7,597 research outputs found
Center Vortices at Strong Couplings
A long-range effective action is derived for strong-coupling lattice SU(2)
gauge theory in D=3 dimensions. It is shown that center vortices emerge as
stable saddlepoints of this action.Comment: Lattice 2000 (Topology and Vacuum), 4 page
Asymptotic Scaling, Casimir Scaling, and Center Vortices
We report on two recent developments in the center vortex theory of
confinement: (i) the asymptotic scaling of the vortex density, as measured in
Monte Carlo simulations; and (ii) an explanation of Casimir scaling and the
adjoint string tension, in terms of the center vortex mechanism.Comment: LATTICE98(confine), 3 pages, 3 figure
What are the Confining Field Configurations of Strong-Coupling Lattice Gauge Theory?
Starting from the strong-coupling SU(2) Wilson action in D=3 dimensions, we
derive an effective, semi-local action on a lattice of spacing L times the
spacing of the original lattice. It is shown that beyond the adjoint
color-screening distance, i.e. for , thin center vortices are stable
saddlepoints of the corresponding effective action. Since the entropy of these
stable objects exceeds their energy, center vortices percolate throughout the
lattice, and confine color charge in half-integer representations of the SU(2)
gauge group. This result contradicts the folklore that confinement in
strong-coupling lattice gauge theory, for D>2 dimensions, is simply due to
plaquette disorder, as is the case in D=2 dimensions. It also demonstrates
explicitly how the emergence and stability of center vortices is related to the
existence of color screening by gluon fields.Comment: 17 pages, 5 figures, latex2
Center Projection With and Without Gauge Fixing
We consider projections of SU(2) lattice link variables onto Z(2) center and
U(1) subgroups, with and without gauge-fixing. It is shown that in the absence
of gauge-fixing, and up to an additive constant, the static quark potential
extracted from projected variables agrees exactly with the static quark
potential taken from the full link variables; this is an extension of recent
arguments by Ambjorn and Greensite, and by Ogilvie. Abelian and center
dominance is essentially trivial in this case, and seems of no physical
relevance. The situation changes drastically upon gauge fixing. In the case of
center projection, there are a series of tests one can carry out, to check if
vortices identified in the projected configurations are physical objects. All
these criteria are satisfied in maximal center gauge, and we show here that
they all fail in the absence of gauge fixing. The non-triviality of center
projection is due entirely to the maximal center gauge-fixing, which pumps
information about the location of extended physical objects into local Z(2)
observables.Comment: 18 pages, 6 figures, Latex2
Evidence for a Center Vortex Origin of the Adjoint String Tension
Wilson loops in the adjoint representation are evaluated on cooled lattices
in SU(2) lattice gauge theory. It is found that the string tension of an
adjoint Wilson loop vanishes, if the loop is evaluated in a sub-ensemble of
configurations in which no center vortex links the loop. This result supports
our recent proposal that the adjoint string tension, in the Casimir-scaling
regime, can be attributed to a center vortex mechanism.Comment: 10 pages, 5 figures, Latex2
The Structure of Projected Center Vortices in Lattice Gauge Theory
We investigate the structure of center vortices in maximal center gauge of
SU(2) lattice gauge theory at zero and finite temperature. In center projection
the vortices (called P-vortices) form connected two dimensional surfaces on the
dual four-dimensional lattice. At zero temperature we find, in agreement with
the area law behaviour of Wilson loops, that most of the P-vortex plaquettes
are parts of a single huge vortex. Small P-vortices, and short-range
fluctuations of the large vortex surface, do not contribute to the string
tension. All of the huge vortices detected in several thousand field
configurations turn out to be unorientable. We determine the Euler
characteristic of these surfaces and find that they have a very irregular
structure with many handles. At finite temperature P-vortices exist also in the
deconfined phase. They form cylindric objects which extend in time direction.
After removal of unimportant short range fluctuations they consist only of
space-space plaquettes, which is in accordance with the perimeter law behaviour
of timelike Wilson loops, and the area law behaviour of spatial Wilson loops in
this phase.Comment: 18 pages, LaTeX2e, 16 eps figures included in text; a misprint in the
abstract correcte
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