title: Spin Resolution of Glueballs in 2+1 Dimensional Lattice Gauge Theory

abstract:
  Conventional lattice gauge theory assigns the lowest spin compatible with the
symmetry channel of a given operator to the state coupling to that operator.
Operators on a cubic lattice, however, are only defined on angles of pi/2,
hence states with spin equal modulo 4 may overlap significantly. This paper
explores a new technique for generating lattice operators that may be placed
onto the lattice at angles other than pi/2, thereby resolving this modulo 4
ambiguity. Calculations of the mass of states with spin equal t o 0, 2, and 4
are performed in the positive parity and charge conjugation channe l and
compared to the spectrum from previous lattice calculations. These masses
compare well for spin 0 and 2, and for spin 4 the mass agrees with a state conv
entionally assigned spin 0, raising the possibility of mis-identification of
the spin of states coupling to some traditional operators.


title:
Lattice Chiral Symmetry in Fermionic Interacting Theories and the
  Antifield Formalism

abstract:
  Recently we have discussed realization of an exact chiral symmetry in
theories with self-interacting fermions on the lattice, based upon an auxiliary
field method. In this paper we describe construction of the lattice chiral
symmetry and discuss its structure in more detail. The antifield formalism is
used to make symmetry consideration more transparent. We show that the quantum
master equation in the antifield formalism generates all the relevant
Ward-Takahashi identities including a Ginsparg-Wilson relation for interacting
theories. Solutions of the quantum master equation are obtained in a closed
form, but the resulting actions are found to be singular. Canonical
transformations are used to obtain four types of regular actions. Two of them
may define consistent quantum theories. Their Yukawa couplings are the same as
those obtained by using the chiral decomposition in the free field algebra.
Inclusion of the complete set of the auxiliary fields is briefly discussed.


title:
A note on Zolotarev optimal rational approximation for the overlap Dirac
  operator

abstract:
  We discuss the salient features of Zolotarev optimal rational approximation
for the inverse square root function, in particular, for its applications in
lattice QCD with overlap Dirac quark. The theoretical error bound for the
matrix-vector multiplication $ H_w (H_w^2)^{-1/2}Y $ is derived. We check that
the error bound is always satisfied amply, for any QCD gauge configurations we
have tested. An empirical formula for the error bound is determined, together
with its numerical values (by evaluating elliptic functions) listed in Table 2
as well as plotted in Figure 3. Our results suggest that with Zolotarev
approximation to $ (H_w^2)^{-1/2} $, one can practically preserve the exact
chiral symmetry of the overlap Dirac operator to very high precision, for any
gauge configurations on a finite lattice.

categories: hep-lat hep-ph hep-th math-ph math.MP physics.comp-ph


title: Numerical simulation tests with light dynamical quarks

abstract:
  Two degenerate flavours of quarks are simulated with small masses down to
about one fifth of the strange quark mass by using the two-step multi-boson
(TSMB) algorithm. The lattice size is 8^3 x 16 with lattice spacing about
0.27fm which is not far from the N_t=4 thermodynamical cross-over line.
Autocorrelations of different physical quantities are estimated as a function
of the quark mass. The eigenvalue spectra of the Wilson-Dirac operator are
investigated.


title: Light Hadron Spectrum and Quark Masses from Quenched Lattice QCD

abstract:
  We present details of simulations for the light hadron spectrum in quenched
QCD carried out on the CP-PACS parallel computer. Simulations are made with the
Wilson quark action and the plaquette gauge action on 32^3x56 - 64^3x112
lattices at four lattice spacings (a \approx 0.1-0.05 fm) and the spatial
extent of 3 fm. Hadronic observables are calculated at five quark masses
(m_{PS}/m_V \approx 0.75 - 0.4), assuming the u and d quarks being degenerate
but treating the s quark separately. We find that the presence of quenched
chiral singularities is supported from an analysis of the pseudoscalar meson
data. We take m_\pi, m_\rho and m_K (or m_\phi) as input. After chiral and
continuum extrapolations, the agreement of the calculated mass spectrum with
experiment is at a 10% level. In comparison with the statistical accuracy of
1-3% and systematic errors of at most 1.7% we have achieved, this demonstrates
a failure of the quenched approximation for the hadron spectrum: the meson
hyperfine splitting is too small, and the octet masses and the decuplet mass
splittings are both smaller than experiment. Light quark masses are calculated
using two definitions: the conventional one and the one based on the
axial-vector Ward identity. The two results converge toward the continuum
limit, yielding m_{ud}=4.29(14)^{+0.51}_{-0.79} MeV. The s quark mass depends
on the strange hadron mass chosen for input: m_s = 113.8(2.3)^{+5.8}_{-2.9} MeV
from m_K and m_s = 142.3(5.8)^{+22.0}_{-0} MeV from m_\phi, indicating again a
failure of the quenched approximation. We obtain \Lambda_{\bar{MS}}^{(0)}=
219.5(5.4) MeV. An O(10%) deviation from experiment is observed in the
pseudoscalar meson decay constants.


title: Gluon Propagator on Coarse Lattices in Laplacian Gauges

abstract:
  The Laplacian gauge is a nonperturbative gauge fixing that reduces to Landau
gauge in the asymptotic limit. Like Landau gauge, it respects Lorentz
invariance, but it is free of Gribov copies; the gauge fixing is unambiguous.
In this paper we study the infrared behavior of the lattice gluon propagator in
Laplacian gauge by using a variety of lattices with spacings from $a = 0.125$
to 0.35 fm, to explore finite volume and discretization effects. Three
different implementations of the Laplacian gauge are defined and compared. The
Laplacian gauge propagator has already been claimed to be insensitive to finite
volume effects and this is tested on lattices with large volumes.


title: I=2 Pion Scattering Length with the Wilson Fermion

abstract:
  The calculation of the I=2 pion scattering length in quenched lattice QCD is
revisited. The calculation is carried out with the Wilson fermion action
employing L\"uscher's finite size scaling method at $\beta=5.9$, 6.1, and 6.3
corresponding to the range of lattice spacing $a\simeq 0.12 - 0.07$ fm. We
obtain in the continuum limit $a_0m_\pi = -0.0410(69)$, which is consistent
with the prediction of chiral perturbation theory $a_0m_\pi=-0.0444(10)$.


title:
Exotic mesons from quantum chromodynamics with improved gluon and quark
  actions on the anisotropic lattice

abstract:
  Hybrid (exotic) mesons, which are important predictions of quantum
chromodynamics (QCD), are states of quarks and anti-quarks bound by excited
gluons. First principle lattice study of such states would help us understand
the role of ``dynamical'' color in low energy QCD and provide valuable
information for experimental search for these new particles. In this paper, we
apply both improved gluon and quark actions to the hybrid mesons, which might
be much more efficient than the previous works in reducing lattice spacing
error and finite volume effect. Quenched simulations were done at $\beta=2.6$
and on a $\xi=3$ anisotropic $12^3\times36$ lattice using our PC cluster. We
obtain $2013 \pm 26 \pm 71$ MeV for the mass of the $1^{-+}$ hybrid meson
${\bar q}qg$ in the light quark sector, and $4369 \pm 37 \pm 99$Mev in the
charm quark sector; the mass splitting between the $1^{-+}$ hybrid meson ${\bar
c}c g$ in the charm quark sector and the spin averaged S-wave charmonium mass
is estimated to be $1302 \pm 37 \pm 99$ MeV. As a byproduct, we obtain $1438
\pm 32 \pm 57$ MeV for the mass of a P-wave $1^{++}$ ${\bar u}u$ or ${\bar d}d$
meson and $1499 \pm 28 \pm 65$ MeV for the mass of a P-wave $1^{++}$ ${\bar
s}s$ meson, which are comparable to their experimental value 1426 MeV for the
$f_1(1420)$ meson. The first error is statistical, and the second one is
systematical. The mixing of the hybrid meson with a four quark state is also
discussed.


title:
Perturbative renormalization factors in domain-wall QCD with improved
  gauge actions

abstract:
  We evaluate renormalization factors of the domain-wall fermion system with
various improved gauge actions at one loop level. The renormalization factors
are calculated for quark wave function, quark mass, bilinear quark operators,
three- and four-quark operators in modified minimal subtraction (MS-bar) scheme
with the dimensional reduction(DRED) as well as the naive dimensional
regularization(NDR). We also present detailed results in the mean field
improved perturbation theory.


title:
Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic
  Field in Two Dimensions

abstract:
  It is shown that the eigenvalue problem for the hermitian Wilson-Dirac
operator of for a uniform magnetic field in two dimensions can be reduced to
one-dimensional problem described by a relativistic analog of the Harper
equation. An explicit formula for the secular equations is given in term of a
set of polynomials. The spectrum exhibits a fractal structure in the infinite
volume limit. An exact result concerning the index theorem for the overlap
Dirac operator is obtained.


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

abstract:
  A knowledge of the radial distributions of quarks inside hadrons could lead
to a better understanding of the QCD description of these hadrons and possibly
suggest forms for phenomenological models. As a step in this direction, in an
earlier work, the charge (vector) and matter (scalar) radial distributions of
heavy-light mesons were measured in the quenched approximation on a 16^3x24
lattice with a lattice spacing of 'a' approx. 0.17 fm, and a hopping parameter
corresponding to a light quark mass about that of the strange quark.
  Here several improvements are now made: 1) The configurations are generated
using dynamical fermions with a approx 0.14 fm; 2) Many more gauge
configurations areincluded; 3) The distributions at many off-axis, in addition
to on-axis, points are measured; 4) The data analysis is much more complete. In
particular, distributions involving excited states are extracted.
  The exponential decay of the charge and matter distributions can be described
by mesons of mass 0.9 +- 0.1 and 1.5 +- 0.1 GeV respectively -- values that are
consistent with those of vector and scalar $q\bar{q}$-states calculated
directly with the same lattice parameters.


title:
Lattice Calculation of Heavy-Light Decay Constants with Two Flavors of
  Dynamical Quarks

abstract:
  We present results for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios in
the presence of two flavors of light sea quarks ($N_f=2$). We use Wilson light
valence quarks and Wilson and static heavy valence quarks; the sea quarks are
simulated with staggered fermions. Additional quenched simulations with
nonperturbatively improved clover fermions allow us to improve our control of
the continuum extrapolation. For our central values the masses of the sea
quarks are not extrapolated to the physical $u$, $d$ masses; that is, the
central values are "partially quenched." A calculation using "fat-link clover"
valence fermions is also discussed but is not included in our final results. We
find, for example, $f_B = 190 (7) (^{+24}_{-17}) (^{+11}_{-2}) (^{+8}_{-0})$
MeV, $f_{B_s}/f_B = 1.16 (1) (2) (2) (^{+4}_{-0})$, $f_{D_s} = 241 (5)
(^{+27}_{-26}) (^{+9}_{-4}) (^{+5}_{-0})$ MeV, and $f_{B}/f_{D_s} = 0.79 (2)
(^{+5}_{-4}) (3) (^{+5}_{-0})$, where in each case the first error is
statistical and the remaining three are systematic: the error within the
partially quenched $N_f=2$ approximation, the error due to the missing strange
sea quark and to partial quenching, and an estimate of the effects of chiral
logarithms at small quark mass. The last error, though quite significant in
decay constant ratios, appears to be smaller than has been recently suggested
by Kronfeld and Ryan, and Yamada. We emphasize, however, that as in other
lattice computations to date, the lattice $u,d$ quark masses are not very light
and chiral log effects may not be fully under control.


