223 research outputs found
Singular gauge potentials and the gluon condensate at zero temperature
We consider a new cooling procedure which separates gluon degrees of freedom
from singular center vortices in SU(2) LGT in a gauge invariant way. Restricted
by a cooling scale fixing the residual SO(3) gluonic action
relative to the string tension, the procedure is RG invariant. In the limit
a pure Z(2) vortex texture is left. This {\it minimal} vortex
content does not contribute to the string tension. It reproduces, however, the
lowest glueball states. With an action density scaling like with ,
it defines a finite contribution to the action density at T=0 in the continuum
limit. We propose to interpret this a mass dimension 4 condensate related to
the gluon condensate. Similarly, this vortex texture is revealed in the Landau
gauge.Comment: 3 pages, 4 figures, Contribution to ''Lattice 2001'' (confinement) to
appear in the Proceedings (Nucl. Phys. B Proc. Suppl.
Gauge potential singularities and the gluon condensate at finite temperatures
The continuum limit of SU(2) lattice gauge theory is carefully investigated
at zero and at finite temperatures. It is found that the continuum gauge field
has singularities originating from center degrees of freedom being discovered
in Landau gauge. Our numerical results show that the density of these
singularities properly extrapolates to a non-vanishing continuum limit. The
action density of the non-trivial Z_2 links is tentatively identified with the
gluon condensate. We find for temperatures larger than the deconfinement
temperature that the thermal fluctuations of the embedded Z_2 gauge theory
result in an increase of the gluon condensate with increasing temperature.Comment: 3 pages, 2 figures, talk presented by K. Langfeld at the 19th
International Symposium on Lattice Field Theory (LATTICE2001), Berlin,
19.-24.8.2001, to appear in the proceeding
Vortex critical behavior at the de-confinement phase transition
The de-confinement phase transition in SU(2) Yang-Mills theory is revisited
in the vortex picture. Defining the world sheets of the confining vortices by
maximal center projection, the percolation properties of the vortex lines in
the hypercube consisting of the time axis and two spatial axis are studied.
Using the percolation cumulant, the temperature for the percolation transition
is seen to be in good agreement with the critical temperature of the thermal
transition. The finite size scaling function for the cumulant is obtained. The
critical index of the finite size scaling function is consistent with the index
of the 3D Ising model.Comment: 4 pages, 4 PS figures, using revtex4, paragraph and refs added, typo
correcte
Center Vortices and the Gribov Horizon
We show how the infinite color-Coulomb energy of color-charged states is
related to enhanced density of near-zero modes of the Faddeev-Popov operator,
and calculate this density numerically for both pure Yang-Mills and gauge-Higgs
systems at zero temperature, and for pure gauge theory in the deconfined phase.
We find that the enhancement of the eigenvalue density is tied to the presence
of percolating center vortex configurations, and that this property disappears
when center vortices are either removed from the lattice configurations, or
cease to percolate. We further demonstrate that thin center vortices have a
special geometrical status in gauge-field configuration space: Thin vortices
are located at conical or wedge singularities on the Gribov horizon. We show
that the Gribov region is itself a convex manifold in lattice configuration
space. The Coulomb gauge condition also has a special status; it is shown to be
an attractive fixed point of a more general gauge condition, interpolating
between the Coulomb and Landau gauges.Comment: 19 pages, 17 EPS figures, RevTeX4; v2: added references, corrected
caption of fig. 11; v3: new data for higher couplings, clarifications on
color-Coulomb potential in deconfined phase, version to appear in JHE
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