title: Lattice QCD equation of state : improving the differential method

abstract:
  We propose an improvement of the differential method for the computation of
the equation of state of QCD from lattice simulations. In contrast to the
earlier differential method our technique yields positive pressure for all
temperatures including in the transition region. Employing it on temporal
lattices of 8, 10 and 12 sites and by extrapolating to zero lattice spacing we
obtained the pressure, energy density, entropy density, specific heat and speed
of sound in quenched QCD for 0.9 < T/Tc < 3. A comparison of our results is
made with those from the dimensional reduction approach and a conformal
symmetric theory at high-temperature.


title: A Numerical Study of Partially Twisted Boundary Conditions

abstract:
  We investigate the use of partially twisted boundary conditions in a lattice
simulation with two degenerate flavours of improved Wilson sea quarks. The use
of twisted boundary conditions on a cubic volume (L^3) gives access to
components of hadronic momenta other than integer multiples of 2*pi/L. Partial
twisting avoids the need for new gluon configurations for every choice of
momentum, while, as recently demonstrated, keeping the finite-volume errors
exponentially small for the physical quantities investigated in this letter. In
this study we focus on the spectrum of pseudo scalar and vector mesons, on
their leptonic decay constants and on Z_P, the matrix element of the pseudo
scalar density between the pseudo scalar meson and the vacuum. The results
confirm the momentum shift imposed by these boundary conditions and in addition
demonstrate that they do not introduce any appreciable noise. We therefore
advocate the use of partially twisted boundary conditions in applications where
good momentum resolution is necessary.


title:
Investigation of the Second Moment of the Nucleon's g1 and g2 Structure
  Functions in Two-Flavor Lattice QCD

abstract:
  The reduced matrix elements a_2 and d_2 are computed in lattice QCD with
N_f=2 flavors of light dynamical (sea) quarks. For proton and neutron targets
we obtain as our best estimates d_2^(p)=0.004(5) and d_2^(n)=-0.001(3),
respectively, in the MSbar scheme at Q^2=5 GeV^2, while for a_2 we find
a_2^(p)=0.077(12) and a_2^(n)=-0.005(5), where the errors are purely
statistical.


title: The Reality of the Fundamental Topological Structure in the QCD Vacuum

abstract:
  Long-range order of a specific kind has recently been found directly in
configurations dominating the regularized QCD path integral. In particular, a
low-dimensional global structure was identified in typical space-time
distributions of topological charge defined via the overlap Dirac matrix. The
presence of the order has been concluded from the fact that the structure
disappears after random permutation of position coordinates in measured
densities. Here we complete the argument for the reality of this structure
(namely the conjecture that its existence is a consequence of QCD dynamics and
not an artifact of the overlap-based definition of lattice topological field)
by showing that the structure ceases to exist after randomizing the space-time
coordinates of the underlying gauge field. This implies that the long-range
order present in the overlap-based topological density is indeed a
manifestation of QCD vacuum, and that the notion of the fundamental structure
(structure involving relevant features at all scales) is viable.


title:
Static quark anti-quark interactions at zero and finite temperature QCD.
  II.Quark anti-quark internal energy and entropy

abstract:
  We analyze the change in free energy, internal energy and entropy due to the
presence of a heavy quark anti-quark pair in a QCD heat bath. The internal
energies and entropies are introduced as intensive observables calculated
through thermal derivatives of the QCD partition function containing additional
static color sources. The quark anti-quark internal energy and, in particular,
the entropy clearly signal the phase change from quark confinement below and
deconfinement above the transition and both observables are introduced such
that they survive the continuum limit. The intermediate and large distance
behavior of the energies reflect string breaking and color screening phenomena.
This is used to characterize the energies which are needed to dissolve heavy
quarkonium states in a thermal medium. Our discussion supports recent findings
which suggest that parts of the quarkonium systems may survive the phase
transition and dissolve only at higher temperatures.


title: QED$_3$ on a space-time lattice: compact versus noncompact formulation

abstract:
  We study quantum electrodynamics in a (2+1)-dimensional space-time with two
flavors of dynamical fermions by numerical simulations on the lattice. We
discretize the theory using both the compact and the noncompact formulations
and analyze the behavior of the chiral condensate and of the monopole density
in the finite lattice regime as well as in the continuum limit. By comparing
the results obtained with the two approaches, we draw some conclusions about
the possible equivalence of the two lattice formulations in the continuum
limit.


title:
Chiral properties of two-flavor QCD in small volume and at large lattice
  spacing

abstract:
  We present results from simulations of two flavors of dynamical overlap
fermions on 8^4 lattices at three values of the sea quark mass and a lattice
spacing of about 0.16 fm. We measure the topological susceptibility and the
chiral condensate. A comparison of the low-lying spectrum of the overlap
operator with predictions from random matrix theory is made. To demonstrate the
effect of the dynamical fermions, we compare meson two-point functions with
quenched results. Algorithmic improvements over a previous publication and the
performance of the algorithm are discussed.


title: Spin 3/2 Penta-quarks in anisotropic lattice QCD

abstract:
  A high-precision mass measurement for the pentaquark (5Q) Theta^+ in
J^P=3/2^{\pm} channel is performed in anisotropic quenched lattice QCD using a
large number of gauge configurations as N_{conf}=1000. We employ the standard
Wilson gauge action at beta=5.75 and the O(a) improved Wilson (clover) quark
action with kappa=0.1210(0.0010)0.1240 on a 12^3 \times 96 lattice with the
renormalized anisotropy as a_s/a_t = 4. The Rarita-Schwinger formalism is
adopted for the interpolating fields. Several types of the interpolating fields
with isospin I=0 are examined such as (a) the NK^*-type, (b) the
(color-)twisted NK^*-type, (c) a diquark-type. The chiral extrapolation leads
to only massive states, i.e., m_{5Q} \simeq 2.1-2.2 GeV in J^P=3/2^- channel,
and m_{5Q} = 2.4-2.6 GeV in J^P=3/2^+ channel. The analysis with the hybrid
boundary condition(HBC) is performed to investigate whether these states are
compact 5Q resonances or not. No low-lying compact 5Q resonance states are
found below 2.1GeV.


title: Lee-Yang zero analysis for the study of QCD phase structure

abstract:
  We comment on the Lee-Yang zero analysis for the study of the phase structure
of QCD at high temperature and baryon number density by Monte-Carlo
simulations. We find that the sign problem for non-zero density QCD induces a
serious problem in the finite volume scaling analysis of the Lee-Yang zeros for
the investigation of the order of the phase transition. If the sign problem
occurs at large volume, the Lee-Yang zeros will always approach the real axis
of the complex parameter plane in the thermodynamic limit. This implies that a
scaling behavior which would suggest a crossover transition will not be
obtained. To clarify this problem, we discuss the Lee-Yang zero analysis for
SU(3) pure gauge theory as a simple example without the sign problem, and then
consider the case of non-zero density QCD. It is suggested that the
distribution of the Lee-Yang zeros in the complex parameter space obtained by
each simulation could be more important information for the investigation of
the critical endpoint in the $(T, \mu_q)$ plane than the finite volume scaling
behavior.


title: Simulating Full QCD with the Fixed Point Action

abstract:
  Due to its complex structure the parametrized fixed point action can not be
simulated with the available local updating algorithms. We constructed, coded,
and tested an updating procedure with 2+1 light flavors, where the targeted
s-quark mass is at its physical value while the u- and d-quarks should produce
pions lighter than 300MeV. In the algorithm a partially global gauge update is
followed by several accept/reject steps, where parts of the determinant are
switched on gradually in the order of their expenses. The trial configuration
that is offered in the last, most expensive, stochastic accept/reject step
differs from the original configuration by a Metropolis + over-relaxation gauge
update over a sub-volume of ~(1.3 fm)^4. The acceptance rate in this
accept/reject step is ~0.4. The code is optimized on different architectures
and is running on lattices with L=1.2fm and 1.8fm at a resolution of a=0.15fm.


title:
Lattice Spacing Dependence of the First Order Phase Transition for
  Dynamical Twisted Mass Fermions

abstract:
  Lattice QCD with Wilson fermions generically shows the phenomenon of a first
order phase transition. We study the phase structure of lattice QCD using
Wilson twisted mass fermions and the Wilson plaquette gauge action are used in
a range of beta values where such a first order phase transition is observed.
In particular, we investigate the dependence of the first order phase
transition on the value of the lattice spacing. Using only data in one phase
and neglecting possible problems arising from the phase transition we are able
to perform a first scaling test for physical quantities using this action.


title: Rare Kaon Decays on the Lattice

abstract:
  We show that long distance contributions to the rare decays K -> pi nu nu-bar
and K -> pi l+ l- can be computed using lattice QCD. The proposed approach
requires well established methods, successfully applied in the calculations of
electromagnetic and semileptonic form factors. The extra power divergences,
related to the use of weak four-fermion operators, can be eliminated using only
the symmetries of the lattice action without ambiguities or complicated
non-perturbative subtractions. We demonstrate that this is true even when a
lattice action with explicit chiral symmetry breaking is employed. Our study
opens the possibility of reducing the present uncertainty in the theoretical
predictions for these decays.


title: Filtered overlap: speedup, locality, kernel non-normality and Z_A~1

abstract:
  We investigate the overlap operator with a UV filtered Wilson kernel. The
filtering leads to a better localization of the operator even on coarse
lattices and with the untuned choice $\rho=1$. Furthermore, the axial-vector
renormalization constant $Z_A$ is much closer to 1, reducing the mismatch with
perturbation theory. We show that all these features persist over a wide range
of couplings and that the details of filtering prove immaterial. We investigate
the properties of the kernel spectrum and find that the kernel non-normality is
reduced. As a side effect we observe that for certain applications of the
filtered overlap a speed-up factor of 2-4 can be achieved.


title: Spontaneous Parity Violation

abstract:
  We disprove the Vafa-Witten theorem on the impossibility of spontaneously
breaking parity in vector-like gauge field theories, identifying a mechanism
driven by quantum fluctuations. With the introduction of a meromorphic Lattice
formulation, defined over 5 dimensions, we demonstrate that the minima of the
free energy can be distinct from the maxima of the partition function :
identifying and evaluating a suitable contour for the partition function
defined such that asymptotic behaviour of the complex action is
non-oscillatory.


title:
Group-theoretical construction of extended baryon operators in lattice
  QCD

abstract:
  The design and implementation of large sets of spatially-extended,
gauge-invariant operators for use in determining the spectrum of baryons in
lattice QCD computations are described. Group-theoretical projections onto the
irreducible representations of the symmetry group of a cubic spatial lattice
are used in all isospin channels. The operators are constructed to maximize
overlaps with the low-lying states of interest, while minimizing the number of
sources needed in computing the required quark propagators. Issues related to
the identification of the spin quantum numbers of the states in the continuum
limit are addressed.


