:
  The Gribov ambiguity problem is studied for compact lattice QED within the
Lorentz gauge. In the Coulomb phase, Gribov copies are mainly caused by double
Dirac sheets and zero-momentum modes of the gauge fields. Removing them by
(non-) periodic gauge transformations allows to reach the absolute extremum of
the Lorentz gauge functional. For standard Lorentz gauge fixing the Wilson
fermion correlator turns out to be strongly effected by the zero-momentum
modes. A reliable fermion mass estimate requires the proper treatment of these
modes.


title: Vortex configurations in the large N limit

abstract:
  We study the properties of vortex-like configurations which are solutions of
the SU(N) Yang-Mills classical equations of motion. We show that these
solutions are concentrated along a two-dimensional wall with size growing with
the number of colors.


title: Domain Wall Fermions in Quenched Lattice QCD

abstract:
  We study the chiral properties and the validity of perturbation theory for
domain wall fermions in quenched lattice QCD at beta=6.0. The explicit chiral
symmetry breaking term in the axial Ward-Takahashi identity is found to be very
small already at Ns=10, where Ns is the size of the fifth dimension, and its
behavior seems consistent with an exponential decay in Ns within the limited
range of Ns we explore. From the fact that the critical quark mass, at which
the pion mass vanishes as in the case of the ordinary Wilson-type fermion,
exists at finite Ns, we point out that this may be a signal of the parity
broken phase and investigate the possible existence of such a phase in this
model at finite Ns. The rho and pi meson decay constants obtained from the
four-dimensional local currents with the one-loop renormalization factor show a
good agreement with those obtained from the conserved currents.


title: Spinodal Decomposition in High Temperature Gauge Theories

abstract:
  After a rapid increase in temperature across the deconfinement temperature $%
T_{d}$, pure gauge theories exhibit unstable long wavelength fluctuations in
the approach to equilibrium. This phenomenon is analogous to spinodal
decomposition observed in condensed matter physics, and also seen in models of
disordered chiral condensate formation. At high temperature, the unstable modes
occur only in the range $0\leq k$ $\leq k_{c}$, where $k_{c}$ is on the order
of the Debye screening mass $m_D$. Equilibration always occurs via spinodal
decomposition for $SU(2) $at temperatures $T>T_{d}$ and for SU(3) for $T\gg
T_{d}$. For SU(3) at temperatures $T\gtrsim T_{d}$, nucleation may replace
spinodal decomposition as the dominant equilibration mechanism. Monte Carlo
simulations of SU(2) lattice gauge theory exhibit the predicted phenomena. The
observed value of $k_c$ is in reasonable agreement with a value predicted from
previous lattice measurements of $m_D$.


title: Universality of the Axial Anomaly in Lattice QCD

abstract:
  We prove that lattice QCD generates the axial anomaly in the continuum limit
under very general conditions on the lattice action, which includes the case of
Ginsparg-Wilson fermions. The ingredients going into the proof are gauge
invariance, locality of the Dirac operator, absence of fermion doubling, the
general form of the lattice Ward identity, and the power counting theorem of
Reisz. The results generalize in an obvious way to SU(N) lattice gauge
theories.


title:
Incorporating Chiral Symmetry in Extrapolations of Octet Baryon Magnetic
  Moments

abstract:
  We explore methods of extrapolating lattice calculations of hadronic
observables to the physical regime, while respecting the constraints of chiral
symmetry and heavy quark effective theory. In particular, we extrapolate
lattice results for magnetic moments of the spin-1/2 baryon octet to the
physical pion mass and compare with experimental measurements. The success
previously reported for extrapolations of the nucleon magnetic moments carries
over to the Sigma baryons. A study of the residual discrepancies in the Xi
baryon moments suggests that it is important to have new simulation data with a
more realistic strange quark mass.


title:
Matrix Distributed Processing: A set of C++ Tools for implementing
  generic lattice computations on parallel systems

abstract:
  We present a set of programming tools (classes and functions written in C++
and based on Message Passing Interface) for fast development of generic
parallel (and non-parallel) lattice simulations. They are collectively called
MDP 1.2.
  These programming tools include classes and algorithms for matrices, random
number generators, distributed lattices (with arbitrary topology), fields and
parallel iterations. No previous knowledge of MPI is required in order to use
them.
  Some applications in electromagnetism, electronics, condensed matter and
lattice QCD are presented.


title:
Non-perturbative beta-function in SU(2) lattice gauge fields
  thermodynamics

abstract:
  The new method of nonperturbative calculation of the beta function in the
lattice gauge theory is proposed. The method is based on the finite size
scaling hypothesis.


title: Numerical analysis of fractional charge solutions on the torus

abstract:
  We study by numerical methods a particular kind of SU(N) Yang-Mills solutions
of the Euclidean equations of motion which appear on the torus when twisted
boundary conditions are imposed. These are instanton-like configurations with
the peculiarity of having fractional topological charge. We focus on those
solutions with minimal non-trivial action $S=8\pi^2/\N$ and extract their
properties in a few different cases, paying special attention to the $N \to
\infty$ limit.


