74 research outputs found
Infinite N phase transitions in continuum Wilson loop operators
We define smoothed Wilson loop operators on a four dimensional lattice and
check numerically that they have a finite and nontrivial continuum limit. The
continuum operators maintain their character as unitary matrices and undergo a
phase transition at infinite N reflected by the eigenvalue distribution closing
a gap in its spectrum when the defining smooth loop is dilated from a small
size to a large one. If this large N phase transition belongs to a solvable
universality class one might be able to calculate analytically the string
tension in terms of the perturbative Lambda-parameter. This would be achieved
by matching instanton results for small loops to the relevant large-N-universal
function which, in turn, would be matched for large loops to an effective
string theory. Similarities between our findings and known analytical results
in two dimensional space-time indicate that the phase transitions we found only
affect the eigenvalue distribution, but the traces of finite powers of the
Wilson loop operators stay smooth under scaling.Comment: 31 pages, 9 figures, typos and references corrected, minor
clarifications adde
Hybrid Monte Carlo with Fat Link Fermion Actions
The use of APE smearing or other blocking techniques in lattice fermion
actions can provide many advantages. There are many variants of these fat link
actions in lattice QCD currently, such as FLIC fermions. The FLIC fermion
formalism makes use of the APE blocking technique in combination with a
projection of the blocked links back into the special unitary group. This
reunitarisation is often performed using an iterative maximisation of a gauge
invariant measure. This technique is not differentiable with respect to the
gauge field and thus prevents the use of standard Hybrid Monte Carlo simulation
algorithms. The use of an alternative projection technique circumvents this
difficulty and allows the simulation of dynamical fat link fermions with
standard HMC and its variants. The necessary equations of motion for FLIC
fermions are derived, and some initial simulation results are presented. The
technique is more general however, and is straightforwardly applicable to other
smearing techniques or fat link actions
Novel fat-link fermion actions
The hadron mass spectrum is calculated in lattice QCD using a novel fat-link
clover fermion action in which only the irrelevant operators of the fermion
action are constructed using smeared links. The simulations are performed on a
16^3 X 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with
n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat Link
Irrelevant Clover (FLIC) action provides scaling which is superior to
mean-field improvement, and offers advantages over nonperturbative O(a)
improvement.Comment: 5 pages, 2 figures, talk given by J.Zanotti at LHP 2001 workshop,
Cairns, Australi
A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
We construct super Yang-Mills theories with extended supersymmetry on
hypercubic lattices of various dimensions keeping one or two supercharges
exactly. Gauge fields are represented by ordinary unitary link variables, and
the exact supercharges are nilpotent up to gauge transformations. Among the
models, we show that the desired continuum theories are obtained without any
fine tuning of parameters for the cases in two-dimensions.Comment: 29 pages, 1 figure, LaTeX, (v2) problem on degenerate vacua
discussed, renormalization arguments modified, (v3) explanations and
references added, published version in JHE
Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
We show that the Ginsparg-Wilson (GW) relation can play an important role to
define chiral structures in {\it finite} noncommutative geometries. Employing
GW relation, we can prove the index theorem and construct topological
invariants even if the system has only finite degrees of freedom. As an
example, we consider a gauge theory on a fuzzy two-sphere and give an explicit
construction of a noncommutative analog of the GW relation, chirality operator
and the index theorem. The topological invariant is shown to coincide with the
1st Chern class in the commutative limit.Comment: Revtex4 file, 5 pages, references added, typo corrected, the final
version to appear in Phys.Rev.
Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
While sign-coherent 4-dimensional structures cannot dominate topological
charge fluctuations in the QCD vacuum at all scales due to reflection
positivity, it is possible that enhanced coherence exists over extended
space-time regions of lower dimension. Using the overlap Dirac operator to
calculate topological charge density, we present evidence for such structure in
pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium
configuration is dominated by two oppositely-charged sign-coherent connected
structures (``sheets'') covering about 80% of space-time. Each sheet is built
from elementary 3-d cubes connected through 2-d faces, and approximates a
low-dimensional curved manifold (or possibly a fractal structure) embedded in
the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18%
of the most intense space-time points organized into a global long-range
structure, involving connected parts spreading over maximal possible distances.
We find that the skeleton is locally 1-dimensional and propose that its
geometrical properties might be relevant for understanding the possible role of
topological charge fluctuations in the physics of chiral symmetry breaking.Comment: 4 pages RevTeX, 4 figures; v2: 6 pages, 5 figures, more explanations
provided, figure and references added, published versio
Improved results for N=(2,2) super Yang-Mills theory using supersymmetric discrete light-cone quantization
We consider the (1+1)-dimensional super Yang--Mills theory
which is obtained by dimensionally reducing super Yang--Mills
theory in four dimension to two dimensions. We do our calculations in the
large- approximation using Supersymmetric Discrete Light Cone
Quantization. The objective is to calculate quantities that might be
investigated by researchers using other numerical methods. We present a
precision study of the low-mass spectrum and the stress-energy correlator
. We find that the mass gap of this theory closes as the
numerical resolution goes to infinity and that the correlator in the
intermediate region behaves like .Comment: 18 pages, 8 figure
Kaon B Parameter in Quenched QCD
I calculate the kaon B-parameter with a lattice simulation in quenched
approximation. The lattice simulation uses an action possessing exact lattice
chiral symmetry, an overlap action. Computations are performed at two lattice
spacings, about 0.13 and 0.09 fm (parameterized by Wilson gauge action
couplings beta=5.9 and 6.1) with nearly the same physical volumes and quark
masses. I describe particular potential difficulties which arise due to the use
of such a lattice action in finite volume. My results are consistent with other
recent lattice determinations using domain-wall fermions.Comment: 23 pages, Revtex, 16 postscript figure
Improved chiral properties of FLIC fermions
Copyright © 2005 Elsevier B.V. All rights reserved.The chiral properties of the fat-link irrelevant clover (FLIC) fermion action are examined. The improved chiral properties of fermion actions incorporating smoothed links are realised in the FLIC action where only the irrelevant operators of the fermion action are constructed with smoothed links. In particular, the histogram of the additive mass renormalisation encountered in chiral-symmetry breaking Wilson-type fermion actions is seen to narrow upon introducing fat links in the irrelevant operators. The exceptional configuration problem of quenched QCD is reduced, enabling access to the light quark mass regime of mÏ/mÏâ1/3. In particular, quenched chiral nonanalytic behaviour is revealed in the light quark mass dependence of the Î-baryon mass. FLIC fermions offer a promising approach to revealing the properties of full QCD at light quark masses. © 2005 Elsevier B.V. All rights reserved.S. Boinepalli, W. Kamleh, D.B. Leinweber, A.G. Williams and J.M. Zanottihttp://www.elsevier.com/wps/find/journaldescription.cws_home/505706/description#descriptio
Scaling behavior of the overlap quark propagator in Landau gauge
The properties of the momentum space quark propagator in Landau gauge are
examined for the overlap quark action in quenched lattice QCD. Numerical
calculations are done on three lattices with different lattice spacings and
similar physical volumes to explore the approach of the quark propagator toward
the continuum limit. We have calculated the nonperturbative momentum-dependent
wave function renormalization function Z(p) and the nonperturbative mass
function M(p) for a variety of bare quark masses and perform an extrapolation
to the chiral limit. We find the behavior of Z(p) and M(p) are in reasonable
agreement between the two finer lattices in the chiral limit, however the data
suggest that an even finer lattice is desirable. The large momentum behavior is
examined to determine the quark condensate.Comment: 9 pages, 5 figures, Revtex 4. Streamlined presentation, additional
data. Final versio
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