title:
Monopole clusters, center vortices, and confinement in a Z(2)
  gauge-Higgs system

abstract:
  We propose to use the different kinds of vacua of the gauge theories coupled
to matter as a laboratory to test confinement ideas of pure Yang-Mills
theories. In particular, the very poor overlap of the Wilson loop with the
broken string states supports the 't Hooft and Mandelstam confinement criteria.
However in the Z(2) gauge-Higgs model we use as a guide we find that the
condensation of monopoles and center vortices is a necessary, but not
sufficient condition for confinement.


title: Independence on the Abelian Projection of Monopole Condensation in QCD

abstract:
  It is proven that dual superconductivity of QCD vacuum in the confining phase
is an intinsic property, independent on the choice of the abelian projection
used to define the monopoles.


title: Supersymmetry on a Spatial Lattice

abstract:
  We construct a variety of supersymmetric gauge theories on a spatial lattice,
including N=4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice
supersymmetry greatly reduces or eliminates the need for fine tuning to arrive
at the desired continuum limit in these examples.


title:
Glueball Properties at Finite Temperature in SU(3) Anisotropic Lattice
  QCD

abstract:
  The thermal properties of the glueballs are studied using SU(3) anisotropic
lattice QCD with beta=6.25, the renormalized anisotropy xi=a_s/a_t=4 over the
lattice of the size 20^3\times N_t with N_t = 24, 26, 28, 30, 33, 34, 35, 36,
37, 38, 40, 43, 45, 50, 72 at the quenched level. To construct a suitable
operator on the lattice, we adopt the smearing method, and consider its
physical meaning in terms of the operator size. First, we construct the
temporal correlators G(t) for the 0^{++} and 2^{++} glueballs, using more than
5,000 gauge configurations at each temperature. We then measure the pole-mass
of the thermal glueballs from G(t). For the lowest 0^{++} glueball, we observe
a significant pole-mass reduction of about 300 MeV near T_c or m_G(T\simeq T_c)
\simeq 0.8 m_G(T\sim 0), while its size remains almost unchanged as rho(T)
\simeq 0.4fm. Finally, for completeness, as an attempt to take into account the
effect of thermal width Gamma(T) at finite temperature, we perform a more
general new analysis of G(t) based on its spectral representation. By adopting
the Breit-Wigner form for the spectral function rho(omega), we perform the
best-fit analysis as a straightforward extension to the standard pole-mass
analysis. The result indicates a significant broadening of the peak as Gamma(T)
\sim 300 MeV as well as rather modest reduction of the peak center of about 100
MeV near T_c for the lowest 0^{++} glueball. The temporal correlators of the
color-singlet modes corresponding to these glueballs above T_c are also
investigated.


title:
On the Landau Ginzburg theory of MAG projected SU(2) lattice gauge
  theory

abstract:
  Maximal Abelian gauge fixing and subsequent Abelian projection of SU(2)
lattice gauge theory defines closed trajectories of magnetic monopoles. These
trajectories can be interpreted in terms of an effective scalar field theory of
the MAG monopoles using the worldline representation of the functional
determinants. Employing the monopole worldlines detected in the numerical
simulation, we show that a scalar bound state exists. The screening mass $m$ of
this state properly scales towards the continuum limit. We find m ~ 1.3 $GeV
when the string tension sigma = 440 MeV is used as reference scale.


title: Modified iterative versus Laplacian Landau gauge in compact U(1) theory

abstract:
  Compact U(1) theory in 4 dimensions is used to compare the modified iterative
and the Laplacian fixing to lattice Landau gauge in a controlled setting, since
in the Coulomb phase the lattice theory must reproduce the perturbative
prediction. It turns out that on either side of the phase transition clear
differences show up and in the Coulomb phase the ability to remove double Dirac
sheets proves vital on a small lattice.


title: f_B and two scales problems in lattice QCD

abstract:
  A novel method to calculate f_B on the lattice is introduced, based on the
study of the dependence of finite size effects upon the heavy quark mass of
flavoured mesons and on a non-perturbative recursive finite size technique. We
avoid the systematic errors related to extrapolations from the static limit or
to the tuning of the coefficients of effective Lagrangian and the results admit
an extrapolation to the continuum limit. We perform a first estimate at finite
lattice spacing, but close to the continuum limit, giving f_B = 170(11)(5)(22)
MeV. We also obtain f_{B_s} = 192(9)(5)(24) MeV. The first error is
statistical, the second is our estimate of the systematic error from the method
and the third the systematic error from the specific approximations adopted in
this first exploratory calculation. The method can be generalized to two--scale
problems in lattice QCD.


title:
Transfer matrix and nonperturbative renormalization of fermionic
  currents in lattice QCD

abstract:
  The functional integral representation for fermionic observables on the
lattice is studied. In particular, Grassmannian representations of the scalar
$\hatJ^{(S)}$ and pseudoscalar $\hatJ^{(P)}$ currents and pseudoscalar
correlator are derived. It is also discussed the connection between the
fermionic Fock space and boundary conditions along the time direction.


title: Chiral measurements in quenched lattice QCD with Fixed Point fermions

abstract:
  We construct a parametrization of a Fixed Point (FP) Dirac operator and apply
it in quenched lattice QCD. The symmetry requirements for a general lattice
Dirac operator are discussed and an efficient way to make a practical
construction of general lattice Dirac operators is provided. We use such a
lattice Dirac operator to approximately solve the Renormalization Group
equation that defines the FP Dirac operator in an iterative procedure. We
discuss the properties of this parametrization and show that its breaking of
chiral symmetry and its scaling violations in hadron specroscopy are much
reduced compared to the Wilson Dirac operator. Furthermore, we discuss the
overlap construction with the parametrized FP Dirac operator and its
properties. Using the Atiyah-Singer index theorem, a consequence of chiral
symmetry, we calculate the quenched topological susceptibility. Finally, we
determine the renormalized low-energy constant Sigma of quenched Chiral
Perturbation Theory using a finite volume scaling technique.


title: Probing hadron wave functions in Lattice QCD

abstract:
  Gauge-invariant equal-time correlation functions are calculated in lattice
QCD within the quenched approximation and with two dynamical quark species.
These correlators provide information on the shape and multipole moments of the
pion, the rho, the nucleon and the $\Delta$.


title: SU(N) gauge theories in 2+1 dimensions -- further results

abstract:
  We calculate the string tension and part of the mass spectrum of SU(4) and
SU(6) gauge theories in 2+1 dimensions using lattice techniques. We combine
these new results with older results for N=2,...,5 so as to obtain more
accurate extrapolations to N=infinity. The qualitative conclusions of the
earlier work are unchanged: SU(N) theories in 2+1 dimensions are linearly
confining as N->infinity; the limit is achieved by keeping g.g.N fixed; SU(3),
and even SU(2), are `close' to SU(infinity). We obtain more convincing evidence
than before that the leading large-N correction is O(1/N.N). We look for the
multiplication of states that one expects in simple flux loop models of
glueballs, but find no evidence for this.


title:
A proposal for simulating QCD at finite chemical potential on the
  lattice

abstract:
  An algorithm to simulate full QCD with 3 colours at nonzero chemical
potential on the lattice is proposed. The algorithm works for small values of
the chemical potential and can be used to extract expectation values of CPT
invariant operators.


title: The deconfinement transition in SU(N) gauge theories

abstract:
  We investigate the properties of the deconfinement transition in SU(4) and
SU(6) gauge theories. We find that it is a `normal' first order transition in
both cases, from which we conclude that the transition is first order in the
N->infinity limit. Comparing our preliminary estimates of the continuum values
of Tc/sqrt(K) with existing values for SU(2) and SU(3) demonstrates a weak
dependence on N for all values of N.


title: Cluster Percolation and Chiral Phase Transition

abstract:
  The Meron Cluster algorithm solves the sign problem in a class of interacting
fermion lattice models with a chiral phase transition. Within this framework,
we study the geometrical features of the clusters built by the algorithm, that
suggest the occurrence of a generalized percolating phase transition at the
chiral critical temperature in close analogy with Fortuin-Kasteleyn percolation
in spin models.


title: Lattice Predictions for Hybrids and Glueballs

abstract:
  I review the results from lattice gauge theory for the properties of the
light 1-+ exotic state and 0++ glueball.


title: Heavy Quark Anti-Quark Free Energy and the Renormalized Polyakov Loop

abstract:
  We calculate the colour averaged and colour singlet free energies of static
quark anti-quark sources placed in a thermal gluonic heat bath. We discuss the
renormalization of these free energies using the short distance properties of
the zero temperature heavy quark potential. This leads to the definition of the
renormalized Polyakov loop as an order parameter for the deconfinement phase
transition of the SU(3) gauge theory which is well behaved in the continuum
limit.


title: Quark confinement and the bosonic string

abstract:
  Using a new type of simulation algorithm for the standard SU(3) lattice gauge
theory that yields results with unprecedented precision, we confirm the
presence of a $\gamma/r$ correction to the static quark potential at large
distances $r$, with a coefficient $\gamma$ as predicted by the bosonic string
theory. In both three and four dimensions, the transition from perturbative to
string behaviour is evident from the data and takes place at surprisingly small
distances.


title: Fine Structure of the QCD String Spectrum

abstract:
  Using advanced lattice methods in Quantum Chromodynamics, three distinct
scales are established in the excitation spectrum of the gluon field around a
static quark-antiquark pair as the color source separation R is varied. On the
shortest length scale, the excitations are consistent with states created by
local gluon field operators arising from a multipole operator product
expansion. An intermediate crossover region below 2 fm is identified with a
dramatic rearrangement of the level orderings. On the largest length scale of
2-3 fm, the spectrum agrees with that expected for string-like excitations. The
energies nearly reproduce asymptotic pi/R string gaps, but exhibit a fine
structure, providing important clues for developing an effective bosonic string
description.


title: Speed and Adaptability of Overlap Fermion Algorithms

abstract:
  We compare the efficiency of four different algorithms to compute the overlap
Dirac operator, both for the speed, i.e., time required to reach a desired
numerical accuracy, and for the adaptability, i.e., the scaling of speed with
the condition number of the (square of the) Wilson Dirac operator. Although
orthogonal polynomial expansions give good speeds at moderate condition number,
they are highly non-adaptable. One of the rational function expansions, the
Zolotarev approximation, is the fastest and is adaptable. The conjugate
gradient approximation is adaptable, self-tuning, and nearly as fast as the ZA.