title: Dynamical Quark Effects on Light Quark Masses

abstract:
  We present results for light quark masses from a systematic lattice QCD study
with two degenerate flavors of dynamical quarks. Simulations are made with a
renormalization-group improved gauge action and a mean-field improved clover
quark action for sea quark masses corresponding to $m_{\rm PS}/m_{\rm V}
\approx 0.8$--0.6 and the lattice spacing $a=0.22$--0.11 fm. In the continuum
limit we find $m_{ud}^{\bar{MS}}(2 {\rm GeV})=3.44^{+0.14}_{-0.22}$ MeV using
the $\pi$ and $\rho$ meson masses as physical input, and $m_s^{\bar{MS}}(2 {\rm
GeV})=88^{+4}_{-6}$ MeV or $90^{+5}_{-11}$ MeV with the $K$ or $\phi$ meson
mass as additional input. The quoted errors represent statistical and
systematic combined, the latter including those from continuum and chiral
extrapolations, and from renormalization factors. Compared to quenched results,
two flavors of dynamical quarks reduce quark masses by about 25%.


title: Fermions obstruct dimensional reduction in hot QCD

abstract:
  We have studied, for the first time, screening masses obtained from
glueball-like correlators in Quantum Chromodynamics with four light dynamical
flavours of quarks in the temperature range 1.5T_c < T < 3T_c, where T_c is the
temperature at which the chiral transition occurs. We have also studied
pion-like and sigma-like screening masses, and found that they are degenerate
in the entire range of T. These obstruct perturbative dimensional reduction
since the lowest glueball screening mass is heavier than them. Extrapolation of
our results suggests that this obstruction may affect the entire range of
temperature expected to be reached even at the Large Hadron Collider.


title: Algebraic Generalization of the Ginsparg-Wilson Relation

abstract:
  A specific algebraic realization of the Ginsparg-Wilson relation in the form
$\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} =
  2a^{2k+1}(\gamma_{5}D)^{2k+2}$ is discussed, where $k$ stands for a
non-negative integer and $k=0$ corresponds to the commonly discussed
Ginsparg-Wilson relation. From a view point of algebra, a characteristic
property of our proposal is that we have a closed algebraic relation for one
unknown operator $D$, although this relation itself is obtained from the
original proposal of Ginsparg and Wilson,
$\gamma_{5}D+D\gamma_{5}=2aD\gamma_{5} \alpha D$, by choosing $\alpha$ as an
operator containing $D$ (and thus Dirac matrices). In this paper, it is shown
that we can construct the operator $D$ explicitly for any value of $k$. We
first show that the instanton-related index of all these operators is
identical. We then illustrate in detail a generalization of Neuberger's overlap
Dirac operator to the case $k=1$. On the basis of explicit construction, it is
shown that the chiral symmetry breaking term becomes more irrelevent for larger
$k$ in the sense of Wilsonian renormalization group. We thus have an infinite
tower of new lattice Dirac operators which are topologically proper, but a
large enough lattice is required to accomodate a Dirac operator with a large
value of $k$.


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

abstract:
  A definition of the Pontryagin index for SU(2) center vortex world-surfaces
composed of plaquettes on a hypercubic lattice is constructed. It is used to
evaluate the topological susceptibility in a previously defined random surface
model for vortices, the parameters of which have been fixed such as to
reproduce the confinement properties of SU(2) Yang-Mills theory. A prediction
for the topological susceptibility is obtained which is compatible with
measurements of this quantity in lattice Yang-Mills theory.


title: A generalized Ginsparg-Wilson relation

abstract:
  We show that, under certain general assumptions, any sensible lattice Dirac
operator satisfies a generalized form of the Ginsparg-Wilson relation (GWR).
Those assumptions, on the other hand, are mostly dictated by large momentum
behaviour considerations. We also show that all the desirable properties often
deduced from the standard GWR hold true of the general case as well; hence one
has, in fact, more freedom to modify the form of the lattice Dirac operator,
without spoiling its nice properties. Our construction, a generalized
Ginsparg-Wilson relation (GGWR), is satisfied by some known proposals for the
lattice Dirac operator. We discuss some of these examples, and also present a
derivation of the GGWR in terms of a renormalization group transformation with
a blocking which is not diagonal in momentum space, but nevertheless commutes
with the Dirac operator.


title:
Global obstructions to gauge-invariance in chiral gauge theory on the
  lattice

abstract:
  It is shown that certain global obstructions to gauge-invariance in chiral
gauge theory, described in the continuum by Alvarez-Gaume and Ginsparg, are
exactly reproduced on the lattice in the Overlap formulation at small non-zero
lattice spacing (i.e. close to the classical continuum limit). As a
consequence, the continuum anomaly cancellation condition $d_R^{abc}=0$ is seen
to be a necessary (although not necessarily sufficient) condition for anomaly
cancellation on the lattice in the Overlap formulation.