title: Charmed meson decay constants in three-flavor lattice QCD

abstract:
  We present the first lattice QCD calculation with realistic sea quark content
of the D^+ meson decay constant f_{D^+}. We use the MILC Collaboration's
publicly available ensembles of lattice gauge fields, which have a quark sea
with two flavors (up and down) much lighter than a third (strange). We obtain
f_{D^+} = 201 +/- 3 +/- 17 MeV, where the errors are statistical and a
combination of systematic errors. We also obtain f_{D_s} = 249 +/- 3 +/- 16 MeV
for the D_s meson.


title: Asymptotic behavior of the ghost propagator in SU3 lattice gauge theory

abstract:
  We study the asymptotic behavior of the ghost propagator in the quenched
SU(3) lattice gauge theory with Wilson action. The study is performed on
lattices with a physical volume fixed around 1.6 fm and different lattice
spacings: 0.100 fm, 0.070 fm and 0.055 fm. We implement an efficient algorithm
for computing the Faddeev-Popov operator on the lattice. We are able to
extrapolate the lattice data for the ghost propagator towards the continuum and
to show that the extrapolated data on each lattice can be described up to
four-loop perturbation theory from 2.0 GeV to 6.0 GeV. The three-loop values
are consistent with those extracted from previous perturbative studies of the
gluon propagator. However the effective $\Lambda_{\ms}$ scale which reproduces
the data does depend strongly upon the order of perturbation theory and on the
renormalization scheme used in the parametrization. We show how the truncation
of the perturbative series can account for the magnitude of the dependency in
this energy range. The contribution of non-perturbative corrections will be
discussed elsewhere.


title: True or Fictitious Flattening? -MEM and the $\theta$ Term-

abstract:
  We study the sign problem in lattice field theory with a $\theta$ term. We
apply the maximum entropy method (MEM) to flattening phenomenon of the free
energy density $f(\theta)$, which originates from the sign problem. In our
previous paper, we applied the MEM by employing the Gaussian topological charge
distribution $P(Q)$ as mock data. In the present paper, we consider models in
which `true' flattening of $f(\theta)$ occurs. These may be regarded as good
examples for studying whether the MEM could correctly detect non trivial phase
structure.


title:
More on the continuum limit of gauge-fixed compact U(1) lattice gauge
  theory

abstract:
  We have verified various proposals that were suggested in our last paper
concerning the continuum limit of a compact formulation of the lattice U(1)
pure gauge theory in 4 dimensions using a nonperturbative gauge-fixed
regularization. Our study reveals that most of the speculations are largely
correct. We find clear evidence of a continuous phase transition in the pure
gauge theory at "arbitrarily" large couplings. When probed with quenched
staggered fermions with U(1) charge, the theory clearly has a chiral transition
for large gauge couplings whose intersection with the phase transition in the
pure gauge theory continues to be a promising area for nonperturbative physics.
We probe the nature of the continuous phase transition by looking at gauge
field propagators in the momentum space and locate the region on the critical
manifold where free photons can be recovered.


title: The pressure of the SU(N) lattice gauge theory at large-N

abstract:
  We calculate bulk thermodynamic properties, such as the pressure, energy
density, and entropy, in SU(4) and SU(8) lattice gauge theories, for the range
of temperatures T <= 2.0Tc and T <= 1.6Tc respectively. We find that the N=4,8
results are very close to each other, and to what one finds in SU(3), and are
far from the asymptotic free-gas value. We conclude that any explanation of the
high-T pressure (or entropy) deficit must be such as to survive the N-->oo
limit. We give some examples of this constraint in action and comment on what
this implies for the relevance of gravity duals.


title: The Color--Flavor Transformation of induced QCD

abstract:
  The Zirnbauer's color-flavor transformation is applied to the $U(N_c)$
lattice gauge model, in which the gauge theory is induced by a heavy chiral
scalar field sitting on lattice sites. The flavor degrees of freedom can
encompass several `generations' of the auxiliary field, and for each
generation, remaining indices are associated with the elementary plaquettes
touching the lattice site. The effective, color-flavor transformed theory is
expressed in terms of gauge singlet matrix fields carried by lattice links. The
effective action is analyzed for a hypercubic lattice in arbitrary dimension.
We investigate the corresponding d=2 and d=3 dual lattices. The saddle points
equations of the model in the large-$N_c$ limit are discussed.


title: Lattice QCD for Novices

abstract:
  This is the "preprint" for a paper that came out in 1998 but for some reason
wasn't posted then.
  Abstract:These lectures are for novices to lattice QCD. They introduce a set
of simple ideas and numerical techniques that can be implemented in a short
period of time and that are capabable of generating nontrivial, nonperturbative
results from lattice QCD. The simplest of these calculations can be completed
on a standard workstation or high-end personal computer.


title:
Quark helicity flip generalized parton distributions from two-flavor
  lattice QCD

abstract:
  We present an initiatory study of quark helicity flip generalized parton
distributions (GPDs) in n_f=2 lattice QCD, based on clover-improved Wilson
fermions for a large number of coupling constants and pion masses. Quark
helicity flip GPDs yield essential information on the transverse spin structure
of the nucleon. In this work, we show first results on their lowest moments and
dipole masses and study the corresponding chiral and continuum extrapolations.


title: Toward a systematic analysis of the fourth-root trick

abstract:
  In this note I briefly discuss ideas related to the so-called fourth-root
trick. A decomposition of the ``rooted'' fermion effective action into Wilson
fermions and a nonlocal, lattice spacing suppressed functional is presented,
complete with link interactions. Some proposals are given for analytical,
nonperturbative studies of the fourth-root trick.


title: Latent heat of the large N finite temperature phase transition

abstract:
  Reduced large N gauge theories have a phase with unbroken center symmetry and
phases in which that symmetry is broken for Polyakov loops in one or more
lattice directions. The phase with unbroken symmetry is associated with the
zero temperature, infinite volume, infinite N theory while the phase in which
the symmetry is broken in just one lattice direction has been conjectured to be
the spatial reduction of the high temperature, infinite volume, infinite N
theory. Measurements of the scaling properties of the latent heat of the
transition between these phases test that hypothesis. The results indicate a
non-zero latent heat in the continuum limit. Substantial finite spacing effects
remain, and finer lattices will be needed to confirm physical scaling.


title:
Continuum and lattice meson spectral functions at nonzero momentum and
  high temperature

abstract:
  We analyse discretization effects in the calculation of high-temperature
meson spectral functions at nonzero momentum and fermion mass on the lattice.
We do so by comparing continuum and lattice spectral functions in the infinite
temperature limit. Complete analytical results for the spectral densities in
the continuum are presented, along with simple expressions for spectral
functions obtained with Wilson and staggered fermions on anisotropic lattices.
We comment on the use of local and point split currents.


title: Non-perturbative Power Corrections to Ghost and Gluon Propagators

abstract:
  We study the dominant non-perturbative power corrections to the ghost and
gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice
simulations. The leading order Wilson coefficients are proven to be the same
for both propagators. The ratio of the ghost and gluon propagators is thus free
from this dominant power correction. Indeed, a purely perturbative fit of this
ratio gives smaller value ($\simeq 270$MeV) of $\Lambda_{\ms}$ than the one
obtained from the propagators separately($\simeq 320$MeV). This argues in
favour of significant non-perturbative $\sim 1/q^2$ power corrections in the
ghost and gluon propagators. We check the self-consistency of the method.


title: Finite-Volume Effects for Two-Hadron States in Moving Frames

abstract:
  We determine the finite-volume corrections to the spectrum and matrix
elements of two-hadron states in a moving frame, i.e. one in which the total
momentum of the two-hadrons is non-zero. The analysis is performed entirely
within field theory and the results are accurate up to exponential corrections
in the volume. Our results for the spectrum are equivalent to those of
Rummukainen and Gottlieb which had been obtained using a relativistic quantum
mechanical approach. A technical step in our analysis is a simple derivation of
the summation formulae relating the loop summations over the momenta of the two
hadrons in finite volume to the corresponding integrals in infinite volume.


title:
Deep-inelastic scattering and the operator product expansion in lattice
  QCD

abstract:
  We discuss the determination of deep-inelastic hadron structure in lattice
QCD. By using a fictitious heavy quark, direct calculations of the Compton
scattering tensor can be performed in Euclidean space that allow the extraction
of the moments of structure functions. This overcomes issues of operator mixing
and renormalisation that have so far prohibited lattice computations of higher
moments. This approach is especially suitable for the study of the twist-two
contributions to isovector quark distributions, which is practical with current
computing resources. While we focus on the isovector unpolarised distribution,
our method is equally applicable to other quark distributions and to
generalised parton distributions. By looking at matrix elements such as
$<\pi^\pm| T [V^\mu(x) A^{\nu}(0)]|0>$ (where $V^\mu$ and $A^\nu$ are vector
and axial-vector heavy-light currents) within the same formalism, moments of
meson distribution amplitudes can also be extracted.


title:
Schroedinger functional formalism for overlap Dirac operator and
  domain-wall fermion

abstract:
  In this proceeding we propose a new procedure to impose the Schroedinger
functional Dirichlet boundary condition on the overlap Dirac operator and the
domain-wall fermion using an orbifolding projection.
  With this procedure the zero mode problem with Dirichlet boundary condition
can easily be avoided.


title:
Finite Volume Corrections to the Two-Particle Decay of States with
  Non-Zero Momentum

abstract:
  We study the effects of finite volume on the two-particle decay rate of an
unstable state with non-zero momentum. First Luscher's field-theoretic relation
between the infinite volume scattering phase shifts and the quantized energy
levels of a finite volume, two-particle system is generalized to the case of
non-zero total momentum and compared with the earlier results of Rummukainen
and Gottlieb. We then use this result and the method of Lellouch and Luscher to
determine the corrections needed for a finite-volume calculation of a
two-particle decay amplitude when the decaying particle has non-vanishing
center-of-mass momentum.


title: Quenched Scaling of Wilson twisted mass fermions

abstract:
  We investigate the scaling behaviour of quenched Wilson twisted mass fermions
at maximal twist applying two definitions of the critical mass. The first
definition uses the vanishing of the pseudoscalar meson mass m_PS while the
second employs the vanishing of the PCAC quark mass m_PCAC. We confirm in both
cases the expected O(a) improvement. In addition, we show that the PCAC quark
mass definition leads to substantially reduced O(a^2) cut-off effects even when
the pseudoscalar meson mass m_PS is as small as 270 MeV. At a fixed value of
m_PS we perform continuum limits for the vector meson mass m_V and for the
pseudoscalar decay constant f_PS and discuss the renormalisation constant Z_V
of the vector current.


