5 research outputs found
Coulomb Energy, Remnant Symmetry, and the Phases of Non-Abelian Gauge Theories
We show that the confining property of the one-gluon propagator, in Coulomb
gauge, is linked to the unbroken realization of a remnant gauge symmetry which
exists in this gauge. An order parameter for the remnant gauge symmetry is
introduced, and its behavior is investigated in a variety of models via
numerical simulations. We find that the color-Coulomb potential, associated
with the gluon propagator, grows linearly with distance both in the confined
and - surprisingly - in the high-temperature deconfined phase of pure
Yang-Mills theory. We also find a remnant symmetry-breaking transition in SU(2)
gauge-Higgs theory which completely isolates the Higgs from the
(pseudo)confinement region of the phase diagram. This transition exists despite
the absence, pointed out long ago by Fradkin and Shenker, of a genuine
thermodynamic phase transition separating the two regions.Comment: 18 pages, 19 figures, revtex
Numerical Study of the Ghost-Gluon Vertex in Landau gauge
We present a numerical study of the ghost-gluon vertex and of the
corresponding renormalization function \widetilde{Z}_1(p^2) in minimal Landau
gauge for SU(2) lattice gauge theory. Data were obtained for three different
lattice volumes (V = 4^4, 8^4, 16^4) and for three lattice couplings \beta =
2.2, 2.3, 2.4. Gribov-copy effects have been analyzed using the so-called
smeared gauge fixing. We also consider two different sets of momenta (orbits)
in order to check for possible effects due to the breaking of rotational
symmetry. The vertex has been evaluated at the asymmetric point (0;p,-p) in
momentum-subtraction scheme. We find that \widetilde{Z}_1(p^2) is approximately
constant and equal to 1, at least for momenta p > ~ 1 GeV. This constitutes a
nonperturbative verification of the so-called nonrenormalization of the Landau
ghost-gluon vertex. Finally, we use our data to evaluate the running coupling
constant \alpha_s(p^2).Comment: 19 pages, 6 figures, 9 tables, using axodraw.sty; minor modifications
in the abstract, introduction and conclusion
Infrared exponents and the strong-coupling limit in lattice Landau gauge
We study the gluon and ghost propagators of lattice Landau gauge in the
strong-coupling limit beta=0 in pure SU(2) lattice gauge theory to find
evidence of the conformal infrared behavior of these propagators as predicted
by a variety of functional continuum methods for asymptotically small momenta
. In the strong-coupling limit, this same
behavior is obtained for the larger values of a^2q^2 (in units of the lattice
spacing a), where it is otherwise swamped by the gauge field dynamics.
Deviations for a^2q^2 < 1 are well parameterized by a transverse gluon mass
. Perhaps unexpectedly, these deviations are thus no finite-volume
effect but persist in the infinite-volume limit. They furthermore depend on the
definition of gauge fields on the lattice, while the asymptotic conformal
behavior does not. We also comment on a misinterpretation of our results by
Cucchieri and Mendes in Phys. Rev. D81 (2010) 016005.Comment: 17 pages, 12 figures. Revised version (mainly sections I and II);
references and comments on subsequent work on the subject added
The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator in the Landau gauge
We prove that the nonlocal gauge invariant mass dimension two operator
can be consistently added to the
Gribov-Zwanziger action, which implements the restriction of the path
integral's domain of integration to the first Gribov region when the Landau
gauge is considered. We identify a local polynomial action and prove the
renormalizability to all orders of perturbation theory by employing the
algebraic renormalization formalism. Furthermore, we also pay attention to the
breaking of the BRST invariance, and to the consequences that this has for the
Slavnov-Taylor identity.Comment: 30 page
Strong-coupling study of the Gribov ambiguity in lattice Landau gauge
We study the strong-coupling limit beta=0 of lattice SU(2) Landau gauge
Yang-Mills theory. In this limit the lattice spacing is infinite, and thus all
momenta in physical units are infinitesimally small. Hence, the infrared
behavior can be assessed at sufficiently large lattice momenta. Our results
show that at the lattice volumes used here, the Gribov ambiguity has an
enormous effect on the ghost propagator in all dimensions. This underlines the
severity of the Gribov problem and calls for refined studies also at finite
beta. In turn, the gluon propagator only mildly depends on the Gribov
ambiguity.Comment: 14 pages, 22 figures; minor changes, matches version to appear in
Eur. Phys. J.