title:
The Lattice Schwinger Model: Confinement, Anomalies, Chiral Fermions and
  All That

abstract:
  In order to better understand what to expect from numerical CORE computations
for two-dimensional massless QED (the Schwinger model) we wish to obtain some
analytic control over the approach to the continuum limit for various choices
of fermion derivative. To this end we study the Hamiltonian formulation of the
lattice Schwinger model (i.e., the theory defined on the spatial lattice with
continuous time) in $A_0=0$ gauge. We begin with a discussion of the solution
of the Hamilton equations of motion in the continuum, we then parallel the
derivation of the continuum solution within the lattice framework for a range
of fermion derivatives. The equations of motion for the Fourier transform of
the lattice charge density operator show explicitly why it is a regulated
version of this operator which corresponds to the point-split operator of the
continuum theory and the sense in which the regulated lattice operator can be
treated as a Bose field. The same formulas explicitly exhibit operators whose
matrix elements measure the lack of approach to the continuum physics. We show
that both chirality violating Wilson-type and chirality preserving SLAC-type
derivatives correctly reproduce the continuum theory and show that there is a
clear connection between the strong and weak coupling limits of a theory based
upon a generalized SLAC-type derivative.


title: Nonperturbative Gauge Fixing and Perturbation Theory

abstract:
  We compare the gauge-fixing approach proposed by Jona-Lasinio and Parrinello,
and by Zwanziger (JPLZ) with the standard Fadeev-Popov procedure, and
demonstrate perturbative equality of gauge-invariant quantities, up to
irrelevant terms induced by the cutoff. We also show how a set of local,
renormalizable Feynman rules can be constructed for the JPLZ procedure.


title: A Lattice Study of the Glueball Spectrum

abstract:
  Glueball spectrum is studied using an improved gluonic action on asymmetric
lattices in the pure SU(3) gauge theory. The smallest spatial lattice spacing
is about $0.08fm$ which makes the extrapolation to the continuum limit more
reliable. In particular, attention is paid to the scalar glueball mass which is
known to have problems in the extrapolation. Converting our lattice results to
physical units using the scale set by the static quark potential, we obtain the
following results for the glueball masses: $M_G(0^{++})=1730(90)MeV$ for the
scalar glueball mass and $M_G(2^{++})=2400(95)MeV$ for the tensor glueball.


title:
The pion_0 to gamma gamma decay and the chiral anomaly in the
  quark-composites approach to QCD

abstract:
  We evaluate the pion_0 into two gammas decay amplitude by an effective action
derived from QCD in the quark composites approach, getting the standard value.
We also verify that our effective action correctly reproduces the chiral
anomaly.


title: Topological susceptibility in full QCD at zero and finite temperature

abstract:
  We present a study of the topological susceptibility $\chi$ on the lattice
for full QCD with 2 and 4 flavours of staggered fermions at zero and finite
temperature T. We find that $\chi$ presents a sharp drop across the
deconfinement transition. We also study the dependence of $\chi$ on the quark
mass at T=0: we have no conclusive evidence for the expected chiral behaviour.


title:
Phase Structure of Four-dimensional Simplicial Quantum Gravity with a
  U(1) Gauge Field

abstract:
  The phase structure of four-dimensional simplicial quantum gravity coupled to
U(1) gauge fields has been studied using Monte-Carlo simulations. The smooth
phase is found in the intermediate region between the crumpled phase and the
branched polymer phase. This new phase has a negative string susceptibility
exponent, even if the number of vector fields (Nv) is 1. The phase transition
between the crumpled phase and the smooth phase has been studied by a finite
size scaling method. From the numerical results, we expect that this model
(coupled to one gauge field) has a higher order phase transition than first
order, which means the possibility to take the continuum limit at the critical
point. Furthermore, we consider a modification of the balls-in-boxes model for
a clear understanding of the relation between the numerical results and the
analytical one.


title: Renormalization of the \Delta B=2 four-quark operators in lattice NRQCD

abstract:
  We calculate perturbative renormalization constants for the \Delta B=2
four-quark operators in lattice NRQCD.
  Continuum operators \bar{b}\gamma_{\mu}(1-\gamma_5)q~
  \bar{b}\gamma_{\mu}(1-\gamma_5)q and
\bar{b}(1-\gamma_5)q~\bar{b}(1-\gamma_5)q, which are necessary in evaluating
the mass and width differences in $B^0_{d(s)}-\bar{B}^0_{d(s)}$ systems, are
matched at one-loop with corresponding lattice operators constructed from the
NRQCD heavy quarks and the ${\cal O}(a)$-improved light quarks. Using these
perturbative coefficients, we also reanalyse our previous simulation results
for the matrix elements of the above operators. Our new results are free from
the systematic error of ${\cal O}(\alpha_s/(aM_b))$ in contrast to the previous
ones with matching coefficients evaluated in the static limit.


title:
A test of the Kugo-Ojima confinement criterion by lattice Landau gauge
  QCD simulations

abstract:
  The first test of the Kugo-Ojima colour confinement criterion by the lattice
Landau gauge QCD simulation is performed. The parameter u which is expected to
be -1\delta^a_b in the continuum theory was found to be -0.7\delta^a_b in the
strong coupling region. The data is analyzed in connection with the theory of
Zwanziger. In the weak coupling region, the expectation value of the horizon
function is negative or consistent to 0.