title: The staggered domain wall fermion method

abstract:
  A different lattice fermion method is introduced. Staggered domain wall
fermions are defined in 2n+1 dimensions and describe 2^n flavors of light
lattice fermions with exact U(1) x U(1) chiral symmetry in 2n dimensions. As
the size of the extra dimension becomes large, 2^n chiral flavors with the same
chiral charge are expected to be localized on each boundary and the full
SU(2^n) x SU(2^n) flavor chiral symmetry is expected to be recovered. SDWF give
a different perspective into the inherent flavor mixing of lattice fermions and
by design present an advantage for numerical simulations of lattice QCD
thermodynamics. The chiral and topological index properties of the SDWF Dirac
operator are investigated. And, there is a surprise ending...


title:
Numerical study for the c-dependence of fractal dimension in
  two-dimensional quantum gravity

abstract:
  We numerically investigate the fractal structure of two-dimensional quantum
gravity coupled to matter central charge c for $-2 \leq c \leq 1$. We
reformulate Q-state Potts model into the model which can be identified as a
weighted percolation cluster model and can make continuous change of Q, which
relates c, on the dynamically triangulated lattice. The c-dependence of the
critical coupling is measured from the percolation probability and
susceptibility. The c-dependence of the string susceptibility of the quantum
surface is evaluated and has very good agreement with the theoretical
predictions. The c-dependence of the fractal dimension based on the finite size
scaling hypothesis is measured and has excellent agreement with one of the
theoretical predictions previously proposed except for the region near
$c\approx 1$.


title: A new proposal for the fermion doubling problem

abstract:
  In this paper I propose the use of a lattice derivative operator that is
equivalent to the ideal SLAC derivative operator in all lattice calculations,
but without the prohibitively expensive computational cost of the latter. A
pedagogical motivation and derivation of the closed form of the SLAC derivative
in position space is presented, and the proposed method for its cost-effective
implementation is presented in detail.


title: Chiral anomalies in the reduced model

abstract:
  On the basis of an observation due to Kiskis, Narayanan and Neuberger, we
show that there is a remnant of chiral anomalies in the reduced model when a
Dirac operator which obeys the Ginsparg-Wilson relation is employed for the
fermion sector. We consider fermions belonging to the fundamental
representation of the gauge group U(N) or SU(N). For vector-like theories, we
determine a general form of the axial anomaly or the topological charge within
a framework of a U(1) embedding. For chiral gauge theories with the gauge group
U(N), a remnant of gauge anomaly emerges as an obstruction to a smooth fermion
integration measure. The pure gauge action of gauge-field configurations which
cause these non-trivial phenomena always diverges in the 't Hooft $N\to\infty$
limit when d>2.


title: Chern-Simons theory on the lattice

abstract:
  We present new proposals for the representation of a Chern-Simons term on the
lattice. In the first part, such a term is constructed from the fermion
determinant, and in the second part directly from the Abelian gauge term. In
both cases, the parity transformation is modified on the lattice without
affecting its continuum limit.


title: Semileptonic B Decays from an NRQCD/D234 Action

abstract:
  Semileptonic, B --> pi, l nubar, decays are studied on quenched anisotropic
lattices using tree-level tadpole improved Symanzik glue, NRQCD heavy quark and
D234 light quark actions. Constrained fitting methods are applied to extract
groundstate contributions to two-point and three-point correlators. We agree
with previous lattice determinations of the form factors. The major source of
systematic error here, as in previous work, comes from the chiral extrapolation
to the physical pion mass. Future calculations must work at lighter quark
masses to resolve this.


title:
A meron cluster solution for the sign problem of the two-dimensional
  O(3) model

abstract:
  The two-dimensional O(3) model at a vacuum angle theta=pi is investigated.
This model has a severe sign problem. By a Wolff cluster algorithm an integer
or half-integer topological charge is assigned to each cluster. The meron
clusters (clusters with half-integer topological charge) are used to construct
an improved estimator for the correlation function of two spins at theta=pi.
Only configurations with 0 and 2 merons contribute to this correlation
function.
  An algorithm, that generates configurations with only 0 and 2 merons, is
constructed and numerical simulations at theta=pi are performed.
  The numerical results indicate the presence of long range correlations at
theta=pi.


title: Nicolai mapping vs. exact chiral symmetry on the lattice

abstract:
  Two-dimensional N=2 Wess-Zumino model is constructed on the lattice through
Nicolai mapping with Ginsparg-Wilson fermion. The Nicolai mapping requires a
certain would-be surface term in the bosonic action which ensures the vacuum
energy cancellation even on the lattice, but inevitably breaks chiral symmetry.
With the Ginsparg-Wilson fermion, the holomorphic structure of the would-be
surface term is maintained, leaving a discrete subgroup of the exact chiral
symmetry intact for a monomial scalar potential. By this feature both boson and
fermion can be kept massless on the lattice without any fine-tuning.


title:
Partial-Global Stochastic Metropolis Update for Dynamical Smeared Link
  Fermions

abstract:
  We performed dynamical simulations with HYP smeared staggered fermions using
the recently proposed partial-global stochastic Metropolis algorithm with
fermion matrix reduction and determinant breakup improvements. In this paper we
discuss our choice of the action parameters and study the autocorrelation time
both with four and two fermionic flavors at different quark mass values on
approximately 10 fm^4 lattices. We find that the update is especially efficient
with two flavors making simulations on larger volumes feasible.


title:
A new proposal for the fermion doubling problem. II. Improving the
  operators for finite lattices

abstract:
  In a previous paper I showed how the ideal SLAC derivative and
second-derivative operators for an infinite lattice can be obtained in simple
closed form in position space, and implemented very efficiently in a stochastic
fashion for practical calculations on finite lattices. In this second paper I
show how the small (order 1/N) errors introduced by truncating the operators to
a finite lattice may be removed by a small adjustment of coefficients, without
incurring any additional computational cost. The derivation of these results is
again presented in a simple, pedagogical fashion.


title: The step scaling function of QCD at negative flavor number

abstract:
  As a computationally less costly test case for full QCD, we investigate an
SU(3) Yang-Mills theory coupled to a bosonic spinor field. This theory
corresponds to QCD with minus two quark flavors and is known as the bermion
model. Our central object of interest is the step scaling function which
describes the scale evolution of the running coupling in the Schrodinger
functional scheme. We develop a suitable algorithm for the simulation of O(a)
improved bermions and compare its performance with unimproved bermions and full
QCD. We study in detail the lattice artefacts and the continuum extrapolation
of the step scaling function from lattice simulations when improvement is used.
Our results are compared to the unimproved bermion and dynamical fermion cases,
and to renormalized perturbation theory in the continuum limit.
  We also examine the step scaling function with massive quarks in the bermion
model. According to the Appelquist-Carazzone theorem the contributions from
matter fields are expected to vanish for large masses, such that the step
scaling function converges to the pure gauge theory case. If one wants to
connect non-perturbatively different effective theories with different numbers
of active quarks over flavor thresholds, lattice artefacts should be reasonably
small. In order to test the feasibility of such a method, we investigate the
step scaling function and its lattice artefacts for several values of the mass.


title: Beyond the quark model of hadrons from lattice QCD

abstract:
  Lattice QCD can give direct information on OZI-violating contributions to
mesons. Here we explore the contributions that split flavour singlet and
non-singlet meson masses. I discuss in detail the spectrum and decays for
scalar mesons (ie including glueball effects). I also review the status of
hybrid mesons and their decays.


title: Screening and confinement in U(1)^{N-1} Abelian effective theories

abstract:
  We discuss the effect of dynamical charged particles in U(1)^{N-1} Abelian
effective theories of QCD. Screening and confinement at zero temperature are
explained qualitatively. The effect of dynamically charged particle is
expressed in terms of an effective action of integer electric currents. When a
screening is expected, the static potential shows a flattening in the
long-range region and a linear behavior in the intermediate region. We show why
the screening is better observed in the Polyakov-loop correlators than in the
Wilson loops. The breaking of the adjoint string is explained without the Z(N)
picture.


title:
An Analytic Variational Study of the Mass Spectrum in 2+1 Dimensional
  SU(3) Hamiltonian Lattice Gauge Theory

abstract:
  We calculate the masses of the lowest lying eigenstates of improved SU(2) and
SU(3) lattice gauge theory in 2+1 dimensions using an analytic variational
approach. The ground state is approximated by a one plaquette trial state and
mass gaps are calculated in the symmetric and antisymmetric sectors by
minimising over a suitable basis of rectangular states.


title:
String Breaking and Monopoles: a Case Study in the 3D Abelian Higgs
  Model

abstract:
  We study the breaking of the string spanned between test charges in the three
dimensional Abelian Higgs model with compact gauge field and fundamentally
charged Higgs field at zero temperature. In agreement with current expectations
we demonstrate that string breaking is associated with pairing of monopoles.
However, the string breaking is not accompanied by an ordinary phase
transition.


title:
Cluster Percolation and Critical Behaviour in Spin Models and SU(N)
  Gauge Theories

abstract:
  The critical behaviour of several spin models can be simply described as
percolation of some suitably defined clusters, or droplets: the onset of the
geometrical transition coincides with the critical point and the percolation
exponents are equal to the thermal exponents. It is still unknown whether,
given a model, one can define at all the droplets. In the cases where this is
possible, the droplet definition depends in general on the specific model at
study and can be quite involved. We propose here a simple general definition
for the droplets: they are clusters obtained by joining nearest-neighbour spins
of the same sign with some bond probability p_B, which is the minimal
probability that still allows the existence of a percolating cluster at the
critical temperature T_c. By means of lattice Monte Carlo simulations we find
that this definition indeed satisfies the conditions required for the droplets,
for many classical spin models, discrete and continuous, both in two and in
three dimensions. In particular, our prescription allows to describe exactly
the confinement-deconfinement transition of SU(N) gauge theories as Polyakov
loop percolation.


title: The Chiral Extrapolation of Strange Matrix Elements in the Nucleon

abstract:
  In current lattice simulations of nucleon properties, the up and down quark
masses are significantly larger than their physical values, while the strange
quark can be included in simulations with its physical mass. When the up and
down quark masses are much smaller than the strange-quark mass the chiral
extrapolation of strange-quark matrix elements in the nucleon from the lattice
up and down quark masses to their physical values can be performed with
two-flavor chiral perturbation theory, thereby avoiding the slow convergence
problem of the three-flavor chiral expansion. We explore the chiral expansion
of several matrix elements of strange operators in the nucleon in two-flavor
chiral perturbation theory and two-flavor partial-quenched chiral perturbation
theory.


title: Does the QCD plasma contain propagating gluons?

