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 $L \ge 5$, 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

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

Fresh look on triality

Investigating the $Z_3$ symmetry in Quantum Chromodynamics (QCD) we show that full QCD with a vacuum of vanishing baryonic number does not lead to metastable phases. Rather in QCD with dynamical fermions, the degeneracy of $Z_3$ phases manifests itself in observables without open triality.Comment: 9 pages, 0 figures, latex, IK-TUW-Preprint 930840

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

Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?

We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975). According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants beta^2 > 8 pi. The consequence of this theorem would be the non-existence of the quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model.Comment: 22 pages, Latex, no figures, revised according to the version accepted for publication in Journal of Physics