291 research outputs found
Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory
The ghost and gluon propagator and the ghost-gluon and three-gluon vertex of
two-dimensional SU(2) Yang-Mills theory in (minimal) Landau gauge are studied
using lattice gauge theory. It is found that the results are qualitatively
similar to the ones in three and four dimensions. The propagators and the
Faddeev-Popov operator behave as expected from the Gribov-Zwanziger scenario.
In addition, finite volume effects affecting these Green's functions are
investigated systematically. The critical infrared exponents of the
propagators, as proposed in calculations using stochastic quantization and
Dyson-Schwinger equations, are confirmed quantitatively. For this purpose
lattices of volume up to (42.7 fm)^2 have been used.Comment: 14 pages, 14 figures, 4 tables, references adde
Role of center vortices in chiral symmetry breaking in SU(3) gauge theory
We study the behavior of the AsqTad quark propagator in Landau gauge on SU(3)
Yang-Mills gauge configurations under the removal of center vortices. In SU(2)
gauge theory, center vortices have been observed to generate chiral symmetry
breaking and dominate the infrared behavior of the quark propagator. In
contrast, we report a weak dependence on the vortex content of the gauge
configurations, including the survival of dynamical mass generation on
configurations with vanishing string tension.Comment: 8 pages, 9 figure
Two loop QCD vertices at the symmetric point
We compute the triple gluon, quark-gluon and ghost-gluon vertices of QCD at
the symmetric subtraction point at two loops in the MSbar scheme. In addition
we renormalize each of the three vertices in their respective momentum
subtraction schemes, MOMggg, MOMq and MOMh. The conversion functions of all the
wave functions, coupling constant and gauge parameter renormalization constants
of each of the schemes relative to MSbar are determined analytically. These are
then used to derive the three loop anomalous dimensions of the gluon, quark,
Faddeev-Popov ghost and gauge parameter as well as the beta-function in an
arbitrary linear covariant gauge for each MOM scheme. There is good agreement
of the latter with earlier Landau gauge numerical estimates of Chetyrkin and
Seidensticker.Comment: 36 latex pages, anc directory contains txt file with anomalous
dimensions, beta-functions, coupling constant mappings, conversion functions
and amplitudes in analytic for
More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
Fixing a gauge in the non-perturbative domain of Yang-Mills theory is a
non-trivial problem due to the presence of Gribov copies. In particular, there
are different gauges in the non-perturbative regime which all correspond to the
same definition of a gauge in the perturbative domain. Gauge-dependent
correlation functions may differ in these gauges. Two such gauges are the
minimal and absolute Landau gauge, both corresponding to the perturbative
Landau gauge. These, and their numerical implementation, are described and
presented in detail. Other choices will also be discussed.
This investigation is performed, using numerical lattice gauge theory
calculations, by comparing the propagators of gluons and ghosts for the minimal
Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is
found that the propagators are different in the far infrared and even at energy
scales of the order of half a GeV. In particular, also the finite-volume
effects are modified. This is observed in two and three dimensions. Some
remarks on the four-dimensional case are provided as well.Comment: 23 pages, 16 figures, 6 tables; various changes throughout most of
the paper; extended discussion on different possibilities to define the
Landau gauge and connection to existing scenarios; in v3: Minor changes,
error in eq. (3) & (4) corrected, version to appear in PR
A brief comment on the similarities of the IR solutions for the ghost propagator DSE in Landau and Coulomb gauges
This brief note is devoted to reconcile the conclusions from a recent
analysis of the IR solutions for the ghost propagator Dyson-Schwinger equations
in Coulomb gauge with previous studies in Landau gauge.Comment: 4 pages, 1 figur
The running coupling from the four-gluon vertex in Landau gauge Yang-Mills theory
We consider the running coupling from the four-gluon vertex in Landau gauge,
SU() Yang-Mills theory as given by a combination of dressing functions of
the vertex and the gluon propagator. We determine these functions numerically
from a coupled set of Dyson-Schwinger equations. We reproduce asymptotic
freedom in the ultraviolet momentum region and find a coupling of order one at
mid-momenta. In the infrared we find a nontrivial (i.e. nonzero) fixed point
which is three orders of magnitude smaller than the corresponding fixed point
in the coupling of the ghost-gluon vertex. This result explains why the
Dyson-Schwinger and the functional renormalization group equations for the two
point functions can agree in the infrared, although their structure is quite
different. Our findings also support Zwanziger's notion of an infrared
effective theory driven by the Faddeev-Popov determinant.Comment: 25 pages, 4 figures; v2: minor clarifications added and typos
corrected, version accepted by PR
Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
We present rigorous upper and lower bounds for the zero-momentum gluon
propagator D(0) of Yang-Mills theories in terms of the average value of the
gluon field. This allows us to perform a controlled extrapolation of lattice
data to infinite volume, showing that the infrared limit of the Landau-gauge
gluon propagator in SU(2) gauge theory is finite and nonzero in three and in
four space-time dimensions. In the two-dimensional case we find D(0) = 0, in
agreement with Ref. [1]. We suggest an explanation for these results. We note
that our discussion is general, although we only apply our analysis to pure
gauge theory in Landau gauge. Simulations have been performed on the IBM
supercomputer at the University of Sao Paulo.Comment: 4 pages, 3 figures, 1 tabl
The influence of Gribov copies on the gluon and ghost propagator
The dependence of the gluon and ghost propagator in pure SU(3) gauge theory
on the choice of Gribov copies in Landau gauge is studied. Simulations were
performed on several lattice sizes at =5.8, 6.0 and 6.2. In the infrared
region the ghost propagator turns out to depend on the choice, while the impact
on the gluon propagator is not resolvable. Also the eigenvalue distribution of
the Faddeev-Popov operator is sensitive to Gribov copies.Comment: Talk presented at Quark Confinement and the Hadron Spectrum VI,
Villasimius, Sardinia, Italy, September 21-25, 2004, 3 pages, 2 figure
Goldstone bosons and fermions in QCD
We consider the version of QCD in Euclidean Landau gauge in which the
restriction to the Gribov region is implemented by a local, renormalizable
action. This action depends on the Gribov parameter , with dimensions
of (mass), whose value is fixed in terms of , by the gap
equation, known as the horizon condition, {\p \Gamma \over \p \gamma} = 0,
where is the quantum effective action. The restriction to the Gribov
region suppresses gluons in the infrared, which nicely explains why gluons are
not in the physical spectrum, but this only makes makes more mysterious the
origin of the long-range force between quarks. In the present article we
exhibit the symmetries of , and show that the solution to the gap
equation, which defines the classical vacuum, spontaneously breaks some of the
symmetries . This implies the existence of massless Goldstone bosons
and fermions that do not appear in the physical spectrum. Some of the Goldstone
bosons may be exchanged between quarks, and are candidates for a long-range
confining force. As an exact result we also find that in the infrared limit the
gluon propagator vanishes like .Comment: 22 pages, typos corrected, improved comparison with lattice dat
Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
We present recent results for the Landau-gauge gluon and ghost propagators in
SU(3) lattice gluodynamics obtained on a sequence of lattices with linear
extension ranging from L=64 to L=96 at , thus reaching "deep
infrared" momenta down to 75 MeV. Our gauge-fixing procedure essentially uses a
simulated annealing technique which allows us to reach gauge-functional values
closer to the global maxima than standard approaches do. Our results are
consistent with the so-called decoupling solutions found for Dyson-Schwinger
and functional renormalization group equations.Comment: 6 pages, 5 figures. References added, minor changes to match
published versio
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