abstract:
  Comparison of two appropriately chosen screening masses of colour singlet
operators in the pure glue QCD plasma indicates that at sufficiently high
temperature it contains a weakly-interacting massive quasi-particle with the
quantum numbers of the electric gluon. Still in the deconfined phase, but
closer to T_c, the same mass ratio is similar to that at zero temperature,
indicating that the propagating modes are more glueball-like, albeit with a
lower scale for the masses. We observe a continuity between these two regimes.


title:
The chemical potential in the transfer matrix and in the path integral
  formulation of QCD on a lattice

abstract:
  We define the chemical potential as the Lagrange multiplier of the baryon
charge operator in the transfer matrix formalism of QCD on a lattice.
Transforming the partition function into an euclidean path integral we get the
Hasenfratz-Karsh action both for Wilson and Kogut-Susskind fermions. In the
latter case the chemical potential in the spin-diagonal basis is half that in
the flavour basis. Some open problems in the spin-diagonal basis are pointed
out.


title: Continuum Determination of Light Quark Masses from Quenched Lattice QCD

abstract:
  We compute the strange and the average up/down quark masses in the quenched
approximation of lattice QCD, by using the O(a)-improved Wilson action and
operators and by implementing the non-perturbative renormalization. Our
computation is performed at four values of the lattice spacing, from which we
could extrapolate to the continuum limit. Our final result for the strange
quark mass (in the MSbar scheme) is ms(2 GeV) = (106 +/- 2 +/- 8) MeV. For the
average up/down quark mass we have ml(2 GeV) = (4.4 +/- 0.1 +/- 0.4) MeV. The
ratio ms/ml = (24.3 +/- 0.2 +/- 0.6).


title: Perturbative calculation of O(a) improvement coefficients

abstract:
  We compute several coefficients needed for O(a) improvement of currents in
perturbation theory, using the Brodsky-Lepage-Mackenzie prescription for
choosing an optimal scale q*. We then compare the results to non-perturbative
calculations. Normalization factors of the vector and axial vector currents
show good agreement, especially when allowing for small two-loop effects. On
the other hand, there are large discrepancies in the coefficients of O(a)
improvement terms. We suspect that they arise primarily from power corrections
inherent in the non-perturbative methods.


title: The transfer matrix with Kogut-Susskind fermions

abstract:
  A transfer matrix for gauge theories on a lattice with Kogut-Susskind
fermions in the flavour basis is constructed and some difficulties in the
spin-diagonal basis are pointed out.


title: Study of the Finite Density State based on SU(2) Lattice QCD

abstract:
  We report our recent numerical studies on two-color QCD with Wilson fermions.
First the phase structure of the system in (kappa,mu)-plane is analyzed by
measuring Polyakov line, baryon number density, gluon energy density and
Polyakov line susceptibility. Then meson and baryon (di-quark) propagators are
investigated. We find that the vector meson mass decreases near mu_c. This
phenomena can be related to the low-mass lepton-pair enhancement observed in
CERES experiment. Since our lattice is small, in order to confirm the results,
we calculate both periodic and anti-periodic boundary condition cases.
Preliminary calculations of color averaged, symmetric and anti-symmetric forces
of qq system obtained from Polyakov line correlations, and gluon propagators
are reported.


title:
K^+ -> pi^+ pi^0 Decays on Finite Volumes and at Next-to-Leading Order
  in the Chiral Expansion

abstract:
  We present the ingredients necessary for the determination of physical K->pi
pi decay amplitudes for Delta I=3/2 transitions, from lattice simulations at
unphysical kinematics and the use of chiral perturbation theory at
next-to-leading order. In particular we derive the expressions for the matrix
elements <pi pi(I=2)|O_W|K>, where O_W is one of the operators appearing in the
Delta S=1 weak Hamiltonian, in terms of low-energy constants at next-to-leading
order in the chiral expansion. The one-loop chiral corrections are evaluated
for arbitrary masses and momenta, both in full QCD and in the quenched
approximation. We also investigate the finite-volume effects in this procedure.


title: Applied lattice gauge calculations: diquark content of the nucleon

abstract:
  As an example of an application of lattice QCD we describe a computation of
four-quark operators in the nucleon. The results are interpreted in a diquark
language.


title: A Geometrical Interpretation of Hyperscaling Breaking in the Ising Model

abstract:
  In random percolation one finds that the mean field regime above the upper
critical dimension can simply be explained through the coexistence of infinite
percolating clusters at the critical point. Because of the mapping between
percolation and critical behaviour in the Ising model, one might check whether
the breakdown of hyperscaling in the Ising model can also be intepreted as due
to an infinite multiplicity of percolating Fortuin-Kasteleyn clusters at the
critical temperature T_c. Preliminary results suggest that the scenario is much
more involved than expected due to the fact that the percolation variables
behave differently on the two sides of T_c.


title:
One loop calculation of the renormalised anisotropy for improved
  anisotropic gluon actions on a lattice

abstract:
  Using the infrared dispersion relation of the on shell gluon, we calculate
the renormalisation of the the anisotropy to one loop in perturbation theory
for lattice Yang-Mills theories, including the Wilson action and actions with
Symanzik and/or tadpole improvement. Using twisted boundary conditions as a
gauge invariant infrared regulator, we show for an SU(3) gauge group in D=3+1
dimensions that the one loop anisotropy is accurate to O(3%) for a range of g^2
and chi covering current simulations. In doing so we also present Feynman rules
for SU(N) gauge groups with generic anisotropy structure (including `3+1' and
`2+2' cases).


title: BCS Diquark Condensation in the 3+1d Lattice NJL Model

abstract:
  We present preliminary evidence of BCS diquark condensation in the 3+1
dimensional Nambu-Jona-Lasinio (NJL) model at non-zero chemical potential (mu)
on the lattice. Large N results are used to match the model's parameters to low
energy, zero density phenomenology. A diquark source j is added in a partially
quenched approximation to enable the measurement of lattice diquark
observables. In particular measurements are made of the diquark condensate and
susceptibilities as functions of j which support the existence of a BCS phase
at high mu.


title: A Study of Charmonium Systems across the Deconfinement Transition

abstract:
  We present results from lattice studies of charmonium systems near the
deconfinement transition temperature. On quenched isotropic lattices with
lattice spacings between 0.02 and 0.05 fm, bar{q} q systems with quark masses
close to the charm mass and with different spin-parity quantum numbers are
studied in the temperature range 0.9 Tc - 3 Tc. Results for temporal
correlators of local operators, and the spectral functions constructed from
them, are discussed. For the pseudoscalar and vector channels, the correlators
are observed to change very little across the deconfinement transition, unlike
in the case of the light quarks.


title:
Confinement and the photon propagator in 3D compact QED: a lattice study
  in Landau gauge at zero and finite temperature

abstract:
  On the lattice we study the gauge boson propagator of three dimensional
compact QED in Landau gauge at zero and non-zero temperature. The
non-perturbative effects are taken into account by the generation of a mass, by
an anomalous dimension and by the photon wave function renormalization. All
these effects can be attributed to the monopoles: they are absent in the
propagator of the singularity-free part of the gauge field. We assess carefully
the Gribov copy problem for the propagator and the parameters emerging from the
fits.


title: New methods to measure phase transition strength

abstract:
  A recently developed technique to determine the order and strength of phase
transitions by extracting the density of partition function zeroes (a
continuous function) from finite-size systems (a discrete data set) is
generalized to systems for which (i) some or all of the zeroes occur in
degenerate sets and/or (ii) they are not confined to a singular line in the
complex plane. The technique is demonstrated by application to the case of free
Wilson fermions.


title: N=2 Wess-Zumino model on the d=2 Euclidean lattice

abstract:
  We examine the N=2 Wess-Zumino model defined on the $d=2$ Euclidean lattice
in connection with a restoration of the Leibniz rule in the limit $a\to0$ in
perturbatively finite theory. We are interested in the difference between the
Wilson and Ginsparg-Wilson fermions and in the effects of extra interactions
introduced by an analysis of Nicolai mapping. As for the Wilson fermion, it
induces a linear divergence to individual tadpole diagrams in the limit
$a\to0$, which is absent in the Ginsparg-Wilson fermion. This divergence
suggests that a careful choice of lattice regularization is required in a
reliable numerical simulation. As for the effects of the extra couplings
introduced by an analysis of Nicolai mapping, the extra couplings do not
completely remedy the supersymmetry breaking in correlation functions induced
by the failure of the Leibniz rule in perturbation theory, though those
couplings ensure the vanishing of vacuum energy arising from disconnected
diagrams. Supersymmetry in correlation functions is recovered in the limit
$a\to 0$ {\em with or without} those extra couplings. In the context of lattice
theory, it may be properly said that supersymmetry does not improve ultraviolet
properties but rather it is well accommodated in theories with good ultraviolet
properties.


title:
New Way to Compute Excited States and Thermodynamics: Monte Carlo
  Hamiltonian

abstract:
  We present a new way to compute thermodynamical observables on the lattice.
We compute excited states and thermodynamical functions in the scalar model via
the Monte Carlo Hamiltonian technique. We find agreement with standard
Lagrangian lattice calculations, but observe lesser fluctuations in the results
from the MC Hamiltonian.


title: A lattice study of the spin structure of the Lambda hyperon

abstract:
  The internal spin structure of the Lambda is of special importance for the
understanding of the spin structure of hadrons in general. The comparison
between the nucleon and Lambda allows for a test of the relevant
flavour-symmetry breaking effects. Using nonperturbatively O(a) improved Wilson
fermions in the quenched approximation we have calculated the first moments of
the unpolarised, longitudinally polarised and transversity quark distribution
functions in the Lambda. The results indicate that flavour symmetry breaking
has little effect on the internal spin structure, in accordance with model
based expectations.


title: One-loop matching coefficients for improved staggered bilinears

abstract:
  We calculate one-loop matching factors for bilinear operators composed of
improved staggered fermions. We compare the results for different improvement
schemes used in the recent literature, all of which involve the use of smeared
links. These schemes aim to reduce, though not completely eliminate, O(a^2)
discretization errors. We find that all these improvement schemes substantially
reduce the size of matching factors compared to unimproved staggered fermions.
The resulting corrections are comparable to, or smaller than, those found with
Wilson and domain-wall fermions. In the best case (``Fat-7'' and mean-field
improved HYP links) the corrections are 10 % or smaller at 1/a = 2 GeV.


title: The phase transition in QCD with broken SU(2) flavour symmetry

abstract:
  We report the first investigation of the QCD transition temperature, T_c, for
two flavours of staggered quarks with unequal masses at lattice spacings of
1/4T. On changing the u/d quark mass ratio in such a way that
m(pi_0)^2/m(pi_+)^2 changes from 1 to 0.78, thus bracketing the physical value
of this ratio, we find that T_c remains unchanged in units of both m_rho and
Lambda_MSbar.


title:
Spectrum of screening masses in the (3+1)D SU(2) pure gauge theory near
  the critical temperature

abstract:
  We study the spectrum of screening masses in the deconfined phase of (3+1)D
SU(2) pure gauge theory near criticality and compare it with the spectrum of
bound states in the broken symmetry phase of the 3D Ising model, which is
related to the gauge theory by universality.