title: The Low-Lying Dirac Spectrum of Staggered Quarks

abstract:
  We investigate and clarify the role of topology and the issues surrounding
the epsilon regime for staggered quarks. We study unimproved and improved
staggered quark Dirac operators on quenched lattice QCD gluon backgrounds
generated using a Symanzik-improved gluon action. For the improved Dirac
operators we find a clear separation of the spectrum into would-be zero modes
and others. The number of would-be zero modes depends on the topological charge
as predicted by the continuum Index Theorem, and the expectation values of
their chirality are large for the most improved actions (approx 0.7). The
remaining modes have low chirality and show clear signs of clustering into
quartets that become degenerate in the continuum limit. We demonstrate that the
lattice spacing and volume dependence of the eigenvalues follow expectations.
Furthermore, the non-zero modes follow the random matrix theory predictions for
all topological charge sectors. The values of the chiral condensate extracted
from fits to the theoretical distributions are consistent with each other, and
with the results obtained from the total density of eigenvalues using the
Banks-Casher relation. We conclude that staggered quarks respond correctly to
QCD topology when both fermion and gauge actions are improved.


title: B_K in Staggered Chiral Perturbation Theory

abstract:
  We calculate the kaon B-parameter, B_K, to next-to-leading order in staggered
chiral perturbation theory. We find expressions for partially quenched QCD with
three sea quarks, quenched QCD, and full QCD with m_u = m_d but not equal to
m_s. We extend the usual power counting to include the effects of using
perturbative (rather than non-perturbative) matching factors. Taste breaking
enters through the O(a^2) terms in the effective action, through O(a^2) terms
from the discretization of operators, and through the truncation of matching
factors. These effects cause mixing with several additional operators,
complicating the chiral and continuum extrapolations. In addition to the
staggered expressions, we present B_K at next-to-leading order in continuum
partially quenched chiral perturbation theory for N_f=3 sea quarks with m_u =
m_d but not equal to m_s.


title: The Upsilon spectrum and m_b from full lattice QCD

abstract:
  We show results for the Upsilon spectrum calculated in lattice QCD including
for the first time vacuum polarization effects for light u and d quarks as well
as s quarks. We use gluon field configurations generated by the MILC
collaboration. The calculations compare the results for a variety of u and d
quark masses, as well as making a comparison to quenched results (in which
quark vacuum polarisation is ignored) and results with only u and d quarks. The
b quarks in the Upsilon are treated in lattice Nonrelativistic QCD through NLO
in an expansion in the velocity of the b quark. We concentrate on accurate
results for orbital and radial splittings where we see clear agreement with
experiment once u, d and s quark vacuum polarisation effects are included. This
now allows a consistent determination of the parameters of QCD. We demonstrate
this consistency through the agreement of the Upsilon and B spectrum using the
same lattice bare b quark mass. A one-loop matching to continuum QCD gives a
value for the b quark mass in full lattice QCD for the first time. We obtain
m_b^{\bar{MS}}(m_b^{\bar{MS}}) = 4.4(3) GeV. We are able to give physical
results for the heavy quark potential parameters, r_0 = 0.469(7) fm and r_1 =
0.321(5) fm. Results for the fine structure in the spectrum and the Upsilon
leptonic width are also presented. We predict the Upsilon - eta_b splitting to
be 61(14) MeV, the Upsilon^{\prime} - eta_b^{\prime} splitting as 30(19) MeV
and the splitting between the h_b and the spin-average of the chi_b states to
be less than 6 MeV. Improvements to these calculations that will be made in the
near future are discussed.


title: Classical Simulation of Quantum Fields II

abstract:
  We consider the classical time evolution of a real scalar field in 2
dimensional Minkowski space with a $\lambda \phi^4$ interaction. We compute the
spatial and temporal two-point correlation functions and extract the
renormalized mass of the interacting theory. We find our results are consistent
with the one- and two-loop quantum computation. We also perform Monte Carlo
simulations of the quantum theory and conclude that the classical scheme is
able to produce more accurate results with a fraction of the CPU time.


title: The B Meson Decay Constant from Unquenched Lattice QCD

abstract:
  We present determinations of the B meson decay constant f_B and of the ratio
f_{B_s}/f_B using the MILC collaboration unquenched gauge configurations which
include three flavors of light sea quarks. The mass of one of the sea quarks is
kept around the strange quark mass, and we explore a range in masses for the
two lighter sea quarks down to m_s/8.
  The heavy b quark is simulated using Nonrelativistic QCD, and both the
valence and sea light quarks are represented by the highly improved (AsqTad)
staggered quark action.
  The good chiral properties of the latter action allow for a much smoother
chiral extrapolation to physical up and down quarks than has been possible in
the past. We find f_B = 216(9)(19)(4) (6) MeV and f_{B_s} /f_B = 1.20(3)(1).


title: R-symmetry in the Q-exact (2,2) 2d lattice Wess-Zumino model

abstract:
  In this article we explore the R-symmetry of the (2,2) 2d Wess-Zumino model.
We study whether or not this symmetry is approximately realized in the Q-exact
lattice version of this theory. Our study is nonperturbative: it relies on
Monte Carlo simulations with dynamical fermions. Irrelevant operators in the
lattice action explicitly break the R-symmetry. In spite of this, it is found
to be a symmetry of the effective potential. We find nonperturbative evidence
that the nonrenormalization theorem of the continuum theory is recovered in the
continuum limit; e.g., there is no additive mass renormalization. In our
simulations we find that Fourier acceleration of the hybrid Monte Carlo
algorithm allows us to avoid difficulties with critical slowing-down.


title: Renormalization of Bilinear Quark Operators for Overlap Fermions

abstract:
  We present non-perturbative renormalization constants of fermionic bilinears
on the lattice in the quenched approximation at beta=6.1 using an overlap
fermion action with hypercubic(HYP)-blocked links. We consider the effects of
the exact zero modes of the Dirac operator and find they are important in
calculating the renormalization constants of the scalar and pseudoscalar
density. The results are given in the RI' and MS bar schemes and compared to
the perturbative calculations.


title: Angular Momentum on the Lattice: The Case of Non-Zero Linear Momentum

abstract:
  The irreducible representations (IRs) of the double cover of the Euclidean
group with parity in three dimensions are subduced to the corresponding cubic
space group. The reduction of these representations gives the mapping of
continuum angular momentum states to the lattice in the case of non-zero linear
momentum. The continuous states correspond to lattice states with the same
momentum and continuum rotational quantum numbers decompose into those of the
IRs of the little group of the momentum vector on the lattice. The inverse
mapping indicates degeneracies that will appear between levels of different
lattice IRs in the continuum limit, recovering the continuum angular momentum
multiplets. An example of this inverse mapping is given for the case of the
``moving'' isotropic harmonic oscillator.


title:
Two-dimensional N=(2,2) super Yang-Mills theory on the lattice via
  dimensional reduction

abstract:
  The N=(2,2) extended super Yang-Mills theory in 2 dimensions is formulated on
the lattice as a dimensional reduction of a 4 dimensional lattice gauge theory.
We use the plaquette action for a bosonic sector and the Wilson- or the
overlap-Dirac operator for a fermion sector. The fermion determinant is real
and, moreover, when the overlap-Dirac operator is used, semi-positive definite.
The flat directions in the target theory become compact and present no subtlety
for a numerical integration along these directions. Any exact supersymmetry
does not exist in our lattice formulation; nevertheless we argue that one-loop
calculable and finite mass counter terms ensure a supersymmetric continuum
limit to all orders of perturbation theory.


title: Lattice QCD at finite density via a new canonical approach

abstract:
  We carry out a finite density calculation based on a canonical approach which
is designed to address the overlap problem. Two degenerate flavor simulations
are performed using Wilson gauge action and Wilson fermions on $4^4$ lattices,
at temperatures close to the critical temperature $T_c\approx 170\MeV$ and
large densities (5 to 20 times nuclear matter density). In this region, we find
that the algorithm works well. We compare our results with those from other
approaches.


title: Universality check of Abelian Monopoles

abstract:
  We study the Abelian projected SU(2) lattice gauge theory after gauge fixing
to the maximally Abelian gauge (MAG). In order to check the universality of the
Abelian dominance we employ the tadpole improved tree level (TI) action. We
show that the density of monopoles in the largest cluster (the IR component) is
finite in the continuum limit which is approximated already at relatively large
lattice spacing. The value itself is smaller than in the case of Wilson action.
We present results for the ratio of the Abelian to non-Abelian string tension
for both Wilson and TI actions for a number of lattice spacings in the range
0.06 fm < a < 0.35 fm. These results show that the ratio is between 0.9 and
0.95 for all considered values of lattice couplings and both actions. We
compare the properties of the monopole clusters in two gauges - in MAG and in
the Laplacian Abelian gauge (LAG). Whereas in MAG the infrared component of the
monopole density shows a good convergence to the continuum limit, we find that
in LAG it is even not clear whether a finite limit exists.


title:
Nonperturbative renormalization of composite operators with overlap
  fermions

abstract:
  We compute non-perturbatively the renormalization constants of composite
operators on a quenched $16^3 \times 28 $ lattice with lattice spacing $a$ =
0.20 fm for the overlap fermion by using the regularization independent (RI)
scheme. The quenched gauge configurations were generated with the Iwasaki
action. We test the relations $Z_A = Z_V$ and $ Z_S=Z_P$ and find that they
agree well {(less than 1%)} above $\mu$ = 1.6 GeV. %even for our lattice with a
coarse lattice spacing. We also perform a Renormalization Group (RG) analysis
at the next-to-next-to-leading order and match the renormalization constants to
the $\bar{\rm MS}$ scheme. The wave-function renormalization $Z_{\psi}$ is
determined from the vertex function of the axial current and $Z_A$ from the
chiral Ward identity. Finally, we examine the finite quark mass behavior for
the renormalization factors of the quark bilinear operators. We find that the
$(pa)^2$ errors of the vertex functions are small and the quark mass dependence
of the renormalization factors to be quite weak.


title: Simple patterns for non-linear susceptibilities near T_c

abstract:
  Non-linear susceptibilities upto the eighth order have been constructed in
QCD with 2 flavours of dynamical quarks. Beyond leading order, they exhibit
peaks at the cross over temperature, T_c. By analyzing their behaviour in
detail, we find that the dominant contributions near T_c come from a set of
operators with a remarkably simple topology. Any effective theory of QCD near
T_c must be able to explain these regularities.