title: Large-Flavor QCD on the Lattice

abstract:
  We study the nature of the QCD vacuum at general number of flavors $N_F$ by
numerical simulations on the lattice. Combining the results with those of the
perturbation theory, we propose the following picture: 1) For $N_F \ge 17$,
there exists only one IR fixed point at vanishing gauge coupling, i.e., the
theory in the continuum limit is trivial. 2) For $16 \ge N_F \ge 7$, there is a
non-trivial fixed point. Therefore, the theory is non-trivial with anomalous
dimensions, however, without quark confinement. 3) For $N_F \le 6$, theories
satisfy both quark confinement and spontaneous chiral symmetry breaking in the
continuum limit.


title: Visualizations of the QCD Vacuum

abstract:
  Action and topological charge densities of the Euclidean-space QCD vacuum are
visualized in three-dimensional slices of a 24^3 x 36 space-time lattice and an
order-a^2 improved 16^3 x 32 lattice. Features include instanton anti-instanton
annihilation and a comparison of standard and over-improved actions used in the
smoothing of the gauge fields.


title: Compact fields and mass generation

abstract:
  It is shown that the free propagator of an angular, i.e. compact, field with
zero lagrangian mass acquires a nonzero propagator mass $\omega$ (`kinematical'
mass generation). To demonstrate this effect the free propagator of the
goldstone boson in an O(2) model with spontaneous symmetry breaking is
calculated. It is shown that this propagator is massive, the mass $\omega$
being a function of the scalar `condensate' ${\bar\phi}$.


title: Magnetic Screening in Hot Non-Abelian Gauge Theory

abstract:
  We analyze the large distance and low-momentum behavior of the magnetic gluon
propagator of the SU(2) gauge theory at finite temperature. Lattice
calculations within the 4-dimensional as well as the effective, dimensionally
reduced 3-dimensional gauge theories in generalized Landau gauges and MAG show
that the magnetic propagator is strongly infrared suppressed in Landau gauges
but stays large and finite in MAG. Despite these differences in the
low-momentum behavior of the propagator calculated in different gauges the
magnetic fields are exponentially screened in all gauges considered. From the
propagator calculated in maximally Abelian gauge we find for the screening
mass, m_M = (1.48 +/- 0.17) T at T=2 T_c.


title: Center Vortices at Strong Couplings and All Couplings

abstract:
  Motivations for the center vortex theory of confinement are discussed. In
particular, it is noted that the abelian dual Meissner effect, which is the
signature of dual superconductivity, cannot adequately describe the confining
force at large distance scales. A long-range effective action is derived from
strong-coupling lattice gauge theory in D=3 dimensions, and it is shown that
center vortices emerge as the stable saddlepoints of this action. Thus, in the
case of strong couplings, the vortex picture is arrived at analytically. I also
respond briefly to a recent criticism regarding maximal center gauge.


title: Domain Wall Fermions with Exact Chiral Symmetry

abstract:
  We show how the standard domain wall action can be simply modified to allow
arbitrarily exact chiral symmetry at finite fifth dimensional extent. We note
that the method can be used for both quenched and dynamical calculations. We
test the method using smooth and thermalized gauge field configurations. We
also make comparisons of the performance (cost) of the domain wall operator for
spectroscopy compared to other methods such as the overlap-Dirac operator and
find both methods are comparable in cost.


title: Chiral Anomaly for a New Class of Lattice Dirac Operators

abstract:
  A new class of lattice Dirac operators which satisfy the index theorem have
been recently proposed on the basis of the algebraic relation
$\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} =
2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands for a non-negative integer and
$k=0$ corresponds to the ordinary Ginsparg-Wilson relation. We analyze the
chiral anomaly and index theorem for all these Dirac operators in an explicit
elementary manner. We show that the coefficient of anomaly is independent of a
small variation in the parameters $r$ and $m_{0}$, which characterize these
Dirac operators, and the correct chiral anomaly is obtained in the (naive)
continuum limit $a\to 0$.


title: An alternative to domain wall fermions

abstract:
  We define a sparse hermitian lattice Dirac matrix, $H$, coupling $2n+1$ Dirac
fermions. When $2n$ fermions are integrated out the induced action for the last
fermion is a rational approximation to the hermitian overlap Dirac operator. We
provide rigorous bounds on the condition number of $H$ and compare them to
bounds for the higher dimensional Dirac operator of domain wall fermions. Our
main conclusion is that overlap fermions should be taken seriously as a
practical alternative to domain wall fermions in the context of numerical QCD.


title: Some remarks on the Ginsparg-Wilson fermion

abstract:
  We note that Fujikawa's proposal of generalization of the Ginsparg-Wilson
relation is equivalent to setting $R = (a \gamma_5 D)^{2k}$ in the original
Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$. An
explicit realization of D follows from the Overlap construction. The general
properties of D are derived. The chiral properties of these higher-order (k >
0) realizations of Overlap Dirac operator are compared to those of the
Neuberger-Dirac operator (k = 0), in terms of the fermion propagator, the axial
anomaly and the fermion determinant in a background gauge field. Our present
results (up to lattice size 16 x 16) indicate that the chiral properties of the
Neuberger-Dirac operator are better than those of higher-order ones.