title: Numerical results from large N reduced QCD_2

abstract:
  Some results in QCD_2 at large N are presented using the reduced model on the
lattice. Overlap fermions are used to compute meson propagators.


title: Baryons in Partially-Quenched Chiral Perturbation Theory

abstract:
  I discuss the inclusion of baryons into partially-quenched chiral
perturbation theory and describe one-loop calculations that have been
performed.


title: Chiral Extrapolation of Hadronic Observables

abstract:
  One of the great challenges of lattice QCD is to produce unambiguous
predictions for the properties of physical hadrons. We review recent progress
with respect to a major barrier to achieving this goal, namely the fact that
computation time currently limits us to large quark mass. Using insights from
the study of the lattice data itself, together with the general constraints of
chiral symmetry, we demonstrate that it is possible to extrapolate accurately
and in an essentially model independent manner from the mass region where
calculations will be performed within the next five years to the chiral limit.


title: A Test of The Source Galerkin Method

abstract:
  Some results of the ongoing development of our Source Galerkin (SG)
nonperturbative approach to numerically solving Quantum Field theories are
presented. This technique has the potential to be much faster than Monte Carlo
methods. SG uses known symmetries and theoretical properties of a theory. In
order to test this approach, we applied it to phi^4 theory in zero dimensions.
This model has been extensively studied and has a known set of exact solutions.
This allows us to broaden the understanding of various properties of the SG
method and to develop techniques necessary for the successful application of
this method to more sophisticated theories.


title:
The factorization method for systems with a complex action -a test in
  Random Matrix Theory for finite density QCD-

abstract:
  Monte Carlo simulations of systems with a complex action are known to be
extremely difficult. A new approach to this problem based on a factorization
property of distribution functions of observables has been proposed recently.
The method can be applied to any system with a complex action, and it
eliminates the so-called overlap problem completely. We test the new approach
in a Random Matrix Theory for finite density QCD, where we are able to
reproduce the exact results for the quark number density. The achieved system
size is large enough to extract the thermodynamic limit. Our results provide a
clear understanding of how the expected first order phase transition is induced
by the imaginary part of the action.


title: Transiting topological sectors with the overlap

abstract:
  The overlap operator provides an elegant definition for the winding number of
lattice gauge field configurations. Only for a set of configurations of measure
zero is this procedure undefined. Without restrictions on the lattice fields,
however, the space of gauge fields is simply connected. I present a simple low
dimensional illustration of how the eigenvalues of a truncated overlap operator
flow as one travels between different topological sectors.


title:
Application of the Maximum Entropy Method to the (2+1)d Four-Fermion
  Model

abstract:
  We investigate spectral functions extracted using the Maximum Entropy Method
from correlators measured in lattice simulations of the (2+1)-dimensional
four-fermion model. This model is particularly interesting because it has both
a chirally broken phase with a rich spectrum of mesonic bound states and a
symmetric phase where there are only resonances. In the broken phase we study
the elementary fermion, pion, sigma and massive pseudoscalar meson; our results
confirm the Goldstone nature of the pi and permit an estimate of the meson
binding energy. We have, however, seen no signal of sigma -> pi pi decay as the
chiral limit is approached. In the symmetric phase we observe a resonance of
non-zero width in qualitative agreement with analytic expectations; in addition
the ultra-violet behaviour of the spectral functions is consistent with the
large non-perturbative anomalous dimension for fermion composite operators
expected in this model.


title: Monopoles, confinement and the photon propagator in QED$_3$

abstract:
  We study the lattice gauge boson propagator of 3D compact QED in Landau gauge
at zero and non-zero temperature. Non-perturbative effects are reflected by the
generation of a mass $m$, by an anomalous dimension $\alpha$ and by the photon
wave function renormalisation $Z$. These effects can be attributed to
monopoles: they are absent in the propagator of the regular part of the gauge
field. The r\^ole of Gribov copies is carefully investigated.


title: The H dibaryon on the lattice

abstract:
  We present our final results for the mass of the six quark flavor singlet
state (J^P=0^+, S=-2) called H dibaryon, which would be the lightest possible
strangelet in the context of strange quark matter. The calculations are
performed in quenched QCD on (8-24)^3 x 30 lattices with the (1,2) Symanzik
improved gauge action and the clover fermion action. Furthermore the fuzzing
technique for the fermion fields and smearing of the gauge fields is applied in
order to enhance the overlap with the ground state. Depending on the lattice
size we observe an H mass slightly above or comparable with the \Lambda\Lambda
threshold for strong decay. Therefore a bound H dibaryon state seemed to be
ruled out by our simulation.


title: Non-compact QED_3 with N_f >=2

abstract:
  Non-compact three-dimensional QED is studied by computer simulations to
understand its chiral symmetry breaking features for N_f>=2, on lattice volumes
up to 50^3 and bare masses as low as ma=0.0000625. We compute the chiral
condensate, scalar and pseudoscalar susceptibilities, and the masses of scalar
and pseudoscalar mesons. Finite volume effects and discretisation artifacts are
carefully monitored. Our results reveal no decisive signal for chiral symmetry
breaking for any N_f>=2. For N_f=2 the dimensionless condensate can be bounded
by beta^2<psibarpsi> <= 5x10^-5. We also present an exploratory study of the
fractionally-charged Polyakov line.


title: The local structure of topological charge fluctuations in QCD

abstract:
  We introduce the Dirac eigenmode filtering of topological charge density
associated with Ginsparg-Wilson fermions as a tool to investigate the local
structure of topological charge fluctuations in QCD. The resulting framework is
used to demonstrate that the bulk of topological charge in QCD does not appear
in the form of unit quantized lumps. This means that the mixing of "would-be"
zeromodes associated with such lumps is probably not the prevalent microscopic
mechanism for spontaneous chiral symmetry breaking in QCD. To characterize the
coherent local behavior in topological charge density at low energy, we compute
the charges contained in maximal coherent spheres enclosing non-overlapping
peaks. We find a continuous distribution essentially ending at ~0.5. Finally,
we study, for the first time, the overlap-operator topological-charge-density
correlators and find consistency with non-positivity at nonzero physical
distance. This represents a non-trivial check on the locality (in gauge paths)
of the overlap Dirac operator for realistic gauge backgrounds.


title: Perturbative improvement of staggered fermions using fat links

abstract:
  We study possibility of improving staggered fermions using various fat links
in order to reduce perturbative corrections to the gauge-invariant staggered
fermion operators. We prove five theorems on SU(3) projection, triviality in
renormalization, multiple SU(3) projections, uniqueness and equivalence. As a
result of these theorems, we show that, at one loop level, the renormalization
of staggered fermion operators is identical between SU(3) projected Fat7 links
and hypercubic links, as long as the action and operators are constructed by
imposing the same perturbative improvement condition. In addition, we propose a
new view of SU(3) projection as a tool of tadpole improvement for the staggered
fermion doublers. As a conclusion, we present alternative choices of
constructing fat links to improve the staggered fermion action and operators,
which deserve further investigation.


title: SYM Correlators and the Maldacena Conjecture

abstract:
  We report on progress in evaluating quantum filed theories with
supersymmetric discrete light-cone quantization (SDLCQ). We compare the method
to lattice gauge theory and point out its relevance for lattice calculations.
As an exciting application we present a test of the Maldacena conjecture. We
test the conjecture by evaluating the correlator of the stress-energy tensor in
the strong coupling field theory and comparing to the string theory prediction
of its behavior as a function of the distance. Our numerical results support
the Maldacena conjecture and are within 10-15% of the predicted results.


title: Computational Methods for UV-Suppressed Fermions

abstract:
  Lattice fermions with suppressed high momentum modes solve the ultraviolet
slowing down problem in lattice QCD. This paper describes a stochastic
evaluation of the effective action of such fermions. The method is a based on
the Lanczos algorithm and it is shown to have the same complexity as in the
case of standard fermions.


title: Dynamics of the 2d Potts model phase transition

abstract:
  The dynamics of 2d Potts models, which are temperature driven through the
phase transition using updating procedures in the Glauber universality class,
is investigated. We present calculations of the hysteresis for the (internal)
energy and for Fortuin-Kasteleyn clusters. The shape of the hysteresis is used
to define finite volume estimators of physical observables, which can be used
to study the approach to the infinite volume limit. We compare with equilibrium
configurations and the preliminary indications are that the dynamics leads to
considerable alterations of the statistical properties of the configurations
studied.


title: Matching coefficients for improved staggered bilinears

abstract:
  We calculate one-loop matching factors for bilinear operators composed of
improved staggered fermions. We compare the results for different improvement
schemes used in the recent literature, including the HYP action and an action
close to the Asqtad action. We find that all improvement schemes substantially
reduce the size of the one-loop contributions to matching factors. The
resulting corrections are comparable to, or smaller than, those found with
Wilson and domain-wall fermions.


title:
Towards the Continuum Limit of the Overlap Quark Propagator in Landau
  Gauge

abstract:
  The properties of the momentum space quark propagator in Landau gauge are
examined for the overlap quark action in quenched lattice QCD. Numerical
calculations were done on two lattices with different lattice spacing $a$ and
similar physical volumes to explore the quark propagator in the continuum
limit. We have calculated the nonperturbative wavefunction renormalization
function $Z(p)$ and the nonperturbative mass function $M(p)$ for a variety of
bare quark masses and perform a simple linear extrapolation to the chiral
limit. We find the behaviour of $Z(p)$ and $M(p)$ in the chiral limit are in
good agreement between the two lattices.


title: $B^0-\bar{B}^0$ mixing in quenched lattice QCD

abstract:
  We present our results of lattice calculations of $B$ parameters, which
parameterize $\Delta B$=2 transition amplitudes together with the leptonic
decay constant. Calculations are made in the quenched approximation at
$\beta$=5.7, 5.9, 6.0 and 6.1, using NRQCD action for heavy quark and the
$O(a)$-improved Wilson action for light quark. The operators are perturbatively
renormalized including the correction of $O(\alpha_s/(aM)^m)$ ($m\ge$0). We
examine the scaling behavior of $B$ parameters, and discuss the systematic
uncertainties based on the results with several different truncations of higher
order terms in 1/M and $\alpha_s$ expansions. We find
$B_{B_d}(m_b)=0.84(3)(5)$,
$B_{B_s}/B_{B_d}=1.020(21)(^{+15}_{-16})(^{+5}_{-0})$ and
$B_{S_s}(m_b)=0.85(1)(5)(^{+1}_{-0})$ in the quenched approximation. The errors
represent statistical and systematic as well as the uncertainty in the
determination of strange quark mass.