title: Lattice renormalization of the static quark derivative operator

abstract:
  We give the analytical expressions and numerical values of radiative
corrections to the covariant derivative operator on the static quark line, used
for the lattice calculation of the Isgur-Wise form factors $\tau_{1/2}(1)$ and
$\tau_{3/2}(1)$. Those corrections induce an enhancement of renormalized
quantities if an hypercubic blocking is applied to the Wilson line, whereas
there is a reduction without such a blocking.


title: Gauge transformations in non-perturbative chiral gauge theories

abstract:
  We reconsider gauge-transformation properties in chiral gauge theories on the
lattice observing all pertinent information and show that these properties are
actually determined in a general way for any gauge group and for any value of
the index. In our investigations we also clarify several related issues.


title: On the renormalized scalar density in quenched QCD

abstract:
  We present a non-perturbative determination of the renormalization factor Z_S
of the scalar density in quenched QCD with overlap fermions. Results are
obtained at four values of the lattice spacing. By combining Z_S with results
for the low-energy constant Sigma we are able to compute the renormalization
group invariant scalar condensate in the continuum limit with a total accuracy
of 7%, excluding dynamical quark effects. Our result translates to
Sigma_msbar(2 GeV)=(285+/-9 MeV)^3 if the scale is set by the kaon decay
constant. We have also performed scaling studies of the pseudoscalar decay
constant and the vector mass. Our results indicate that quantities computed
using overlap quarks exhibit excellent scaling behaviour, with small residual
lattice artifacts.


title: Charmonium Spectrum from Quenched QCD with Overlap Fermions

abstract:
  We present the first study of the charmonium spectrum using overlap fermions,
on quenched configurations. Simulations are performed on $16^3 \times 72$
lattices, with Wilson gauge action at $\beta$ = 6.3345. We demonstrate that we
have discretization errors under control at about 5%. We obtain 88(4) MeV for
hyperfine splitting using the $r_0$ scale, and 121(6) MeV using the
($1\bar{P}-1\bar{S}$) scale. This paper raises the possibility that the
discrepancy between the lattice results and the experimental value for
charmonium hyperfine splitting can be resolved using overlap fermions to
simulate the charm quark on lattice.


title:
Vector Meson Mass Corrections at O(a^2) in PQChPT with Wilson and
  Ginsparg-Wilson quarks

abstract:
  We derive the mixed as well as unmixed lattice heavy meson chiral Lagrangian
up to order O(a^2), with Wilson and Ginsparg-Wilson fermions. We consider two
flavor partially quenched QCD and calculate vector meson mass corrections up to
order O(a^2), including the corrections associated with the violation of
rotational O(4) symmetry down to the hypercubic group. Our calculations also
include the one-loop, phenomenological contribution from the \rho -> \pi\pi
decay channel. The final result is a chiral-continuum extrapolation formula
with model dependent coefficients from which one can recover the physical \rho
meson mass from the large amount of current lattice data. As a verification of
our result, the chiral-continuum extrapolation formula is compared with that
used in numerical simulations.


title:
Exact Extended Supersymmetry on a Lattice: Twisted N=2 Super Yang-Mills
  in Two Dimensions

abstract:
  We propose a lattice action for two dimensional super Yang-Mills theory with
a twisted N=2 supersymmetry. The extended supersymmetry is fully and exactly
realized on the lattice. The method employed is quite general and its extension
to the N=4 supersymmetry in four dimensions is briefly presented. The lattice
has a new type of ``fermionic'' links, where odd Grassmann variables,
supercharges and fermionic connections sit. The Leibniz rule is preserved on
the lattice, although in a modified ``shifted'' form that takes into account
the link nature of both derivatives and supercharges. Superfields are
semi-local objects and superfield expansion is naturally embedded in the
lattice structure. The Dirac-K\"ahler twist generates the extended twisted
supersymmetry, turning the multiplicity of species doublers into the
multiplicity due to the extended supersymmetry. In this way the balance between
bosonic and fermionic degrees of freedom is preserved.


title: Chirally improving Wilson fermions III. The Schr\"odinger functional

abstract:
  We show that it is possible to construct a lattice Schroedinger functional
for standard Wilson fermions, where the expectation values of ${\cal R}_5$-even
operators are O($a$) improved, up to terms coming from the boundaries.


title: Effective Field Theories for Quantum Chromodynamics on the Lattice

abstract:
  Light and heavy-light (b) hadrons are among the most interesting and among
the most challenging quantities to calculate in lattice gauge theory. One would
like to avoid discretization effects from very heavy quarks and to calculate
chiral extrapolations and to calculate finite volume effects from light quarks
or to minimize these effects. For this one uses effective theories: Chiral
Perturbation Theory and Nonrelativistic QCD or Heavy Quark Effective Theory.
Lattice results are reviewed on hadrons containing light quarks and light and b
quarks, and discussed in the framework of effective theories.


title: Flavour Breaking Effects of Wilson twisted mass fermions

abstract:
  We study the flavour breaking effects appearing in the Wilson twisted mass
formulation of lattice QCD. In this quenched study, we focus on the mass
splitting between the neutral and the charged pion, determining the neutral
pion mass with a stochastic noise method to evaluate the disconnected
contributions. We find that these disconnected contributions are significant.
Using the Osterwalder-Seiler interpretation of the connected piece of the
neutral pion correlator, we compute the corresponding neutral pion mass to
study with more precision the scaling behaviour of the mass splitting.


title:
One-loop matching of Delta S=2 four-quark operators with improved
  staggered fermions

abstract:
  We compute O(alpha_s) lattice-to-continuum perturbative matching coefficients
for the Delta S=2 flavor changing four-quark operators for the Asqtad improved
staggered action. In conjunction with lattice simulations with three flavors of
light, dynamical quarks, our results yield an unquenched determination of B_K,
the parameter that determines the amount of indirect CP violation in the
neutral kaon system. Its value is an important input for the unitarity triangle
analysis of weak decays.


title: About a possible 3rd order phase transition at T=0 in 4D gluodynamics

abstract:
  We revisit the question of the convergence of lattice perturbation theory for
a pure SU(3) lattice gauge theory in 4 dimensions. Using a series for the
average plaquette up to order 10 in the weak coupling parameter beta^{-1}, we
show that the analysis of the extrapolated ratio and the extrapolated slope
suggests the possibility of a non-analytical power behavior of the form
(1/\beta -1/5.7(1))^{1.0(1)}, in agreement with another analysis based on the
same asumption. This would imply that the third derivative of the free energy
density diverges near beta =5.7. We show that the peak in the third derivative
of the free energy present on 4^4 lattices disappears if the size of the
lattice is increased isotropically up to a 10^4 lattice. On the other hand, on
4 x L^3 lattices, a jump in the third derivative persists when L increases. Its
location coincides with the onset of a non-zero average for the Polyakov loop.
We show that the apparent contradiction at zero temperature can be resolved by
moving the singularity in the complex 1/\beta plane. If the imaginary part of
the location of the singularity Gamma is within the range 0.001< Gamma < 0.01,
it is possible to limit the second derivative of P within an acceptable range
without affecting drastically the behavior of the perturbative coefficients. We
discuss the possibility of checking the existence of these complex
singularities by using the strong coupling expansion or calculating the zeroes
of the partition function.


title: Non-perturbative quark mass renormalization in two-flavor QCD

abstract:
  The running of renormalized quark masses is computed in lattice QCD with two
flavors of massless O(a) improved Wilson quarks. The regularization and flavor
independent factor that relates running quark masses to the renormalization
group invariant ones is evaluated in the Schroedinger Functional scheme. Using
existing data for the scale r_0 and the pseudoscalar meson masses, we define a
reference quark mass in QCD with two degenerate quark flavors. We then compute
the renormalization group invariant reference quark mass at three different
lattice spacings. Our estimate for the continuum value is converted to the
strange quark mass with the help of chiral perturbation theory.


title: Adjoint modes as probes of gauge field structure

abstract:
  We show how zero-modes and quasi-zero-modes of the Dirac operator in the
adjoint representation can be used to construct an estimate of the action
density distribution of a pure gauge field theory, which is less sensitive to
the ultraviolet fluctuations of the field. This can be used to trace the
topological structures present in the vacuum. The construction relies on the
special properties satisfied by the supersymmetric zero-modes.


title: Reconsidering gauge-Higgs continuity

abstract:
  The 3-d Z(2) lattice gauge-Higgs theory is cast in a partial axial gauge
leaving a residual Z(2) symmetry, global in two directions and local in one. It
is shown both analytically and numerically that this symmetry breaks
spontaneously in the Higgs phase and is unbroken in the confinement phase.
Therefore they must be separated everywhere by a phase transition, in
contradiction to a theorem by Fradkin and Shenker. It relied on a fully fixed
unitary gauge, which prohibits this phase transition explicitly. Thus the
unfixed gauge theory is not, in this case, equivalent to the unitary-gauge
version.


title:
Comparison of perturbative RG theory with lattice data for the 4d Ising
  model

abstract:
  Predictions for (phi^4)_4 theory from renormalization-group-improved
perturbation theory, as formulated by Luescher and Weisz, are compared to
published (and some unpublished) data from lattice Monte-Carlo simulations of
the 4-dimensional Ising model. Good agreement is found in all but one
respect:-- the change in the wavefunction-renormalization constant Z_R across
the phase transition is significantly greater than predicted. A related
observation is that propagator data in the broken phase show deviations from
free-propagator form -- deviations that become larger, not smaller, closer to
the continuum limit. More data closer to the critical point are needed to
clarify the situation.


title: Lattice QCD Study for Confinement and Hadrons

abstract:
  Using SU(3) lattice QCD, we perform the detailed studies of the three-quark
and the multi-quark potentials. From the accurate calculation for more than 300
different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm
3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear
potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for
Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in
maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we
perform the accurate calculation for the 1st excited-state 3Q potential $V_{\rm
3Q}^{\rm e.s.}$ by diagonalizing the QCD Hamiltonian in the presence of three
quarks, and find a large gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv
V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a
physical reason of the success of the quark model. $\Delta E_{\rm 3Q}$ is found
to be reproduced by the ``inverse Mercedes Ansatz'', which indicates a
complicated bulk excitation for the gluonic-excitation mode. We study also the
tetra-quark and the penta-quark potentials in lattice QCD, and find that they
are well described by the OGE Coulomb plus multi-Y type linear potential, which
supports the flux-tube picture even for the multi-quarks.


title: Glueball Regge Trajectories

abstract:
  We investigate the spectrum of glueballs in 3D and 4D SU(N) gauge theories.
Our motivation is to determine whether the states lie on straight Regge
trajectories. To this end we develop new lattice techniques to reliably
determine the states carrying higher spin. It has been conjectured for a long
time that glueballs are the physical states lying on the pomeron, the
trajectory responsible for the slowly rising hadronic cross-sections at large
centre-of-mass energy.