title: On The Origin of the OZI Rule in QCD

abstract:
  The OZI rule is prominent in hadronic phenomena only because OZI violation is
typically an order of magnitude smaller than expected from large N_c arguments.
With its standard ^3P_0 pair creation operator for hadronic decays by flux tube
breaking, the quark model respects the OZI rule at tree level and exhibits the
cancellations between OZI-violating meson loop diagrams required for this
dramatic suppression. However, if the quark model explanation for these
cancellations is correct, then OZI violation would be expected to be large in
the nonet with the same quantum numbers as the pair creation operator: the
0^{++} mesons. Experiment is currently unable to identify these mesons, but we
report here on a lattice QCD calculation which confirms that the OZI rule
arises from QCD in the vector and axial vector mesons as observed, and finds a
large violation of the rule in the scalar mesons as anticipated by the quark
model. In view of this result, we make some remarks on possible connections
between the ^3P_0 pair creation model, scalar mesons, and the U_A(1) anomaly
responsible for the large OZI violation which drives the \eta' mass. In
particular, we note that our result favors the large N_c and not the instanton
interpretation of the solution to the \eta' mass problem.


title:
Tricritical scaling at the N_t=6 chiral phase transition for 2 flavour
  lattice QCD with staggered quarks

abstract:
  We have simulated lattice QCD directly in the chiral limit of zero quark mass
by adding an additional, irrelevant 4-fermion interaction to the standard
action. Using lattices having temporal extent of six and spatial extents of
twelve and eighteen, we find that the theory with 2 massless staggered quark
flavors has a second order finite temperature phase transition. The critical
exponents $\beta_{mag}$, $\delta$ and $\nu$ are measured and favour tricritical
behaviour over that expected by universality arguments. The pion screening mass
is consistent with zero below the transition, but is degenerate with the
nonzero $\sigma(f_0)$ mass above the transition, indicating the restoration of
chiral symmetry.

categories: hep-lat cond-mat.stat-mech hep-ph physics.comp-ph


title:
Perturbative renormalization of the first two moments of non-singlet
  quark distributions with overlap fermions

abstract:
  Using the overlap-Dirac operator proposed by Neuberger, we have computed in
lattice QCD the one-loop renormalization factors of ten operators which measure
the lowest two moments of unpolarized and polarized non-singlet quark
distributions. These factors are necessary to extract physical numbers from
Monte Carlo simulations made with overlap fermions.
  An exact chiral symmetry is maintained in all our results, and the
renormalization constants of corresponding unpolarized and polarized operators
which differ by a $\gamma_5$ matrix have the same value. We have considered two
lattice representations for each continuum operator. The computations have been
carried out using the symbolic language FORM, in a general covariant gauge. In
some simple cases they have also been checked by hand.


title:
Green's Function Monte Carlo study of SU(3) lattice gauge theory in
  (3+1)D

abstract:
  A `forward walking' Green's Function Monte Carlo algorithm is used to obtain
expectation values for SU(3) lattice Yang-Mills theory in (3+1) dimensions. The
ground state energy and Wilson loops are calculated, and the finite-size
scaling behaviour is explored. Crude estimates of the string tension are
derived, which agree with previous results at intermediate couplings; but more
accurate results for larger loops will be required to establish scaling
behaviour at weak coupling.


title: Vortices and confinement in hot and cold D=2+1 gauge theories

abstract:
  We calculate the variation with temperature of the vortex free energy in
D=2+1 SU(2) lattice gauge theories. We do so both above and below the
deconfining transition at T=Tc. We find that this quantity is zero at all T for
large enough volumes. For T<Tc this observation is consistent with the fact
that the phase is linearly confining; while for T>Tc it is consistent with the
conventional expectation of `spatial' linear confinement. In small spatial
volumes this quantity is shown to be non-zero. The way it decreases to zero
with increasing volume is shown to be controlled by the (spatial) string
tension and it has the functional form one would expect if the vortices being
studied were responsible for the confinement at low T, and for the `spatial'
confinement at large T. We also discuss in detail some of the direct numerical
evidence for a non-zero spatial string tension at high T, and we show that the
observed linearity of the (spatial) potential extends over distances that are
large compared to typical high-T length scales.


title: Non-Gaussian numerical errors versus mass hierarchy

abstract:
  We probe the numerical errors made in renormalization group calculations by
varying slightly the rescaling factor of the fields and rescaling back in order
to get the same (if there were no round-off errors) zero momentum 2-point
function (magnetic susceptibility). The actual calculations were performed with
Dyson's hierarchical model and a simplified version of it. We compare the
distributions of numerical values obtained from a large sample of rescaling
factors with the (Gaussian by design) distribution of a random number generator
and find significant departures from the Gaussian behavior. In addition, the
average value differ (robustly) from the exact answer by a quantity which is of
the same order as the standard deviation. We provide a simple model in which
the errors made at shorter distance have a larger weight than those made at
larger distance. This model explains in part the non-Gaussian features and why
the central-limit theorem does not apply.