title: A Linux PC cluster for lattice QCD with exact chiral symmetry

abstract:
  A computational system for lattice QCD with exact chiral symmetry is
described. The platform is a home-made Linux PC cluster, built with
off-the-shelf components. At present this system constitutes of 64 nodes, with
each node consisting of one Pentium 4 processor (1.6/2.0/2.5 GHz), one Gbyte of
PC800/PC1066 RDRAM, one 40/80/120 Gbyte hard disk, and a network card. The
computationally intensive parts of our program are written in SSE2 codes. The
speed of this system is estimated to be 70 Gflops, and its price/performance is
better than $1.0/Mflops for 64-bit (double precision) computations in quenched
QCD. We discuss how to optimize its hardware and software for computing quark
propagators via the overlap Dirac operator.


title:
A Lattice Fermion Doublet With A Generalization Of The Ginsparg-Wilson
  Relation

abstract:
  We present a new staggered discretization of the Dirac operator. In
comparison with standard staggered fermions, real and imaginary parts are
located in different nodes. Doubling gives only a doublet of Dirac fermions
which we propose to interpret as a physical (lepton or quark) doublet. Contrary
to usual staggered fermions, we have no exact chiral symmetry but obtain a
generalization of the Ginsparg-Wilson relation.


title: Light hadron properties with improved staggered quarks

abstract:
  Preliminary results from simulations with 2+1 dynamical quark flavors at a
lattice spacing of 0.09 fm are combined with earlier results at a=0.13 fm. We
examine the approach to the continuum limit and investigate the dependence of
the pseudoscalar masses and decay constants as the sea and valence quark masses
are separately varied.


title: Interacting staggered domain wall fermions

abstract:
  The behavior of staggered domain wall fermions in the presence of gauge
fields is presented. In particular, their response to gauge fields with
nontrivial topology is discussed.


title: The Thermal Width of the Glueball at Non-Zero Temperature

abstract:
  We use SU(3) anisotropic lattice QCD at quenched level to study the 0++
glueball correlator at various temperature taking into account the possible
existence of the thermal width in the ground-state peak. For this purpose, we
adopt the Breit-Wigner ansatz for the appropriate fit-function for the lattice
data obtained with 5,500-9,900 gauge configurations at each T. The results show
the significant thermal width broadening as Gamma(T_c) \sim 300 MeV with a
reduction in the peak center as Delta omega_0(T_c) \sim 100 MeV near the
critical temperature T_c.


title: The Color-Flavor Transformation and Lattice QCD

abstract:
  We present the color-flavor transformation for gauge group SU(N_c) and
discuss its application to lattice QCD.


title: Quenched Chiral Log and Light Quark Mass from Overlap Fermions

abstract:
  We study the quenched chiral behavior of the pion with mass as low as
$\approx 180$ MeV. The calculation is done on a quenched lattice of size
$16^3\times 28$ and $a = 0.2$ fm with 80 configurations using overlap fermions
and an improved gauge action. Using an improved constrained curve fitting
technique, we find that the ground state pseudoscalar mass versus bare quark
mass behavior is well controlled with small statistical errors; this permits a
reliable fit of the quenched chiral log effects, a determination of the chiral
log parameter ($\delta = 0.26(3)$), and an estimate of the renormalized mass of
the light quark ($m^{\bar{MS}}(\mu=2 {\rm GeV}) = 3.7(3) {\rm MeV}$).


title: Lattice supersymmetry

abstract:
  A method is proposed for latticizing a class of supersymmetric gauge
theories, including N=4 super Yang-Mills. The technique is inspired by recent
work on ``deconstruction''. Part of the target theory's supersymmetry is
realized exactly on the lattice, reducing or eliminating the need for fine
tuning. (Talk based on the paper "Supersymmetry on a Spatial Lattice",
hep-lat/0206019, by D.B.K., Emmanuel Katz and Mithat Unsal).


title:
Static quark potential and string tension for compact U(1) in (2+1)
  dimensions

abstract:
  Compact U(1) lattice gauge theory in (2+1) dimensions is studied on
anisotropic lattices using Standard Path Integral Monte Carlo techniques. We
extract the static quark potential and the string tension from 1.0 <= Dtau <=
0.333 simulations at 1.0 <= beta <= 3.0. Estimating the actual value of the
renormalization constant, (c = 44), we observe the evidence of scaling in the
string tension for 1.4142 <= beta <= 2.5; with the asymptotic behaviour in the
large-beta limit given by K sqrt(beta) = e^(-2.494 beta +2.29). Extrapolations
are made to the extreme anisotropic or "Hamiltonian" limit, and comparisons are
made with previous estimates obtained by various other methods in the
Hamiltonian formulation.


title: Lanczos Methods for UV-Suppressed Fermions

abstract:
  In this talk I indroduce lattice fermions with suppressed cutoff modes. Then
I present Lanczos based methods for stochastic evaluation of the fermion
determinant.


title: Gauge Problem of Monopole Dynamics in SU(2) Lattice Gauge Theory

abstract:
  Gauge problem of monopole dynamics is studied in SU(2) lattice gauge theory.
We study first abelian and monopole contributions to the static potential in
four smooth gauges, i.e., Laplacian Abelian (LA), Maximally Abelian Wilson Loop
(MAWL) and L-type gauges in comparison with Maximally Abelian (MA) gauge. They
all reproduce the string tension in good agreement with the SU(2) string
tension. MA gauge is not the only choice of the good gauge which is suitable
for the color confinement mechanism. Using an inverse Monte-Carlo method and
the blockspin transformation, we determine effective monopole actions and the
renormalization group (RG) flows of its coupling constants in various abelian
projection schemes. Every RG flow looks to converge to a unique curve which
suggests gauge independence in the infrared region.


title: Progress report on the staggered epsilon'/epsilon project

abstract:
  We report on progress and future plans for calculating kaon weak matrix
elements for epsilon'/epsilon using staggered fermions.


title:
M_pi^2 versus m_q: comparing CP-PACS and UKQCD data to Chiral
  Perturbation Theory

abstract:
  I present a selection of CP-PACS and UKQCD data for the pseudo-Goldstone
masses in $N_f=2$ QCD with doubly degenerate quarks. At least the more chiral
points should be consistent with Chiral Perturbation Theory for the latter to
be useful in an extrapolation to physical masses. I find consistency with the
chiral prediction but no striking evidence for chiral logs. Nonetheless, the
consistency guarantees that the original estimate, by Gasser and Leutwyler, of
the $N_f=2$ QCD low-energy scale $\Lambda_3$ was not entirely wrong.


title: Universality and RG-improved gauge actions

abstract:
  The reference energy scale r_0 is evaluated for RG-improved Iwasaki and DBW2
gauge actions (N_f = 0), at values of the deconfinement coupling beta_c
corresponding to N_t = 3,4,6,8. The universality of r_0 T_c between Iwasa ki
and Wilson action is confirmed; the scaling behaviour and the influence of th e
violation of positivity in the extraction of effective masses are investigated.


title: Ultralocality on the lattice

abstract:
  It is shown that the nonlocal Dirac operator yielded by a lattice model that
preserves chiral symmetry and uniqueness of fields, approaches to an ultralocal
and invariant under translations operator when the size of the lattice tends to
zero.


title: Kaon B-parameter using Overlap Fermions

abstract:
  I present first results from an in-progress calculation of B_K in quenched
approximation using overlap fermions. My particular implementation of the
overlap uses a kernel with nearest and next-nearest neighbor interactions and
HYP-blocked gauge connections. Matching to the continuum NDR regularization is
done perturbatively. I present preliminary results at beta=5.9 and 6.1 (lattice
spacings 0.125 and 0.09 fm) for quark masses, pseudoscalar decay constants, and
B-parameter -- B_K(NDR(mu=2 GeV) is 0.66(3-4).


title:
Empirical Baye's Method and Test in Very Light Quark Range from The
  Overlap Lattice QCD

abstract:
  Based on Bayesian theorem an empirical Baye's method is discussed. A
programming chart for mass spectrum fitting is suggested. A weakly constrained
way for getting priors to solve the chiral log data fitting singularity is
tested.


title:
Recent results from systematic parameterizations of Ginsparg-Wilson
  fermions

abstract:
  The Fixed Point Dirac Operator and Chirally Improved Fermions both use large
numbers of gauge paths and the full Dirac structure to approximate a solution
of the Ginsparg-Wilson equation. After a brief review of the two approaches we
present recent results for quenched QCD with pion masses down to 210 MeV. We
discuss the limits and advantages of approximate parameterizations and outline
future perspectives.


title: Axial anomaly with the overlap-Dirac operator in arbitrary dimensions

abstract:
  We evaluate for arbitrary even dimensions the classical continuum limit of
the lattice axial anomaly defined by the overlap-Dirac operator. Our
calculational scheme is simple and systematic. In particular, a powerful
topological argument is utilized to determine the value of a lattice integral
involved in the calculation. When the Dirac operator is free of species
doubling, the classical continuum limit of the axial anomaly in various
dimensions is combined into a form of the Chern character, as expected.


title:
An Exact Algorithm for Any-flavor Lattice QCD with Kogut-Susskind
  Fermion

abstract:
  We propose an exact simulation algorithm for lattice QCD with dynamical
Kogut-Susskind fermion in which the N_f-flavor fermion operator is defined as
the N_f/4-th root of the Kogut-Susskind (KS) fermion operator. The algorithm is
an extension of the Polynomial Hybrid Monte Carlo (PHMC) algorithm to KS
fermions. The fractional power of the KS fermion operator is approximated with
a Hermitian Chebyshev polynomial, with which we can construct an algorithm for
any number of flavors. The error which arises from the approximation is
corrected by the Kennedy-Kuti noisy Metropolis test. Numerical simulations are
performed for the two-flavor case for several lattice parameters in order to
confirm the validity and the practical feasibility of the algorithm. In
particular tests on a 16^4 lattice with a quark mass corresponding to
m_{PS}/m_V ~ 0.68 are successfully accomplished. We conclude that our algorithm
provides an attractive exact method for dynamical QCD simulations with KS
fermions.


title: Hadronic Spectral Functions above the QCD Phase Transition

abstract:
  We extract the spectral functions in the scalar, pseudo-scalar, vector, and
axial vector channels above the deconfinement phase transition temperature (Tc)
using the maximum entropy method (MEM). We use anisotropic lattices, 32^3 * 32,
40, 54, 72, 80, and 96 (corresponding to T = 2.3 Tc --> 0.8 Tc), with the
renormalized anisotropy xi = 4.0 to have enough temporal data points to carry
out the MEM analysis. Our result suggests that the spectral functions continue
to possess non-trivial structures even above Tc and in addition that there is a
qualitative change in the state of the deconfined matter between 1.5 Tc and 2
Tc.


title: Large N reduction with overlap fermions

abstract:
  We revisit quenched reduction with fermions and explain how some old problems
can be avoided using the overlap Dirac operator.


title: Strongly coupled N=1 SYM theory on the lattice

abstract:
  We propose a strong coupling expansion as a possible tool to obtain
qualitative and quantitative informations about N=1 SYM theory. We point out
the existence of a mapping between strongly coupled lattice N=1 SYM theory and
a generalized SO(4) antiferromagnetic spin system.