title:
Plaquette representation for 3D lattice gauge models: I. Formulation and
  perturbation theory

abstract:
  We develop an analytical approach for studying lattice gauge theories within
the plaquette representation where the plaquette matrices play the role of the
fundamental degrees of freedom. We start from the original Batrouni formulation
and show how it can be modified in such a way that each non-abelian Bianchi
identity contains only two connectors instead of four. In addition, we include
dynamical fermions in the plaquette formulation. Using this representation we
construct the low-temperature perturbative expansion for U(1) and SU(N) models
and discuss its uniformity in the volume. The final aim of this study is to
give a mathematical background for working with non-abelian models in the
plaquette formulation.


title: Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

abstract:
  The vacuum type of SU(2) gluodynamics is studied using Monte-Carlo
simulations in maximally Abelian (MA) gauge and in Landau (LA) gauge, where the
dual Meissner effect is observed to work. The dual Meissner effect is
characterized by the coherence and the penetration lengths. Correlations
between Wilson loops and electric fields are evaluated in order to measure the
penetration length in both gauges. The coherence length is shown to be fixed in
the MA gauge from measurements of the monopole density around the static
quark-antiquark pair. It is also shown numerically that a dimension 2 gluon
operator A^+A^-(s) and the monopole density has a strong correlation as
suggested theoretically. Such a correlation is observed also between the
monopole density and A^2(s)= A^+A^-(s) + A^3A^3(s) condensate if the remaining
U(1) gauge degree of freedom is fixed to U(1) Landau gauge (U1LA). The
coherence length is determined numerically also from correlations between
Wilson loops and A^+A^-(s) and A^2(s) in MA + U1LA gauge. Assuming that the
same physics works in the LA gauge, we determine the coherence length from
correlations between Wilson loops and A^2(s). Penetration lengths and coherence
lengths in the two gauges are almost the same. The vacuum type of the
confinement phase in both gauges is near to the border between the type 1 and
the type 2 dual superconductors.


abstract:
  We propose a method to calculate the Greens function of a free massive scalar
field on the lattice numerically to very high precision. For masses m < 2 (in
lattice units) the massive Greens function can be expressed recursively in
terms of the massless Greens function and just two additional mass-independent
constants.


title: Interactions of confining strings in SU(3) gluodynamics

abstract:
  We study the interaction energy of the confining strings in the static
rectangular tetraquark system in SU(3) gluodynamics. Using a two-state
approximation we calculate the energy eigenvalues and corresponding
eigenvectors of string states of different geometry. The interactions are
studied both for the co-aligned and for the counter-aligned parallel strings as
the functions of positions of the tetraquark constituents. We formulate a
simple soap-film model and show that with a good accuracy the string
interaction energy corresponding to the ground state of the tetraquark system
can be described by this soap-film model.


title: Center flux correlation in SU(2) Yang-Mills theory

abstract:
  By using the method of center projection the center vortex part of the gauge
field is isolated and its propagator is evaluated in the center Landau gauge,
which minimizes the open 3-dimensional Dirac volumes of non-trivial center
links bounded by the closed 2-dimensional center vortex surfaces. The center
field propagator is found to dominate the gluon propagator (in Landau gauge) in
the low momentum regime and to give rise to an OPE correction to the latter of
${\sqrt{\sigma}}/{p^3}$.The screening mass of the center vortex field vanishes
above the critical temperature of the deconfinement phase transition, which
naturally explains the second order nature of this transition consistent with
the vortex picture. Finally, the ghost propagator of maximal center gauge is
found to be infrared finite and thus shows that the coset fields play no role
for confinement.


title: Understanding Parton Distributions from Lattice QCD

abstract:
  I examine the past lattice QCD calculations of three representative
observables, the transverse quark distribution, momentum fraction, and axial
charge, and emphasize the prospects for not only quantitative comparison with
experiment but also qualitative understanding of QCD.


title: Extrapolation Formulas for Neutron EDM Calculations in Lattice QCD

abstract:
  Lattice QCD is rapidly progressing toward being able to reliably compute the
electric dipole moment of the neutron as a function of the strong CP-violating
parameter theta. Present day calculations are performed at unphysical values of
the light quark masses, in volumes that are not exceptionally large and at
lattice spacings that are not exceptionally small. We use chiral perturbation
theory to determine the leading contributions to the neutron electric dipole
moment at finite volume, and in partially-quenched calculations.


title: Monte Carlo Hamiltonian of lattice gauge theory

abstract:
  We discuss how the concept of the Monte Carlo Hamiltonian can be applied to
lattice gauge theories.


title: The Kaon B-parameter from Quenched Domain-Wall QCD

abstract:
  We present numerical results for the kaon B-parameter, B_K, determined in the
quenched approximation of lattice QCD. Our simulations are performed using
domain-wall fermions and the renormalization group improved, DBW2 gauge action
which combine to give quarks with good chiral symmetry at finite lattice
spacing. Operators are renormalized non-perturbatively using the RI/MOM scheme.
We study scaling by performing the simulation on two different lattices with
a^{-1} = 1.982(30) and 2.914(54) GeV. We combine this quenched scaling study
with an earlier calculation of B_K using two flavors of dynamical, domain-wall
quarks at a single lattice spacing to obtain
B_K(MS,NDR,mu=2GeV)=0.563(21)(39)(30), were the first error is statistical, the
second systematic (without quenching errors) and the third estimates the error
due to quenching.


title: Isospin breaking and the chiral condensate

abstract:
  With two degenerate quarks, the chiral condensate exhibits a jump as the
quark masses pass through zero. I discuss how this single transition splits
into two Ising like transitions when the quarks are made non-degenerate. The
order parameter is the expectation of the neutral pion field. The transitions
represent long distance coherent phenomena occuring without the Dirac operator
having vanishingly small eigenvalues.


title: The Ademollo-Gatto theorem for lattice semileptonic decays

abstract:
  We present the results of the calculation of the Kl3 semileptonic form factor
at zero momentum transfer, f(0), obtained at one-loop in partially quenched
Chiral Perturbation Theory (with either Nf=2, or Nf=3, and with generic valence
and sea quark masses). We show that for Nf=2, when the masses of the valence
and sea light quarks are equal, the correction is of the order (MK^2-Mpi^2)^3.
The formulae presented here can be useful for the mass extrapolation of the
results obtained in lattice simulations to the physical point.


title: Non-equilibrium Higgs transition in classical scalar electrodynamics

abstract:
  Real time rearrangement of particle spectra is studied numerically in a U(1)
Gauge+Higgs system, in the unitary gauge and in three spatial dimensions. The
cold system starts from the symmetric phase. Evolution of the partial energy
densities and pressures reveal well-defined equations of state for the
longitudinal and transversal gauge fields very early. Longitudinal modes are
excited more efficiently and thermalize the slowest. Hausdorff-dimension of the
Higgs-defect manifold, eventually seeding vortex excitations is thoroughly
discussed. Scaling dependence of the vortex density on the characteristic time
of the symmetry breaking transition is established.


title: Localization of lattice fermions: lessons for overlap

abstract:
  Lattice fermions in a fluctuating gauge field can show localization, much
like electrons in a disordered potential. We study the spectrum of localized
and extended states of supercritical Wilson fermions in gauge ensembles
generated with plaquette and improved actions. When the Wilson fermion operator
is used to construct the overlap kernel, the mobility edge, that is the
boundary between the localized and extended states, determines the range of the
kernel.


title: Overlap hypercube fermions in QCD with light quarks

abstract:
  We report on simulation results with overlap hypercube fermions (overlap HF)
- a type of exactly chiral lattice fermions - and their link to chiral
perturbation theory. We first sketch the construction of the overlap HF and
discuss its high level of locality. Next we show applications in the p-regime
of QCD, where we evaluate m_{\pi}, m_{\rho}, the quark mass according to the
PCAC relation, the renormalisation constant Z_A and the pion decay constant
F_{\pi} as functions of the bare quark mass. F_{\pi} is then reconsidered at
even smaller quark masses in the epsilon-regime, along with the scalar
condensate \Sigma. In that context we also discuss results for the topological
charges and susceptibility.


title: Symmetry and scaling in the Q-exact lattice (2,2) 2d Wess-Zumino model

abstract:
  As a nonperturbative check on the Q-exact lattice formulation, we demonstrate
that the continuum R-symmetries are recovered. We locate the critical domain of
the lattice theory. Aspects of the continuum nonrenormalization theorems are
found to be respected at finite lattice spacing. Preliminary attempts to
extract critical exponents--another nonperturbative check--are discussed. All
of our results are obtained from Monte Carlo simulations with dynamical
fermions.


title:
Clebsch-Gordan Construction of Lattice Interpolating Fields for Excited
  Baryons

abstract:
  Large sets of baryon interpolating field operators are developed for use in
lattice QCD studies of baryons with zero momentum. Operators are classified
according to the double-valued irreducible representations of the octahedral
group. At first, three-quark smeared, local operators are constructed for each
isospin and strangeness and they are classified according to their symmetry
with respect to exchange of Dirac indices. Nonlocal baryon operators are
formulated in a second step as direct products of the spinor structures of
smeared, local operators together with gauge-covariant lattice displacements of
one or more of the smeared quark fields. Linear combinations of direct products
of spinorial and spatial irreducible representations are then formed with
appropriate Clebsch-Gordan coefficients of the octahedral group. The
construction attempts to maintain maximal overlap with the continuum SU(2)
group in order to provide a physically interpretable basis. Nonlocal operators
provide direct couplings to states that have nonzero orbital angular momentum.


title: Baryons with Ginsparg-Wilson quarks in a staggered sea

abstract:
  We determine the masses and magnetic moments of the octet baryons in chiral
perturbation theory formulated for a mixed lattice action of Ginsparg-Wilson
valence quarks and staggered sea quarks. Taste-symmetry breaking does not occur
at next-to-leading order in the combined lattice-spacing and chiral expansion.
Expressions derived for masses and magnetic moments are required for addressing
lattice artifacts in mixed-action simulations of these observables.


