451 research outputs found
't Hooft-Polyakov monopoles in lattice SU(N)+adjoint Higgs theory
We investigate twisted C-periodic boundary conditions in SU(N) gauge field
theory with an adjoint Higgs field. We show that with a suitable twist for even
N one can impose a non-zero magnetic charge relative to residual U(1) gauge
groups in the broken phase, thereby creating a 't Hooft-Polyakov magnetic
monopole. This makes it possible to use lattice Monte-Carlo simulations to
study the properties of these monopoles in the quantum theory.Comment: 15 pages, 6 figure
Lattice Landau gauge via Stereographic Projection
The complete cancellation of Gribov copies and the Neuberger 0/0 problem of
lattice BRST can be avoided in modified lattice Landau gauge. In compact U(1),
where the problem is a lattice artifact, there remain to be Gribov copies but
their number is exponentially reduced. Moreover, there is no cancellation of
copies there as the sign of the Faddeev-Popov determinant is positive. Applied
to the maximal Abelian subgroup this avoids the perfect cancellation amongst
the remaining Gribov copies for SU(N) also. In addition, based on a definition
of gauge fields on the lattice as stereographically-projected link variables,
it provides a framework for gauge fixed Monte-Carlo simulations. This will
include all Gribov copies in the spirit of BRST. Their average is not zero, as
demonstrated explicitly in simple models. This might resolve present
discrepancies between gauge-fixed lattice and continuum studies of QCD Green's
functions.Comment: 5 pages, talk presented at the 8th Conference Quark Confinement and
the Hadron Spectrum, September 1-6, 2008, Mainz, German
Modified Lattice Landau Gauge
We propose a modified lattice Landau gauge based on stereographically
projecting the link variables on the circle S^1 -> R for compact U(1) or the
3-sphere S^3 -> R^3 for SU(2) before imposing the Landau gauge condition. This
can reduce the number of Gribov copies exponentially and solves the Gribov
problem in compact U(1) where it is a lattice artifact. Applied to the maximal
Abelian subgroup this might be just enough to avoid the perfect cancellation
amongst the Gribov copies in a lattice BRST formulation for SU(N), and thus to
avoid the Neuberger 0/0 problem. The continuum limit of the Landau gauge
remains unchanged.Comment: 7 pages, 2 figures, for the proceedings of the XXV International
Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg,
German
Numerical Study of the Gluon Propagator in Lattice Landau Gauge: the Three-Dimensional Case
We study the infrared behavior of the gluon propagator in lattice Landau
gauge, for pure SU(2) lattice gauge theory in a three-dimensional lattice.
Simulations are done for nine different values of the coupling , from
(strong coupling) to (in the weak-coupling region).
In the limit of large lattice volumes, we observe in all cases a gluon
propagator decreasing as the momentum goes to zero.Comment: LATTICE98(confine
What the Infrared Behavior of QCD Green Functions can tell us about Confinement in the Covariant Gauge
We review aspects of confinement in the covariant and local description of
QCD and discuss to what extend our present knowledge of the infrared behavior
of QCD Green functions can support this description. In particular, we
emphasize: the positivity violations of transverse gluon and quark states, the
Kugo-Ojima confinement criterion, and the conditions necessary to avoid the
decomposition property for colored clusters. We summarize how these issues
relate to the infrared behavior of the propagators in Landau gauge QCD as
extracted from solutions to truncated Dyson-Schwinger equations and lattice
simulations.Comment: 10 Pages, 7 Figures, LaTeX2.09, invited talk presented by L. v.
Smekal at ``Quark Confinement and the Hadron Spectrum IV'', Vienna, July 4-8,
200
The Infrared Behavior of QCD Propagators in Landau Gauge
Some features of the solutions to the truncated Dyson-Schwinger
equations(DSEs) for the propagators of QCD in Landau gauge are summarized. In
particular, the Kugo-Ojima confinement criterion is realized, and positivity of
transverse gluons is manifestly violated in these solutions. In Landau gauge,
the gluon-ghost vertex function offers a convenient possibility to define a
nonperturbative running coupling. The infrared fixed point obtained from this
coupling which determines the 2-point interactions of color-octet quark
currents implies the existence of unphysical massless states which are
necessary to escape the cluster decomposition of colored clusters. The gluon
and ghost propagators, and the nonperturbative running coupling, are compared
to recent lattice simulations. A significant deviation of the running coupling
from the infrared behavior extracted in simulations of 3-point functions is
attributed to an inconsistency of asymmetric subtraction schemes due to a
consequence of the Kugo-Ojima criterion: infrared enhanced ghosts.Comment: 4 pages, no figures, talk given by R.A. at ``Quark Nuclear Physics
2000'', Adelaide, Feb. 21 - 25, 200
- …