title: Semileptonic B Decays from an NRQCD/D234 Action

abstract:
  Semileptonic B decays are studied on quenched anisotropic lattices using
Symanzik improved glue, NRQCD heavy quark and D234 light quark actions. We
employ constrained fits to extract ground state contributions to two- and
three-point correlators. Results for the B --> pi, l nubar decay form factors
are compared with previous lattice results. We find that our systematic errors
(excluding quenching errors) are dominated by chiral extrapolation
uncertainties.


title: Strange matrix elements of the nucleon

abstract:
  Results for the disconnected contributions to matrix elements of the vector
current and scalar density have been obtained for the nucleon from the Wilson
action at beta=6 using a stochastic estimator technique and 2000 quenched
configurations. Various methods for analysis are employed and chiral
extrapolations are discussed.


title: Unquenched domain wall quarks with TSMB

abstract:
  The numerical simulation of domain wall quarks with the two-step multi-boson
(TSMB) algorithm is investigated.
  Tests are performed on a 8^3*4 lattice with N_f=2 quark flavours.


title: Improved Wilson QCD simulations at light quark masses

abstract:
  We present preliminary results from UKQCD simulations at light quark masses
using two flavours of non-pertubatively improved Wilson fermions. We report on
the performance of the standard HMC algorithm at these quark masses where
m_pi/m_rho < 0.5 in comparison with simulations using improved staggered
quarks.


title: Quenched chiral logarithms in lattice QCD with overlap Dirac quarks

abstract:
  We examine quenched chiral logarithms in lattice QCD with overlap Dirac
quarks. From our data of m_pi^2, we determine the coefficient of quenched
chiral logarithm delta = 0.203(14), 0.176(17), 0.193(17) and 0.200(13) for
lattices of sizes 8^3 times 24, 10^3 times 24, 12^3 times 24 and 16^3 times 32
respectively. Also, for the first three lattice sizes, we measure the index
susceptibility of the overlap Dirac operator, and use the exact relation
between the index susceptibility and the eta' mass in quenched chiral
perturbation theory to obtain an independent determination of delta =
0.198(27), 0.173(24), 0.169(22), which are in good agreement with those
determined from m_pi^2.


title: Hamiltonian study of Supersymmetric Yang-Mills Quantum Mechanics

abstract:
  New results obtained within the recently developed approach to supersymmetric
quantum mechanical systems are presented. The method does not suffer from the
sign problem in any dimensions and is capable to provide any quantum observable
with controllable systematic error. Discussed results include: the spectrum and
Witten index of the D=4 system, and the spectrum of zero volume glueballs in
higher 3 < D < 11 dimensions.


title: Experiences with the multi-level algorithm

abstract:
  Small expectation values are difficult to measure in Monte Carlo calculations
as they tend to get swamped by noise. Recently an algorithm has been proposed
by Luscher and Weisz which allows one to measure expectation values which
previously could not be measured reliably in Monte Carlo simulations. We will
test our implementation of this algorithm by looking at Polyakov loop
correlators and then explore ways of applying it for measuring large Wilson
loops.


title: On systematic errors due to quenching in epsilon-prime over epsilon

abstract:
  Recently, we pointed out that chiral transformation properties of penguin
operators change in the transition from unquenched to (partially) quenched QCD.
As a consequence, new operators appear in (partially) quenched QCD penguins,
introducing ambiguities which should be considered a quenching artifact. Here
we discuss more specifically the effects of this phenomenon on the quenched
Delta I=1/2 K to pi pi amplitude, and in particular, its potential numerical
effect on recent lattice estimates for epsilon-prime over epsilon.


title: Excited baryons from Bayesian priors and overlap fermions

abstract:
  Using the constrained-fitting method based on Bayesian priors, we extract the
masses of the two lowest states of octet and decuplet baryons with both
parities. The calculation is done on quenched 16^3x28 lattices of a=0.2 fm
using an improved gauge action and overlap fermions, with the pion mass as low
as 180 MeV. The Roper state N(1440)1/2+ is clearly observed for the first time
as the 1st-excited state of the nucleon from the standard interpolating field.
Together with other baryons, our preliminary results indicate that the
level-ordering of the low-lying baryon states on the lattice is largely
consistent with experiment. The realization is helped by cross-overs between
the excited 1/2+ and 1/2- states in the region of pion mass from 300 to 400
MeV.


title:
Chiral Limit of Staggered Fermions at Strong Couplings: A Loop
  Representation

abstract:
  The partition function of two dimensional massless staggered fermions
interacting with U(N) gauge fields is rewritten in terms of loop variables in
the strong coupling limit. We use this representation of the theory to devise a
non-local Metropolis algorithm to calculate the chiral susceptibility. For
small lattices our algorithm reproduces exact results quite accurately.
Applying this algorithm to large volumes yields rather surprising results. In
particular we find $m_\pi \neq 0$ for all $N$ and it increases with $N$. Since
the talk was presented we have found reasons to believe that our algorithm
breaks down for large volumes questioning the validity of our results.


title: Center Symmetry and Abelian Projection at Finite Temperature

abstract:
  At finite temperature, there is an apparent conflict between Abelian
projection and critical universality. For example, should the deconfinement
transition of an SU(2) gauge theory projected to U(1) lie in the Z(2)
universality class of the parent SU(2) theory or in the U(1) universality
class? I prove that the projected theory lies in the universality class of the
parent gauge theory. The mechanism is shown to be non-local terms in the
projected effective action involving Polyakov loops. I connect this to the
recent work by Dunne et al. on the deconfinement transition in the 2+1
dimensional Georgi-Glashow model.


title:
A Phenomenological Treatment of Chiral Symmetry Restoration and
  Deconfinement

abstract:
  A phenomenological expression for the thermodynamic potential of gluons and
quarks is constructed which incorporates the features of deconfinement and
chiral symmetry restoration known from lattice simulations. The thermodynamic
potential is a function of the Polyakov loop and chiral condensate expectation
values. The gluonic sector uses a successful model for pure (SU(N_c)) gauge
theories in which the Polyakov loop eigenvalues are the fundamental order
parameters for deconfinement. The quark sector is given by a Nambu-Jona-Lasinio
model in which a constant background (A_0) field couples the chiral condensate
to the Polyakov loop. We consider the case of (N_f = 2) in detail. For two
massless quarks, we find a second order chiral phase transition. Confinement
effects push the transition to higher temperatures, but the entropy associated
with the gluonic sector acts in the opposite direction. For light mass quarks,
only a rapid crossover occurs. For sufficiently heavy quarks, a first order
deconfinement transition emerges. This simplest model has one adjustable
parameter, which can be set from the chiral transition temperature for light
quarks. It predicts all thermodynamic quantities as well as the behavior of the
chiral condensate and the Polyakov loop over a wide range of temperatures.


title:
Numerical studies of confinement in the Landau gauge by the larger
  lattice simulation

abstract:
  Figure 1 and Figure 2(right) are replaced and the slope parameter $\alpha_D$
is corrected to -0.4.


title: Screening of hot gluon

abstract:
  We calculate electric and magnetic masses of gluons between T = T_c and 6T_c
using lattice QCD (quantum chromodynamics) in the quench approximation. We find
that magnetic mass has finite values in this region, and the temperature
dependence of the electric mass is consistent with that determined using the
hard-thermal-loop perturbation. The hard-thermal-loop resummation improves
significantly the magnitude of the electric mass comparing to the leading order
perturbation. Both screening masses have little gauge dependence.


title: SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

abstract:
  SU(2) lattice gauge theory with four flavors of quarks is simulated at
nonzero chemical potential mu and temperature T and the results are compared to
the predictions of Effective Lagrangians. Simulations on 16^4 lattices indicate
that at zero T the theory experiences a second order phase transition to a
diquark condensate state which is well described by mean field theory. Nonzero
T and mu are studied on 12^3 times 6 lattices. For low T, increasing mu takes
the system through a line of second order phase transitions to a diquark
condensed phase. Increasing T at high mu, the system passes through a line of
first order transitions from the diquark phase to the quark-gluon plasma phase.


title: QCD in Extreme Environments

abstract:
  I review present challenges that QCD in extreme environments presents to
lattice gauge theory. Recent data and impressions from RHIC are emphasized.
Physical pictures of heavy ion wavefunctions, collisions and the generation of
the Quark Gluon Plasma are discussed, with an eye toward engaging the lattice
and its numerical methods in more interaction with the experimental and
phenomenological developments. Controversial, but stimulating scenarios which
can be confirmed or dismissed by lattice methods are covered. In the second
half of the talk, several promising developments presented at the conference
Lattice 2002 are reviewed.


title: The QCD equation of state at nonzero densities: lattice result

abstract:
  In this letter we give the equation of state of QCD at finite temperatures
and densities. The recently proposed overlap improving multi-parameter
reweighting technique is used to determine observables at nonvanishing chemical
potentials. Our results are obtained by studying n_f=2+1 dynamical staggered
quarks with semi-realistic masses on N_t=4 lattices.


title: Improved performance of QCD code on ALiCE

abstract:
  We present results for the performance of QCD code on ALiCE, the Alpha-Linux
Cluster Engine at Wuppertal. We describe the techniques employed to optimise
the code, including the metaprogramming of assembler kernels, the effects of
data layout and an investigation into the overheads incurred by the
communication.


title: The deconfining phase transition in SU(N) gauge theories

abstract:
  We report on our ongoing investigation of the deconfining phase transition in
SU(4) and SU(6) gauge theories. We calculate the critical couplings while
taking care to avoid the influence of a nearby bulk phase transition. We
determine the latent heat of the phase transition and investigate the order and
the strength of the transition at large N. We also report on our determination
of the critical temperature expressed in units of the string tension in the
large N limit.


title: Loop inequalities and confinement

abstract:
  We consider correlation inequalities that follow from the well-known loop
equations of LGT, and their analogues in spin systems. They provide a way of
bounding long range by short or intermediate range correlations. In several
cases the method easily reproduces results that otherwise require considerable
effort to obtain. In particular, in the case of the 2-dimensional O(N) spin
model, where large N analytical results are available, the absence of a phase
transition and the exponential decay of correlations for all $\beta$ is easily
demonstrated. We report on the possible application of this technique to the
analogous 4-dimensional problem of area law for the Wilson loop in LGT at large
$\beta$.


title:
New Algorithm of the Finite Lattice Method for the High-temperature
  Expansion of the Ising Model in Three Dimensions

abstract:
  We propose a new algorithm of the finite lattice method to generate the
high-temperature series for the Ising model in three dimensions. It enables us
to extend the series for the free energy of the simple cubic lattice from the
previous series of 26th order to 46th order in the inverse temperature. The
obtained series give the estimate of the critical exponent for the specific
heat in high precision.