title: A Transverse Lattice QCD Model for Mesons

abstract:
  This thesis describes work done by me during my tenure as a Ph.D. student at
the Centre for High Energy Physics, Indian Institute of Science, Bangalore.
Chapter 1 is a brief introduction to QCD. In Chapter 2, we formulate QCD in the
large-$N_{c}$ and strong transverse coupling limits, and then exactly integrate
out all the gauge degrees of freedom to obtain the generating functional for
quark-antiquark bilinears. We study the chiral properties of our limiting
theory in Chapter 3, for naive as well as Wilson fermions, and obtain a
recursive relation for the chiral condensate. In Chapter 4, we obtain the
homogeneous integral equation satisfied by the meson states of our theory.
Comparison of this equation with the corresponding one for the 't~Hooft model
allows us to infer many physical meson properties. Our results are consistent
with phenomenological expectations, and this is the first time that such
results have been obtained from $(3+1)$-dim QCD, with only quark and gluon
degrees of freedom and no ad hoc model assumptions. Extraction of precise
values requires numerical solution of the integral equation; we have not yet
carried that out and we describe our outlook for further investigations at the
end of Chapter 4. Three appendices supplement our analysis. Our notation and
conventions are listed in Appendix A. The known results for mesons in the
't~Hooft model and in strong coupling lattice QCD are rederived, in Appendix B
and in Appendix C respectively, using the same methodology as followed in the
thesis. That allows convenient comparison, as well as demonstrates the
advantage of our approach over these two well-studied approximations to QCD.


title:
In search of a Hagedorn transition in SU(N) lattice gauge theories at
  large-N

abstract:
  We investigate on the lattice the metastable confined phase above Tc in SU(N)
gauge theories, for N=8,10, and 12. In particular we focus on the decrease with
the temperature of the mass of the lightest state that couples to Polyakov
loops. We find that at T=Tc the corresponding effective string tension
\sigma_{eff}(T) is approximately half its value at T=0, and that as we increase
T beyond Tc, while remaining in the confined phase, \sigma_{eff}(T) continues
to decrease. We extrapolate \sigma_{eff}(T) to even higher temperatures, and
interpret the temperature where it vanishes as the Hagedorn temperature T_H.
For SU(12) we find that T_H/Tc=1.116(9), when we use the exponent of the
three-dimensional XY model for the extrapolation, which seems to be slightly
preferred over a mean-field exponent by our data.


title:
Two Particle States in a Box and the $s$-Matrix in Multi-Channel
  Scattering

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


title:
Heavy quark propagators with improved precision using domain
  decomposition

abstract:
  We show that, in four dimensions, the quark propagator is affected by
round-off errors for large values of the quark mass am and the time extent T/a
even when double precision arithmetics is used to compute it. We introduce a
definition of the solver residual which is sensitive to the problem and apply a
Schwarz alternating procedure to compute the propagator in a number of
sub-domains in the time direction. The effectiveness of the method is
demonstrated in a numerical computation of the free one-dimensional Dirac
propagator.


title:
Spontaneous chiral-symmetry breaking of lattice QCD with massless
  dynamical quarks

abstract:
  One of the most challenging issues in QCD is the investigation of spontaneous
chiral-symmetry breaking, which is characterized by the non-vanishing chiral
condensate when the bare fermion mass is zero. In standard methods, one has to
perform expensive lattice simulations at multiple bare quark masses, and employ
some modeled function to extrapolate the data to the chiral limit. This paper
applies the probability distribution function method to computing the chiral
condensate in lattice QCD with massless dynamical quarks, without any ambiguous
mass extrapolation. The results for staggered quarks indicates that the method
might be a more efficient alternative for investigating the spontaneous
chiral-symmetry breaking in lattice QCD.


title: Dynamical overlap fermions: techniques and results

abstract:
  We summarize our recent investigations of lattice QCD with dynamical overlap
fermions. We sketch algorithmic issues and our approach to solving them. We
show our measurement of the topological susceptibility. We describe a
computation of the chiral condensate using an analysis of the distribution of
eigenmodes of the Dirac operator and Random Matrix Theory.


title: Finite Size Effect in Excited Baryon Spectroscopy

abstract:
  We investigate the finite size effect on masses of excited baryons in
quenched lattice QCD simulation. For this purpose, we perform numerical
simulations at three different lattice sizes, La\simeq 1.6, 2.2 and 3.2 fm. The
gauge configurations are generated with the single plaquette gauge action at
\beta=6/g^2=6.2, and the quark propagator are computed with the Wilson fermion
action. To access to two parity states of the nucleon and four different
spin-parity states of the \Delta baryon, the appropriate spin/parity projection
are carried out. We find that the spatial lattice size is required to be as
large as 3 fm to remove the finite size effect on excited baryons even in the
heavy quark region (M_\pi/M_\rho\simeq 0.82, 0.87), where that on the nucleon
is negligible. On our largest lattice (La\simeq 3.2 fm), all mass spectra of
the J^P=1/2^\pm nucleons and the J^P=1/2^\pm, 3/2^\pm \Delta baryons are
roughly consistent with experimental values after naive chiral extrapolation.


title: Two Color QCD beyond the BEC regime

abstract:
  We present results of simulations of Two Color QCD using two flavors of
Wilson quark in the fundamental representation, at non-zero quark chemical
potential mu, on an 8^3x16 lattice. Results for the quark number density, quark
and gluon energy densities, and superfluid condensate are qualitatively
distinct from the behaviour expected on the assumption that the dominant
degrees of freedom are tightly bound scalar diquarks which Bose condense;
rather the scaling with mu is more suggestive of a Fermi surface disrupted by a
Cooper pair condensate. We also present evidence both for screening of the
static potential, and color deconfinement, arising solely as a result of a
non-zero quark density.


title: Ghost condensation on the lattice

abstract:
  We perform a numerical study of ghost condensation -- in the so-called
Overhauser channel -- for SU(2) lattice gauge theory in minimal Landau gauge.
The off-diagonal components of the momentum-space ghost propagator G^{cd}(p)
are evaluated for lattice volumes V = 8^4, 12^4, 16^4, 20^4, 24^4 and for three
values of the lattice coupling: \beta = 2.2, 2.3, 2.4. Our data show that the
quantity \phi^b(p) = \epsilon^{bcd} G^{cd}(p) / 2 is zero within error bars,
being characterized by very large statistical fluctuations. On the contrary,
|\phi^b(p)| has relatively small error bars and behaves at small momenta as
L^{-2} p^{-z}, where L is the lattice side in physical units and z \approx 4.
We argue that the large fluctuations for \phi^b(p) come from spontaneous
breaking of a global symmetry and are associated with ghost condensation. It
may thus be necessary (in numerical simulations at finite volume) to consider
|\phi^b(p)| instead of \phi^b(p), to avoid a null average due to tunneling
between different broken vacua. Also, we show that \phi^b(p) is proportional to
the Fourier-transformed gluon field components {\widetilde A}_{\mu}^b(q). This
explains the L^{-2} dependence of |\phi^b(p)|, as induced by the behavior of |
{\widetilde A}_{\mu}^b(q) |. We fit our data for |\phi^b(p)| to the theoretical
prediction (r / L^2 + v) / (p^4 + v^2), obtaining for the ghost condensate v an
upper bound of about 0.058 GeV^2. In order to check if v is nonzero in the
continuum limit, one probably needs numerical simulations at much larger
physical volumes than the ones we consider. As a by-product of our analysis, we
perform a careful study of the color structure of the inverse Faddeev-Popov
matrix in momentum space.


title: A New Method for Determining $F_\pi$ on the Lattice

abstract:
  We derive the two-point spectral correlation function of the Dirac operator
with a specific external source in the $\epsilon$-regime of QCD. This
correlation function has a unique and strong dependence on $F_\pi$, and thus
provides an novel way to extract $F_\pi$ from lattice simulations. We test the
method in a quenched lattice simulation with staggered fermions.


title:
Simulating nonequilibrium quantum fields with stochastic quantization
  techniques

abstract:
  We present lattice simulations of nonequilibrium quantum fields in
Minkowskian space-time. Starting from a non-thermal initial state, the
real-time quantum ensemble in 3+1 dimensions is constructed by a stochastic
process in an additional (5th) ``Langevin-time''. For the example of a
self-interacting scalar field we show how to resolve apparent unstable Langevin
dynamics, and compare our quantum results with those obtained in classical
field theory. Such a direct simulation method is crucial for our understanding
of collision experiments of heavy nuclei or other nonequilibrium phenomena in
strongly coupled quantum many-body systems.

categories: hep-lat cond-mat.other hep-ph hep-th nucl-th


title:
Nonperturbative $O(a)$ improvement of the Wilson quark action with the
  RG-improved gauge action using the Schr\"odinger functional method

abstract:
  We perform a nonperturbative determination of the $O(a)$-improvement
coefficient $c_{\rm SW}$ and the critical hopping parameter $\kappa_c$ for
$N_f$=3, 2, 0 flavor QCD with the RG-improved gauge action using the
Schr\"odinger functional method. In order to interpolate $c_{\rm SW}$ and
$\kappa_c$ as a function of the bare coupling, a wide range of $\beta$ from the
weak coupling region to the moderately strong coupling points used in
large-scale simulations is studied. Corrections at finite lattice size of
$O(a/L)$ turned out to be large for the RG-improved gauge action, and hence we
make the determination at a size fixed in physical units using a modified
improvement condition. This enables us to avoid $O(a)$ scaling violations which
would remain in physical observables if $c_{\rm SW}$ determined for a fixed
lattice size $L/a$ is used in numerical simulations.


title:
Phase structures of strong coupling lattice QCD with overlap fermions at
  finite temperature and chemical potential

abstract:
  We perform the first study of lattice QCD with overlap fermions at finite
temperature $T$ and chemical potential $\mu$. We start from the Taylor expanded
overlap fermion action, and derive in the strong coupling limit the effective
free energy by mean field approximation. On the ($\mu,T$) plane and in the
chiral limit, there is a tricritical point, separating the second order chiral
phase transition line at small $\mu$ and large $T$, and first order chiral
phase transition line at large $\mu$ and small $T$.


title: The effect of sea quarks on the mass of the charm quark from Lattice QCD

abstract:
  We compute the mass of the charm quark using both quenched and dynamical
lattice QCD calculations. We examine the effects of mass dependent lattice
artifacts by comparing two different formalisms for the heavy quarks. We take
the continuum limit of the charm mass in quenched QCD by extrapolating from
three different lattice spacings. At a fixed lattice spacing, the mass of the
charm quark is compared between quenched QCD and dynamical QCD with a sea quark
mass around strange. In the continuum limit of quenched QCD, we find
m_c(m_c)=1.29(7)(13) GeV. No evidence was seen for unquenching.


title:
Low Energy Constants from the zero mode contribution to the
  pseudo-scalar correlator

abstract:
  We apply different types of overlap operators in quenched QCD simulations to
compute the zero mode contribution to the pseudo-scalar correlator. In
particular we use the conventional Neuberger Dirac operator and the overlap
hypercube Dirac operator. Confronting our data with the analytical predictions
by Chiral Perturbation Theory we evaluate the pion decay constant and the
parameter \alpha of the quenched chiral Lagrangian.