title: Decoupling of Layers in the Three-dimensional Abelian Higgs Model

abstract:
  The Abelian Higgs model with anisotropic couplings in 2+1 dimensions is
studied in both the compact and non-compact formulations. Decoupling of the
space-like planes takes place in the extreme anisotropic limit, so charged
particles and gauge fields are presumably localized within these planes. The
behaviour of the model under the influence of an external magnetic field is
examined in the compact case and yields further characterization of the phases.


title: K0-K0bar Mixing with Wilson Fermions without Subtractions

abstract:
  By using suitable Ward identities, we show that it is possible to compute
K0-K0bar mixing without subtracting the terms generated by explicit chiral
symmetry breaking present in Wilson-like lattice actions. The accuracy in the
determination of the amplitudes is of O(a), which is the best one attainable in
the absence of improvement.


title: A disorder analysis of the Ising model

abstract:
  Lattice studies of monopole condensation in QCD are based on the construction
of a disorder parameter, a creation operator of monopoles which is written in
terms of the gauge fields. This procedure is expected to work for any system
which presents duality. We check it on the Ising model in 2d, which is exactly
solvable. The output is an amusing exercise in statistical mechanics.


title:
Gauge anomaly cancellations in SU(2)_L \times U(1)_Y Electroweak theory
  on the lattice

abstract:
  We consider the cohomological classification of the 4+2-dimensional
topological field, which is proposed by L\"uscher, for SU(2)_L \times U(1)_Y
electroweak theory. The dependence on the admissible abelian gauge field of
U(1)_Y is determined through topological argument, with SU(2)_L gauge field
fixed as background. We then show the exact cancellation of the local gauge
anomaly of the mixed type {SU(2)_L}^2 \times U(1)_Y at finite lattice spacing,
as well as {U(1)_Y}^3, using the pseudo reality of SU(2)_L and the anomaly
cancellation conditions in the electroweak theory given in terms of the
hyper-charges of U(1)_Y.


title:
Center-vortex dominance after dimensional reduction of SU(2) lattice
  gauge theory

abstract:
  The high-temperature phase of SU(2) Yang-Mills theory is addressed by means
of dimensional reduction with a special emphasis on the properties of center
vortices. For this purpose, the vortex vacuum which arises from center
projection is studied in pure 3-dimensional Yang-Mills theory as well as in the
3-dimensional adjoint Higgs model which describes the high temperature phase of
the 4-dimensional SU(2) gauge theory. We find center-dominance within the
numerical accuracy of 10%.


title:
What are the Confining Field Configurations of Strong-Coupling Lattice
  Gauge Theory?

abstract:
  Starting from the strong-coupling SU(2) Wilson action in D=3 dimensions, we
derive an effective, semi-local action on a lattice of spacing L times the
spacing of the original lattice. It is shown that beyond the adjoint
color-screening distance, i.e. for $L \ge 5$, thin center vortices are stable
saddlepoints of the corresponding effective action. Since the entropy of these
stable objects exceeds their energy, center vortices percolate throughout the
lattice, and confine color charge in half-integer representations of the SU(2)
gauge group. This result contradicts the folklore that confinement in
strong-coupling lattice gauge theory, for D>2 dimensions, is simply due to
plaquette disorder, as is the case in D=2 dimensions. It also demonstrates
explicitly how the emergence and stability of center vortices is related to the
existence of color screening by gluon fields.


title:
A High Precision Study of the QQ(bar) Potential from Wilson Loops in the
  Regime of String Breaking

abstract:
  For lattice QCD with two sea quark flavours we compute the static quark
antiquark potential V(R) in the regime where string breaking is expected. In
order to increase statistics, we make full use of the lattice information by
including all lattice vectors R to any possible lattice separation in the
infrared regime. The corresponding paths between the lattice points are
constructed by means of a generalized Bresenham algorithm as known from
computer graphics. As a results we achieve a determination of the unquenched
potential in the range .8 to 1.5 fm with hitherto unknown precision.
Furthermore, we demonstrate some error reducing methods for the evaluation of
the transition matrix element between two- and four-quark states.


title: String breaking on a lattice

abstract:
  String breaking is a non-perturbative long-distance feature of QCD that is
involved in for example meson decays. A mixing analysis of lattice operators at
zero temperature gives the level splitting and mixing energy between the broken
and unbroken string states.


title: Quantum Spin Formulation of the Principal Chiral Model

abstract:
  We formulate the two-dimensional principal chiral model as a quantum spin
model, replacing the classical fields by quantum operators acting in a Hilbert
space, and introducing an additional, Euclidean time dimension. Using coherent
state path integral techniques, we show that in the limit in which a large
representation is chosen for the operators, the low energy excitations of the
model describe a principal chiral model in three dimensions. By dimensional
reduction, the two-dimensional principal chiral model of classical fields is
recovered.


title: String Breaking as a Mixing Phenomenon in the SU(2) Higgs Model

abstract:
  We study the potential of a static quark anti-quark pair in the confinement
``phase'' of the SU(2) Higgs model. Around separation r_b, the confining string
of the gauge field breaks by formation of a dynamical pair of light quarks. The
ground state and first excited state static potentials are determined by a
variational technique from a matrix correlation in which suitably smeared gauge
and Higgs fields enter. Our results at beta=2.4 clearly show string breaking
(r_b ~ 1.9r_0). The investigation of properly defined overlaps confirms the
interpretation of string breaking as a level crossing phenomenon between
string-type and meson-type states. We study the scaling properties of the
static potentials along a line of constant physics, varying the lattice spacing
by a factor of 2. Our results show compatibility with scaling within tiny
errors.