title: Non-perturbative BRST invariance and what it might be good for

abstract:
  We construct a local, gauge-fixed, lattice Yang-Mills theory with an exact
BRST invariance, and with the same perturbative expansion as the standard
Yang-Mills theory. The ghost sector, and some of its BRST transformation rules,
are modified to get around Neuberger's theorem. A special term is introduced in
the action to regularize the Gribov horizons, and the limit where the regulator
is removed is discussed. We conclude with a few comments on what might be the
physical significance of this theory. We speculate that there may exist new
strong-interaction phases apart from the anticipated confinement phase.


title: Grand-Canonical simulation of 4D simplicial quantum gravity

abstract:
  A thorough numerical examination for the field theory of 4D quantum gravity
(QG) with a special emphasis on the conformal mode dependence has been studied.
More clearly than before, we obtain the string susceptibility exponent of the
partition function by using the Grand-Canonical Monte-Carlo method. Taking
thorough care of the update method, the simulation is made for 4D Euclidean
simplicial manifold coupled to $N_X$ scalar fields and $N_A$ U(1) gauge fields.
The numerical results suggest that 4D simplicial quantum gravity (SQG) can be
reached to the continuum theory of 4D QG. We discuss the significant property
of 4D SQG.


title: Towards a strong-coupling theory of QCD at finite density

abstract:
  We apply strong-coupling perturbation theory to the QCD lattice Hamiltonian.
We begin with naive, nearest-neighbor fermions and subsequently break the
doubling symmetry with next-nearest-neighbor terms. The effective Hamiltonian
is that of an antiferromagnet with an added kinetic term for baryonic
"impurities," reminiscent of the t-J model of high-T_c superconductivity. As a
first step, we fix the locations of the baryons and make them static. Following
analyses of the t-J model, we apply large-N methods to obtain a phase diagram
in the (N_c,N_f) plane at zero temperature and baryon density. Next we study a
simplified U(3) toy model, in which we add baryons to the vacuum. We use a
coherent state formalism to write a path integral which we analyze with mean
field theory, obtaining a phase diagram in the (n_B,T) plane.


title: Currents, chemical potential and boundary conditions in lattice QCD

abstract:
  A connection between the operator fermionic currents $\hatJ$ and
corresponding `Grassmannian' currents $J$ in the functional integral formalism
is studied. The QCD action with non--zero chemical potential $\mu$ is derived.
A connection between the fermionic Fock space and boundary conditions along the
forth direction is discussed.


title: CP breaking in lattice chiral gauge theory

abstract:
  The CP symmetry is not manifestly implemented for the local and doubler-free
Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify
where the effects of this CP breaking appear.


title: Improving the Quark Number Susceptibilities for Staggered Fermions

abstract:
  Quark number susceptibilities approach their ideal gas limit at sufficiently
high temperatures. As in the case of other thermodynamic quantities, this limit
itself is altered substantially on lattices with small temporal extent, N_t =
4-8, making it thus difficult to check the validity of perturbation theory.
Unlike other observables, improving susceptibilities or number densities is
subject to constraints of current conservation and absence of chemical
potential dependent divergences. We construct such an improved number density
and susceptibility for staggered fermions and show that they approximate the
continuum ideal gas limit better on small temporal lattices.


title: The quark mass and $\mu$ dependence of the QCD chiral critical point

abstract:
  In order to study the QCD chiral critical point we investigate Binder
Cumulants of the chiral condensate. The results were obtained from simulations
of 3 and 2+1 flavors of standard staggered fermions and 3 flavors of p4
improved staggered fermions. The quark masses used are close to the physical
quark mass. To extract the dependence on quark mass and chemical potential we
apply a new reweighting technique based on a Taylor expansion of the action.
The reweighting accuracy is ${\cal O}(m)$ for the standard and ${\cal O}(m^2)$,
${\cal O}(\mu^2)$ for the p4 action.


title: A Hamiltonian lattice study of the two-dimensional Wess-Zumino model

abstract:
  We investigate a Hamiltonian lattice version of the two-dimensional
Wess-Zumino model by Quantum Monte Carlo simulations. In order to study the
pattern of supersymmetry breaking, we measure the ground state energy and the
correlation length along a trajectory approaching the continuum limit. The
algorithm is very effective in measuring the ground state energy, and adequate
for the correlation length.


title: SO(3) Yang-Mills theory on the lattice

abstract:
  We numerically investigate the phase structure of pure SO(3) LGT at zero and
non-zero temperature in the presence of a Z2 blind monopole chemical potential.
The physical meaning of the different phases, a possible symmetry breaking
mechanism as well as the existence of an order parameter for the finite
temperature phase transition are discussed.


title: The QCD phase transition at high temperature and low density

abstract:
  We study the thermal properties of QCD in the presence of a small quark
chemical potential $\mu$. Derivatives of the phase transition point with
respect to $\mu$ are computed at $\mu=0$ for 2 and 3 flavors of p-4 improved
staggered fermions on a $16^3\times4$ lattice. Moreover we contrast the case of
isoscalar and isovector chemical potentials, quantify the effect of $\mu\not=0$
on the equation of state, and comment on the screening effect by dynamical
quarks and the complex phase of the fermion determinant in QCD with
$\mu\not=0$.


title: QCD on 2+2 anisotropic lattices

abstract:
  We discuss the implementation of QCD on 2+2 anisotropic lattices. Technical
details regarding the choice of the action as well as perturbative and
non-perturbative improvement are analyzed. The physical applications of the
program are presented.


title: On Witten's global anomaly for higher SU(2) representations

abstract:
  The spectral flow of the overlap operator is computed numerically along a
path connecting two gauge fields which differ by a topologically non-trivial
gauge transformation. The calculation is performed for SU(2) in the 3/2 and 5/2
representation. An even-odd pattern for the spectral flow as predicted by
Witten is verified. The results are, however, more complicated than naively
expected.


title: Confining proprties of a gas of Z(2) vortices

abstract:
  Vortex solutions are studied in an SO(3) gauge theory spontaneously broken to
SO(2). These vortices have a Z(2) magnetic charge. A dilute gas of Z(2)
vortices is studied taking into account vortex-vortex interactions. By going to
a dual representation we show that odd charges are confined with a string
tension which decreases exponentially with the inverse coupling.


title: A phase transition due to thick vortices in SU(2) lattice gauge theory

abstract:
  SU(2) lattice gauge theory is studied after eliminating thin monopoles and
the smallest thick monopoles. Kinematically this constraint allows thick vortex
loops which produce long range Z(2) fluctuations. The thick vortex loops are
identified in a three dimensional simulation. A condensate of thick vortices
persists even after the thin vortices have all disappeared. They decouple at a
slightly lower temperature (higher $\beta$) than the thin vortices and drive a
Z(2) like phase transition.


title: One Loop Renormalization of Fermilab Fermions

abstract:
  We discuss the current status of our automatic perturbation theory program as
applied to Fermilab Fermions. We give an overview of our methods, a discussion
of tree level matching, and one loop results for the coefficients of the higher
dimension kinetic operators.


title: Unquenched Numerical Stochastic Perturbation Theory

abstract:
  The inclusion of fermionic loops contribution in Numerical Stochastic
Perturbation Theory (NSPT) has a nice feature: it does not cost so much
(provided only that an FFT can be implemented in a fairly efficient way).
Focusing on Lattice SU(3), we report on the performance of the current
implementation of the algorithm and the status of first computations
undertaken.


title:
New algorithm of the high-temperature expansion for the Ising model in
  three dimensions

abstract:
  New algorithm of the finite lattice method is presented to generate the
high-temperature expansion series of the Ising model. It enables us to obtain
much longer series in three dimensions when compared not only to the previous
algorithm of the finite lattice method but also to the standard graphical
method. It is applied to extend the high-temperature series of the simple cubic
Ising model from beta^{26} to beta^{46} for the free energy and from beta^{25}
to beta^{32} for the magnetic susceptibility.


title:
$K^{+}\to\pi^{+}\pi^{0}$ decays at next-to-leading order in the chiral
  expansion on finite volumes

abstract:
  We present the ingredients for determining $K^{+}\to\pi^{+}\pi^{0}$ matrix
elements via the combination of lattice QCD and chiral perturbation theory
($\chi$PT). By simulating these matrix elements at unphysical kinematics, it is
possible to determine all the low-energy constants (LECs) for constructing the
physical $K^{+}\to\pi^{+}\pi^{0}$ amplitudes at next-to-leading order (NLO) in
the chiral expansion. In this work, the one-loop chiral corrections are
calculated for arbitrary meson four-momenta, in both $\chi$PT and quenched
$\chi$PT (q$\chi$PT), and the finite-volume effects are studied.


title: Simulating non-commutative field theory

abstract:
  Non-commutative (NC) field theories can be mapped onto twisted matrix models.
This mapping enables their Monte Carlo simulation, where the large N limit of
the matrix models describes the continuum limit of NC field theory. First we
present numeric results for 2d NC gauge theory of rank 1, which turns out to be
renormalizable. The area law for the Wilson loop holds at small area, but at
large area we observe a rotating phase, which corresponds to an Aharonov-Bohm
effect. Next we investigate the NC phi^4 model in d=3 and explore its phase
diagram. Our results agree with a conjecture by Gubser and Sondhi in d=4, who
predicted that the ordered regime splits into a uniform phase and a phase
dominated by stripe patterns.


title:
The Upsilon Spectrum from Lattice QCD with 2+1 Flavors of Dynamical
  Quarks

abstract:
  We describe the bottomonium spectrum obtained on the MILC configurations
which incorporate 2+1 flavors of dynamical quarks. We compare to quenched and 2
flavor results also on MILC configurations. We show that the lattice spacing
determination using different quantities shows clear signs of convergence with
2+1 flavors and give results for the leptonic width and hyperfine splitting, in
the form of the ratio of the 1st excited state of the Upsilon to that of the
ground state.


title: Recent results on the running coupling in QCD with two massless flavours

abstract:
  We report on the latest results on the running coupling of two flavour QCD in
the Schr\"odinger functional scheme. Results for the step scaling function are
obtained from simulations on lattices $L/a=8$ and $L/a=16$ which confirm the
first results from lattices $L/a=4,5,6$ presented one year ago by the ALPHA
collaboration. We also discuss some algorithmic aspects, in particular
concerning the occurrence of metastable states. A modified sampling, in order
to estimate the proper weight of these states in the path integral, is proposed
and tested.


title: Chiral Nonanalytic Behaviour: The Edinburgh Plot

abstract:
  The Edinburgh Plot is a scale independent way of presenting lattice QCD
calculations over a wide range of quark masses. In this sense it is appealing
as an indicator of how the approach to physical quark masses is progressing.
The difficulty remains that even the most state of the art calculations are
still at quark masses that are too heavy to apply dimensionally-regulated
chiral perturbation theory. We present a method allowing predictions of the
behaviour of the Edinburgh plot, in both the continuum, and on the lattice.