title: Lattice Chirality and its uses at large N

abstract:
  A brief overview of the authors' work on lattice chirality and its
application to the numerical study of planar QCD is presented.


title:
Screening of heavy quark free energies at finite temperature and
  non-zero baryon chemical potential

abstract:
  We analyze the dependence of heavy quark free energies on the baryon chemical
potential (mu_b) in 2-flavour QCD using improved (p4) staggered fermions with a
bare quark mass of m/T = 0.4. By performing a 6th order Taylor expansion in the
chemical potential which circumvents the sign problem. The Taylor expansion
coefficients of colour singlet and colour averaged free energies are calculated
and from this the expansion coefficients for the corresponding screening masses
are determined. We find that for small mu_b the free energies of a static quark
anti-quark pair decrease in a medium with a net excess of quarks and that
screening is well described by a screening mass which increases with increasing
mu_b. The mu_b-dependent corrections to the screening masses are well described
by perturbation theory for T > 2 T_c. In particular, we find for all
temperatures above T_c that the expansion coefficients for singlet and colour
averaged screening masses differ by a factor 2.


title:
Determining the low energy parameters of Wilson Chiral Perturbation
  Theory

abstract:
  We report preliminary results of a Wilson Chiral Perturbation Theory (WChPT)
analysis of twisted mass lattice QCD data. The quenched data, previously
published by two different groups, was generated with two definitions for the
critical quark mass and shows a strong non-linear quark mass dependence for
small quark masses for the pion mass definition (``bending phenomenon''). We
find that WChPT describes this characteristic curvature fairly well. Fits to
the data provide estimates for combinations of low-energy parameters, even
though the errors are sizable.


title:
Lattice calculation of low energy constants with Ginsparg-Wilson type
  fermions

abstract:
  We present a quenched lattice calculation of low energy constants using the
chirally improved Dirac operator. Several lattice sizes at different lattice
spacings are studied. We systematically compare various methods for computing
these quantities, using pseudoscalar and axial vector correlators. We find
consistent results for the different approaches, giving rise to f_\pi =
96(2)(4) MeV, f_K = 106(1)(8) MeV, f_K/f_\pi=1.11(1)(2), Sigma= -(286(4)(31)
MeV)^3, the average light quark mass m = 4.1(2.4) MeV and m_s = 101(8) MeV.


title:
Implementing Hybrid Monte Carlo with stout-smeared chirally improved
  Dirac operators

abstract:
  We discuss our implementation of dynamical Ginsparg-Wilson type fermions
using a stout-smeared chirally improved Dirac operator. Such operators have
been studied extensively in quenched calculations within the
Bern-Graz-Regensburg (BGR) collaboration. Here we discuss the development and
testing of the Hybrid Monte Carlo algorithm with this Dirac operator. We study
the chiral properties of this operator in a dynamical setup, comparing, e.g.,
the spectra of the operator for the dynamical and quenched cases. We then
discuss quantitative features of the algorithm like autocorrelation and
performance.


title: First results from dynamical chirally improved fermions

abstract:
  We simulate Quantum Chromodynamics in four Euclidean dimensions with two
(degenerate mass) flavors of dynamical quarks. The Dirac operator is the
so-called chirally improved operator that has been studied so far in quenched
calculations. We now present results of an implementation with the Hybrid Monte
Carlo (HMC) algorithm including stout smearing. Our results are from an 8^3x16
lattice with tadpole improved Luescher-Weisz gauge action. We present our
estimate of the lattice spacing, the pi and rho meson masses and evidence for
tunneling between different topological sectors.


title: Studying glueball masses in non-Abelian LGT with the LW algorithm

abstract:
  We address a study of glueball masses in the confining regime of SU(2) in D=3
using an algorithm inspired by the multi-level scheme. Our method, which
exploits the locality of the action to achieve high precision results, is based
on a technique already used for compact QED, and generalises it to the
non-Abelian case. We discuss the main features of this method, in comparison
with other algorithms that have been used in similar studies.


title: Automated Methods in Chiral Perturbation Theory on the Lattice

abstract:
  We present a method to automatically derive the Feynman rules for mesonic
chiral perturbation theory with a lattice regulator. The Feynman rules can be
output both in a human-readable format and in a form suitable for an automated
numerical evaluation of lattice Feynman diagrams. The automated method
significantly simplifies working with improved or extended actions. Some
applications to the study of finite-volume effects will be presented.


title:
B0-B0bar mixing in the static approximation from the Schroedinger
  Functional and twisted mass QCD

abstract:
  We discuss the renormalisation properties of parity-odd Delta B=2 operators
with the heavy quark treated in the static approximation. Via twisted mass QCD
(tmQCD), these operators provide the matrix elements relevant for the B0-B0bar
mixing amplitude. The layout of a non-perturbative renormalisation programme
for the operator basis, using Schroedinger Functional techniques, is described.
Finally, we report our results for a one-loop perturbative study of various
renormalisation schemes with Wilson-type lattice regularisations, which allows,
in particular, to compute the NLO anomalous dimensions of the operators in the
SF schemes of interest.


title: Observations on discretization errors in twisted-mass lattice QCD

abstract:
  I make a number of observations concerning discretization errors in
twisted-mass lattice QCD that can be deduced by applying chiral perturbation
theory including lattice artifacts. (1) The line along which the PCAC quark
mass vanishes in the twisted mass-twisted mass plane makes an angle to the
untwisted mass axis which is a direct measure of O(a) terms in the chiral
Lagrangian, and is found numerically to be large; (2) Numerical results for
pionic quantities in the mass plane show the qualitative properties predicted
by chiral perturbation theory, in particular an asymmetry in slopes between
positive and negative untwisted quark masses; (3) By extending the description
of the ``Aoki regime'' (where m_q is of size a^2 Lambda_QCD^3) to
next-to-leading order in chiral perturbation theory I show how the phase
transition lines and lines of maximal twist (using different definitions)
extend into this region, and give predictions for the functional form of pionic
quantities; (4) I argue that the recent claim that lattice artifacts at maximal
twist have apparent infrared singularities in the chiral limit results from
expanding about the incorrect vacuum state. Shifting to the correct vacuum (as
can be done using chiral perturbation theory) the apparent singularities are
summed into non-singular, and furthermore predicted, forms. I further argue
that there is no breakdown in the Symanzik expansion in powers of lattice
spacing, and no barrier to simulating at maximal twist in the Aoki regime.


title: The chiral transition of N_f=2 QCD with fundamental and adjoint fermions

abstract:
  We study QCD with two staggered Dirac fermions both in the fundamental (QCD)
and the adjoint representation (aQCD) near the chiral transition. The aim is to
find the universality class of the chiral transition and to verify Goldstone
effects below the transition. We investigate aQCD, because in that theory the
deconfinement and the chiral transitions occur at different temperatures
T_d<T_c. Here, we show that the scaling behaviour of the chiral condensate in
the vicinity of \beta_c is in full agreeement with that of the 3d O(2)
universality class. In the region T_d<T<T_c we confirm the quark mass
dependence of the chiral condensate which is expected due to the existence of
Goldstone modes like in 3d O(N) spin models. For fundamental QCD we use the
p4-action. Here, we find Goldstone effects below T_c like in aQCD and the 3d
O(N) spin models, however no O(2)/O(4) scaling near the chiral transition
point. The result for QCD may be a consequence of the coincidence of the
deconfinement transition with the chiral transition.


title:
Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model
  Embedding

abstract:
  We investigate SU(2) gauge fields topology using new approach, which exploits
the well known connection between SU(2) gauge theory and quaternionic
projective sigma-models and allows to formulate the topological charge density
entirely in terms of sigma-model fields. The method is studied in details and
for thermalized vacuum configurations is shown to be compatible with
overlap-based definition. We confirm that the topological charge is distributed
in localized four dimensional regions which, however, are not compatible with
instantons. Topological density bulk distribution is investigated at different
lattice spacings and is shown to possess some universal properties.


title:
Additive and multiplicative renormalization of topological charge with
  improved gluon/fermion actions: A test case for 3-loop vacuum calculations,
  using overlap or clover fermions

abstract:
  We calculate perturbative renormalization properties of the topological
charge, using the standard lattice discretization given by a product of twisted
plaquettes. We use the overlap and clover action for fermions, and the Symanzik
improved gluon action for 4- and 6-link loops.
  We compute the multiplicative renormalization of the topological charge
density to one loop; this involves only the gluon part of the action. The power
divergent additive renormalization of the topological susceptibility is
calculated to 3 loops.
  Our work serves also as a test case of the techniques and limitations of
lattice perturbation theory, it being the first 3-loop computation in the
literature involving overlap fermions.


title: An Algorithmic Approach to Quantum Field Theory

abstract:
  The lattice formulation provides a way to regularize, define and compute the
Path Integral in a Quantum Field Theory. In this paper we review the
theoretical foundations and the most basic algorithms required to implement a
typical lattice computation, including the Metropolis, the Gibbs sampling, the
Minimal Residual, and the Stabilized Biconjugate inverters. The main emphasis
is on gauge theories with fermions such as QCD. We also provide examples of
typical results from lattice QCD computations for quantities of
phenomenological interest.


title: Phases of planar QCD on the torus

abstract:
  At infinite N, continuum Euclidean SU(N) gauge theory defined on a
symmetrical four torus has a rich phase structure with phases where the finite
volume system behaves as if it had infinite extent in some or all of the
directions. In addition, fermions are automatically quenched, so planar QCD
should be cheaper to solve numerically that full QCD. Large N is a relatively
unexplored and worthwhile direction of research in lattice field theory.


title:
Topological charge renormalization: A test case for 3-loop vacuum
  calculations using overlap fermions and Symanzik improved gluons

abstract:
  We calculate perturbative renormalization properties of the topological
charge, using the standard lattice discretization given by a product of twisted
plaquettes. We use the overlap and clover action for fermions, and the Symanzik
improved gluon action for 4- and 6-link loops.
  We compute the multiplicative renormalization of the topological charge
density to one loop; this involves only the gluon part of the action. The power
divergent additive renormalization of the topological susceptibility is
calculated to 3 loops.