title: Sea Quark Effects on Quarkonia

abstract:
  We study the effects of two dynamical sea quarks on the spectrum of heavy
quarkonia. Within the non-relativistic approach to Lattice QCD we found
sizeable changes to the hyperfine splitting, but we could not observe any
changes for the fine structure. We also investigated the scaling behaviour of
our results for several different lattice spacings.


title:
Instability in the Molecular Dynamics Step of Hybrid Monte Carlo in
  Dynamical Fermion Lattice QCD Simulations

abstract:
  We investigate instability and reversibility within Hybrid Monte Carlo
simulations using a non-perturbatively improved Wilson action. We demonstrate
the onset of instability as tolerance parameters and molecular dynamics step
sizes are varied. We compare these findings with theoretical expectations and
present limits on simulation parameters within which a stable and reversible
algorithm is obtained for physically relevant simulations. Results of
optimisation experiments with respect to tolerance prarameters are also
presented.


title: Unquenched Charmonium with NRQCD

abstract:
  We present the results from a series of lattice simulations of the charmonium
system using a highly-improved NRQCD action, both in the quenched
approximation, and with n_f = 2 light dynamical quarks. The spectra show some
evidence for quenching effects of roughly 10% in the S- and P-hyperfine spin
splittings---probably too small to account for the severe underestimates in
these quantities seen in previous quenched charmonium simulations. We also find
estimates for the magnitude of other systematic effects---in particular, the
choice of the tadpole factor can alter spin splittings at the 10-20% level, and
radiative corrections may be as large as 40% for charmonium. We conclude that
quenching is just one of a collection of important effects that require
attention in precision heavy-quark simulations.


title:
Comment on "On the Origin of the OZI Rule in QCD", by N. Isgur and H. B.
  Thacker

abstract:
  We comment on the recent paper (hep-lat/0005006) by Isgur and Thacker on the
origin of the OZI rule in QCD. We show that instantons explain the sign and
magnitude of the observed OZI-violating amplitude in all mesonic channels, not
just in the $\eta'$ channel. We comment on the role of instantons in hadronic
spectroscopy and the relation between instantons and the large $N_c$ limit of
QCD.


title: RI/MOM Renormalization Window and Goldstone Pole Contamination

abstract:
  We perform a comparative study of the ratio of lattice (Wilson fermion)
renormalization constants Z_P/Z_S, obtained non-perturbatively from the RI/MOM
renormalization conditions and from Ward Identities of on- and off-shell
Green's functions. The off-shell Ward Identity used in this work relies on
correlation functions with non-degenerate quark masses. We find that, due to
discretization effects, there is a 10-15% discrepancy between the two Ward
Identity determinations at current bare couplings (beta values). The RI/MOM
result is in the same range and has a similar systematic error of 10-15%. Thus,
contrary to a previous claim, the contamination of the RI/MOM result from the
presence of a Goldstone pole at scales of about 2 GeV is subdominant, compared
to finite cutoff effects.


title:
The masses of the mesons and baryons. Part III. The size of the
  particles

abstract:
  The size of the stable elementary particles is investigated with the standing
wave model. The particle size follows from the magnitude of the radiation
pressure. It is shown that the outward directed radiation pressure is balanced
by the inward directed elastic force per unit area in the cubic nuclear
lattice, provided that the sidelength of the lattice is 10^(-13) cm, which
agrees with the measured radius of the proton r = 0.8 \times 10^(-13) cm,
within the uncertainty of the parameters.


title:
The Critical Mass of Wilson Fermions: A Comparison of Perturbative and
  Monte Carlo Results

abstract:
  We calculate the critical value of the hopping parameter, $\kappa_c$, in
Lattice QCD with Wilson fermions, to two loops in perturbation theory.
  This quantity is an additive renormalization; as such, it is characterized
not only by the standard caveats regarding the asymptotic nature of
perturbative results, but also by a linear divergence in the lattice spacing.
Consequently, our calculation tests rather stringently the limits of
applicability of perturbation theory.
  We compare our results to non perturbative evaluations of $\kappa_c$ coming
from Monte Carlo simulations.
  Finally, we apply a tadpole improvement technique on our results; this shifts
them quite favourably towards the non perturbative values.


title: Numerical tests of the Kugo-Ojima color confinement criterion

abstract:
  The Kugo-Ojima color confinement criterion, which is based on the BRST
symmetry of QCD is numerically tested by the lattice Landau gauge simulation.
We first discuss the BRST symmetry on the lattice and the Gribov copy problem.
The horizon function defined by Zwanziger based on the U-linear definition of
the gauge field and that based on log U are compared. The parameter u which is
expected to be $-1\delta^a_b$ in the continuum theory was found to be
$-0.7\delta^a_b$ in the strong coupling region. There are about 20% difference
between the two horizon functions, but in the weak coupling region, the
expectation value of the horizon function is suggested to be zero or negative.