title:
Hadronic light-by-light scattering contribution to the muon g-2 from
  lattice QCD : Methodology

abstract:
  The hadronic light-by-light scattering contribution to the muon g-2 is the
most troublesome component of its theoretical prediction; (1) it cannot be
determined from the other measurable quantities, (2) the dimensional argument
and the estimation based on hadronic models imply that the magnitude of this
contribution may be comparable to the discrepancy between the standard model
prediction and the experimental value. The direct approach to evaluate the
hadronic light-by-light scattering contribution requires the evaluation of the
correlation function of {\it four} hadronic electromagnetic currents, and the
summation of it over two independent four-momenta of off-shell photons, which
is far from the reach of direct lattice simulation. Here we propose an
alternative method using combined (QCD + QED) lattice simulations to evaluate
the hadronic light-by-light scattering contribution.


title:
Bianchi Identities and Degeneracy of Chromomagnetic Fields in SU(2)
  Gluodynamics

abstract:
  We investigate the non-Abelian Bianchi identities in pure SU(2) lattice
Yang-Mills theory in three and four dimensions. The non-Abelian Stokes theorem
proposed recently allows to formulate the Bianchi identities in terms of local
physical fluxes. Then the violation of Bianchi identities becomes a well
defined concept ultimately related to chromomagnetic fields degeneracy points.
We present numerical evidences that in D=4 the suppression of the Bianchi
identities violation destroys confinement while the removal of the degeneracy
points drives the theory to the topologically non-trivial sector.


title:
Finite-temperature chiral transition in QCD with quarks in the
  fundamental and adjoint representation

abstract:
  We study the nature of the finite-temperature chiral transition in QCD with
N_f light quarks in the fundamental and adjoint representation. Universality
and renormalization-group (RG) arguments show that the possibility of having a
continuous transition is related to the existence of a stable fixed point (FP)
in the RG flow of a 3D Landau-Ginzburg-Wilson Phi^4 theory with the same chiral
symmetry-breaking pattern. The RG flow of these theories is studied by
field-theoretical approaches, computing and analyzing high-order perturbative
series, up to six loops. According to this RG analysis, the transition in QCD
can be continuous only for N_f=2. In this case it belongs to the 3D O(4)
universality class. We also find a stable FP corresponding to a 3D universality
class with symmetry breaking U(2)_L x U(2)_R -> U(2)_V, which implies that the
transition can be continuous also if the axial-anomaly effects are suppressed
at Tc. In the case of quarks in the adjoint representation, we can have a
continuous transition for N_f=1,2. For N_f=1 it belongs to the O(3)
universality class. For N_f=2 it belongs to a new 3D universality class
characterized by the symmetry breaking SU(4)->SO(4).


title: Large N

abstract:
  Some mysterious features of the strong interactions become easily understood
if our usual QCD with N=3 is `close to' SU(oo) and if the latter theory is
confining. N=oo theories are theoretically simpler; in particular there has
been much progress in constructing weak-coupling duals in string theory. In
this poster I will describe some of the things that recent lattice calculations
tell us about the large-N limit of SU(N) gauge theories in 3+1 dimensions. The
focus is on confinement, how close SU(oo) is to SU(3), new stable strings at
larger N, the Pomeron, deconfinement, topology, 't Hooft string tensions. I
also allude to other topics, such as the high-T pressure deficit, chiral
physics and the phases of the theory.


title: Laplacian modes probing gauge fields

abstract:
  We show that low-lying eigenmodes of the Laplace operator are suitable to
represent properties of the underlying SU(2) lattice configurations. We study
this for the case of finite temperature background fields, yet in the
confinement phase. For calorons as classical solutions put on the lattice, the
lowest mode localizes one of the constituent monopoles by a maximum and the
other one by a minimum, respectively. We introduce adjustable phase boundary
conditions in the time direction, under which the role of the monopoles in the
mode localization is interchanged. Similar hopping phenomena are observed for
thermalized configurations. We also investigate periodic and antiperiodic modes
of the adjoint Laplacian for comparison.
  In the second part we introduce a new Fourier-like low-pass filter method. It
provides link variables by truncating a sum involving the Laplacian eigenmodes.
The filter not only reproduces classical structures, but also preserves the
confining potential for thermalized ensembles. We give a first characterization
of the structures emerging from this procedure.


title:
String tensions and deconfinement transition in the SU(4) center vortex
  model

abstract:
  A center vortex model for the infrared sector of SU(4) Yang-Mills theory is
constructed such as to reproduce both the ratio between the zero-temperature
quark and diquark string tensions known from lattice Yang-Mills theory, as well
as the properties of the deconfinement transition. On this basis, the
temperature dependence of the spatial quark and diquark string tensions is
predicted. Though still phenomenologically viable, details of the construction
of the SU(4) center vortex model corroborate previous arguments that modeling
infrared Yang-Mills dynamics purely in terms of vortex world-surface
characteristics may become less appropriate as the number of colors is
increased.


title: Lattice and renormalons in heavy quark physics

abstract:
  Perturbative expansions of QCD observables in powers of $\alpha_s$ are
believed to be asymptotic and non-Borel summable due to the existence of
singularities in the Borel plane (renormalons). This fact is connected with the
factorization of scales (which is inherent to QCD and asymptotic freedom) and
jeopardizes the convergence of the perturbative expansion and the accurate
determination of power-suppressed corrections. This problem is more acute for
physical systems composed by one or more heavy quarks. In lattice regulations,
it reflects on the appearance of power-like divergences in the inverse of the
lattice spacing for a series of quantities ($\bar \Lambda$, gluelump masses,
the singlet and hybrid potentials, ...) making that the continuum limit can not
be reached for them. Nevertheless, all these problems are solved within the
framework of effective field theories with renormalon substraction. This allows
us to obtain convergent perturbative series and to unambiguously define power
corrections. In particular, one can connect with lattice results. Remarkably
enough the dependence on the lattice spacing can be predicted by perturbation
theory. This framework has been applied to the prediction of the gluelump
masses and the singlet and octet (hybrid) potentials at short distances, as
well as to their comparison with lattice simulations. Overall, very good
agreement with data is obtained.


title: Hadronic decays

abstract:
  Hadronic decays and transitions are a key ingredient of hadronic physics. I
discuss how hadronic decays can be explored in lattice gauge theory and review
studies undertaken. I also discuss the impact of decays on masses and how
lattice studies can explore the nature of a hadronic state: namely whether it
is a molecular or quark-antiquark state. A brief discussion of lattice
exploration of pentaquark states is presented.


title:
Study of the systematic errors in the calculation of renormalization
  constants of the topological susceptibility on the lattice

abstract:
  We present a study of the systematic effects in the nonperturbative
evaluation of the renormalization constants which appear in the
field-theoretical determination of the topological susceptibility in pure
Yang-Mills theory. The study is performed by computing the renormalization
constants on configurations that have been calibrated by use of the
Ginsparg-Wilson formalism and by cooling.


title: Interaction studies of a heavy-light meson-baryon system

abstract:
  We study time correlation functions of operators representing heavy-light
K-Lambda like systems at various relative distances r. The heavy quarks, one in
each hadron, are treated as static. An anisotropic and asymmetric lattice is
used with Wilson fermions. Our goal is to extract an adiabatic potential and
thus learn about the physics of the five-quark system viewed as an hadronic
molecule.


title: Theoretical issues with staggered fermion simulations

abstract:
  The legality of the "rooting trick" in dynamical staggered fermion
simulations is discussed, i.e. whether the theory with the Boltzmann weight
$\det^{1/4}(D_\mathrm{st})$ yields the right continuum limit. Since the problem
is unsolved, pieces of evidence in favor and against are collected and
examined.


title:
Light hadron and diquark spectroscopy in quenched QCD with overlap
  quarks on a large lattice

abstract:
  A simulation of quenched QCD with the overlap Dirac operator has been
completed using 100 Wilson gauge configurations at beta = 6 on an 18^3 x 64
lattice and at beta = 5.85 on a 14^3 x 48 lattice, both in Landau gauge. We
present results for light meson and baryon masses, meson final state "wave
functions," and other observables, as well as some details on the numerical
techniques that were used. Our results indicate that scaling violations, if
any, are small. We also present an analysis of diquark correlations using the
quark propagators generated in our simulation.


title: Hybrid Exotic Meson Decay Width

abstract:
  We present results of a decay width calculation for a hybrid exotic meson(h,
JPC=1-+) in the decay channel h to pi+a1. This calculation uses quenched
lattice QCD and Luescher's finite box method. Operators for the h and pi+a1
states are used in a correlation matrix which was expanded by varying the
smearing and fuzzing levels at source and sink points. Scattering phase shifts
for a discrete set of relative pi+a1 momenta are determined using eigenvalues
of the correlation matrix and formulae derived by Luescher. The phase shift
data is very sparse, but fits to a Breit-Wigner model are made, resulting in a
decay width of about 80 MeV.


title: Quark mass dependence of baryon properties

abstract:
  I discuss the quark mass dependence of various baryon properties derived from
chiral perturbation theory. Such representations can eventually be used as
chiral extrapolation functions when lattice data at sufficiently small quark
masses become available. The quark mass dependence is encoded in loop and
contact term contributions, the latter given in terms of low-energy constants.
I stress the importance of utilizing phenomenological input to constrain a
certain class of low-energy constants and discuss the ensuing theoretical
uncertainty for various baryon observables, like the nucleon and the baryon
octet masses, the nucleon isovector anomalous magnetic moment and the
axial-vector coupling of the nucleon. I stress the role of resonance decoupling
and present first results for the delta mass based on an effective field theory
in which the nucleon-delta mass splitting is counted as a small parameter. I
also discuss briefly the pion mass dependence of the nuclear force as derived
from chiral nuclear effective field theory.


title: Pion form factor with chirally improved fermions

abstract:
  We present results for Monte Carlo calculations of the electromagnetic vector
and scalar form factors of the pion in a quenched simulation. We work at a
lattice spacing of 0.15 fm and use two lattice volumes up to a spatial size of
2.4 fm. The pion form factors in the space-like region are determined for pion
masses down to 340 MeV.


title: Infrared exponents of Yang-Mills theory

abstract:
  In this talk I summarise recent results on the infrared exponents of
SU($N_c$)-Yang-Mills theory. I discuss a self-consistent power law solution for
the Dyson-Schwinger equations for general 1PI-Greens functions in the infrared.
The corresponding running coupling has a fixed point at zero momentum, which
turns out to be universal and gauge invariant within a class of transverse
gauges. When calculated on a torus the infrared exponents of the ghost and
gluon propagators differ from the corresponding continuum solutions. They
agree, however, well with results from lattice calculations.


title: Three Dimensional N=2 Supersymmetry on the Lattice

abstract:
  We show how 3-dimensional, N=2 supersymmetric theories, including super QCD
with matter fields, can be put on the lattice with existing techniques, in a
way which will recover supersymmetry in the small lattice spacing limit.
Residual supersymmetry breaking effects are suppressed in the small lattice
spacing limit by at least one power of the lattice spacing a.