title: On the colour confinement and the minimal surface

abstract:
  In the analysis of the energy of the four-quark system obtained in the SU(2)
lattice Monte Carlo, the f-model in which the transition potential is expressed
in the form $f=f_c exp(-k_A b_s A-k_P\sqrt{b_s}P)$, where A is the area and P
is the perimeter of the Wilson loop, was successful in the simple
configurations of the four quarks. In the case of tetrahedral geometry, an
estimation of the minimal surface whose contours run the positions of the four
quarks is necessary. We show that the regular surface approximation whose area
can be calculated analytically, is a good approximation for evaluating the
minimal surface. The numerical value of the coefficient $k_A b_s$ is close to
$2 fm^{-2}$ which is the density of the $Z_2$ vortex in the SU(2) lattice Monte
Carlo.


title: Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions

abstract:
  The chiral symmetry relation and scaling of the overlap fermions are studied
numerically on the quenched lattices at 3 couplings with about the same
physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation
is satisfied to better than 1% down to the smallest quark mass at $m_0a =
0.006$. We also obtain the quark mass from the PCAC relation and the
pseudoscalar masses. The renormalization group invariant quark mass is shown to
be fairly independent of scale. The $\pi$ and $\rho$ masses at a fixed
$m_{\pi}/m_{\rho}$ ratio indicate small $O(a^2)$ corrections. It is found that
the critical slowing down sets in abruptly at a very small quark mass close to
those of the physical u and d quarks.


title: Three-Quark Potential in SU(3) Lattice QCD

abstract:
  The static three-quark (3Q) potential is measured in the SU(3) lattice QCD
with $12^3 \times 24$ and $\beta=5.7$ at the quenched level. From the 3Q Wilson
loop, the 3Q ground-state potential $V_{\rm 3Q}$ is extracted using the
smearing technique for the ground-state enhancement. With accuracy better than
a few %, $V_{\rm 3Q}$ is well described by a sum of a constant, the two-body
Coulomb term and the three-body linear confinement term $\sigma_{\rm 3Q} L_{\rm
min}$, where $L_{\rm min}$ denotes the minimal length of the color flux tube
linking the three quarks. By comparing with the Q-$\bar {\rm Q}$ potential, we
find a universal feature of the string tension, $\sigma_{\rm 3Q} \simeq
\sigma_{\rm Q \bar Q}$, as well as the one-gluon-exchange result for the
Coulomb coefficient, $A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar Q}$.


title: Do Instantons of the CP(N-1) Model Melt?

abstract:
  In the two-dimensional CP(N-1) model one can parametrize exact many-instanton
solutions via N `constituents' (called `zindons'). This parameterization
allows, in principle, a complete `melting' of individual instantons. The model
is therefore well suited to study whether dynamics prefers a dilute or a
strongly overlapping ensemble of instantons. We study the statistical mechanics
of instantons both analytically and numerically. We find that at N=2 the
instanton system collapses into zero-size instantons. At N=3,4 we find that
well-isolated instantons are dynamically preferred though 15-25% of instantons
have a considerable overlap with others.


title:
A gauge invariant study of the monopole condensation in non Abelian
  lattice gauge theories

abstract:
  We investigate the Abelian monopole condensation in finite temperature SU(2)
and SU(3) pure lattice gauge theories. To this end we introduce a gauge
invariant disorder parameter built up in terms of the lattice Schr\"odinger
functional. Our numerical results show that the disorder parameter is different
from zero and Abelian monopole condense in the confined phase. On the other
hand our numerical data suggest that the disorder parameter tends to zero, in
the thermodynamic limit, when the gauge coupling constant approaches the
critical deconfinement value. In the case of SU(3) we also compare the
different kinds of Abelian monopoles which can be defined according to the
choice of the Abelian subgroups.


title: Topological Obstruction in Block-spin Transformations

abstract:
  Block-spin transformations from a fine lattice to a coarse one are shown to
give rise to a one-to-one correspondence between the zero-modes of the
Ginsparg-Wilson Dirac operators. The index is then preserved under the blocking
process. Such a one-to-one correspondence is violated and the block-spin
transformation becomes necessarily ill-defined when the absolute value of the
index is larger than 2rN, where N is the number of the sites on the coarse
lattice and r is the dimension of the gauge group representation of the fermion
variables.


title:
Extension to order $\beta^{23}$ of the high-temperature expansions for
  the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic
  lattices

abstract:
  Using a renormalized linked-cluster-expansion method, we have extended to
order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$
and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on
the sc and the bcc lattices. A study of these expansions yields updated direct
estimates of universal parameters, such as exponents and amplitude ratios,
which characterize the critical behavior of $\chi$ and $\xi$. Our best
estimates for the inverse critical temperatures are
  $\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. For the
susceptibility exponent we get $\gamma=1.2375(6)$ and for the correlation
length exponent we get $\nu=0.6302(4)$.
  The ratio of the critical amplitudes of $\chi$ above and below the critical
temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for
$\xi$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling
amplitude ratio we obtain $a^+_{\xi}/a^+_{\chi}=0.87(6)$.