arXiv subjects
Publications and source records attributed to J. Greensite.
We review arguments for center dominance in center gauges where vortex locations are correctly identified. We introduce an appealing interpretation of the maximal center gauge, discuss problems with Gribov copies, and a cure to the problems through the direct Laplacian center gauge. We study correlations between direct and indirect Laplacian center gauges.
We develop a picture of the QCD string as a chain of constituent gluons, bound by attractive nearest-neighbor forces which may be treated perturbatively. This picture accounts for both Casimir scaling at large N, and the asymptotic center dependence of the static quark potential. We discuss the relevance, to the gluon-chain picture, of recent three-loop results for the static quark potential. A variational framework is presented for computing the minimal energy and wavefunction of a long gluon chain, which enables us to derive both the logarithmic broadening of the QCD flux tube (``roughening''), and the existence of a Luscher -c/R term in the potential.
We introduce a variation of direct maximal center gauge fixing: the "direct Laplacian" center gauge. The new procedure consists of first fixing to the Laplacian adjoint Landau gauge, followed by overrelaxation to the nearby Gribov copy of the direct maximal center gauge. Certain shortcomings of maximal center gauge, associated with Gribov copies, are overcome in the new gauge, in particular center dominance is recovered.
We introduce a variation of direct maximal center gauge fixing: the ``direct Laplacian'' center gauge. The new procedure overcomes certain shortcomings of maximal center gauge, associated with Gribov copies, that were pointed out by Bornyakov et al. in hep-lat/0009035.
We review the equivalence of maximal center gauge fixing to the problem of finding the best fit, to a given lattice gauge field, by a thin vortex configuration. This fit is necessarily worst at the location of P-plaquettes. We then compare the fits achieved in Gribov copies generated by (i) over-relaxation; (ii) over-relaxation after Landau gauge preconditioning; and (iii) simulated annealing. Simulated annealing yields the best fit if all links on the lattice are included, but the situation changes if we consider only the lattice volume exterior to P-plaquettes. In this exterior region, the fit is best for Gribov copies generated by over-relaxation, and worst for Gribov copies generated after Landau gauge preconditioning. The two fitting criteria (including or not including the P-plaquettes) yield string tensions differing by -34% to +20% respectively, relative to the full string tension. Our usual procedure (``quenched minimization'') seems to be a compromise between these criteria, and yields string tensions at an intermediate value close to the full string tension.
We use the finite temperature AdS/CFT approach to demonstrate logarithmic broadening of the confining QCD3 flux tube as a function of quark separation. This behavior indicates that, unlike lattice QCD, there is no roughening transition in the AdS/CFT formulation, which raises the interesting possibility of extrapolating strong coupling results to weak couplings by the use of resummation techniques. In the zero-temperature non-confining limit, we find that this logarithmic broadening of the field strength distribution is absent. Our results are obtained numerically at strong couplings, in the supergravity approximation.
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.
We review lattice evidence showing that center-vortex condensation is a serious candidate for the mechanism of colour confinement in quantum chromodynamics.
We study the dependence of the center-projected string tension on both the lattice size, and the number of gauge copies used for maximal center gauge fixing. We show that a recent finding of Bornyakov, Komarov, Polikarpov, and Veselov (hep-lat/0002017), indicating a substantial breakdown of center dominance in maximal center gauge, is only obtained for rather small lattice volumes, and is not found in numerical simulations on larger lattices. It is shown that center-projected Creutz ratios approach the full asymptotic string tension as lattice size increases, and that the P-vortex density is consistent, at moderately weak couplings, with 2-loop scaling behavior.
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.
Motivations for the center vortex theory of confinement are discussed. In particular, it is noted that the abelian dual Meissner effect, which is the signature of dual superconductivity, cannot adequately describe the confining force at large distance scales. A long-range effective action is derived from strong-coupling lattice gauge theory in D=3 dimensions, and it is shown that center vortices emerge as the stable saddlepoints of this action. Thus, in the case of strong couplings, the vortex picture is arrived at analytically. I also respond briefly to a recent criticism regarding maximal center gauge.
We address two questions related to the procedure of identifying center vortices based on center projection in maximal center gauge: 1. How does the procedure work, why is it expected to locate center vortices relevant for confinement, and why does it in some cases fail, on lattice configurations preconditioned in a special way? 2. Does the mechanism work the same way for 3 colors instead of 2? (The paper is an abridged version of two recent e-prints, hep-lat/9910033 and hep-lat/9911006.)
The dominance of center degrees of freedom is observed in SU(3) lattice gauge theory in maximal center gauge. The full asymptotic string tension is reproduced, after center projection, by the center elements alone. When center vortices are removed from lattice configurations, the string tension tends to zero. This provides further evidence for the role played by center vortices in the mechanism of color confinement in quantum chromodynamics, but more extensive simulations with a better gauge-fixing procedure are still needed.
We argue that the ``vortex-finding'' property of maximal center gauge, i.e. the ability of this gauge to locate center vortices inserted by hand on any given lattice, is the key to its success in extracting the vortex content of thermalized lattice configurations. We explain how this property comes about, and why it is expected not only in maximal center gauge, but also in an infinite class of gauge conditions based on adjoint-representation link variables. In principle, the vortex-finding property can be foiled by Gribov copies. This fact is relevant to a gauge-fixing procedure devised by Kovacs and Tomboulis, where we show that the loss of center dominance, found in their procedure, is explained by a corresponding loss of the vortex-finding property. The association of center dominance with the vortex-finding property is demonstrated numerically in a number of other gauges.
We investigate the structure of center projected vortices of SU(2) lattice gauge theory at zero and finite temperature. 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. This vortex is an unorientable surface and has a very irregular structure with many handles. Small P-vortices, and short-range fluctuations of the large vortex surface, do not contribute to the string tension. At finite temperature P-vortices exist also in the deconfined phase. However, they form cylindric objects which extend in time direction and consist only of space-space plaquettes.
We present several new results which pertain to the successes of center projection in maximal center gauge (MCG). In particular, we show why any center vortex, inserted "by hand" into a thermalized lattice configuration, will be among the set of vortices found by the center projection procedure. We show that this "vortex-finding property" is lost when gauge-field configurations are fixed to Landau gauge prior to the maximal center gauge fixing; this fact accounts for the loss of center dominance in the corresponding projected configurations. Variants of maximal center (adjoint Landau) gauge are proposed which correctly identify relevant center vortices.
We report on a breakdown of both monopole dominance and positivity in abelian-projected lattice Yang-Mills theory. The breakdown is associated with observables involving two units of the abelian charge. We find that the projected lattice has at most a global $Z_2$ symmetry in the confined phase, rather than the global U(1) symmetry that might be expected in a dual superconductor or monopole Coulomb gas picture. Implications for monopole and center vortex theories of confinement are discussed.
We find that Polyakov lines, computed in abelian-projected SU(2) lattice gauge theory in the confined phase, have finite expectation values for lines corresponding to two units of the abelian electric charge. This means that the abelian-projected lattice has at most Z(2), rather than U(1), global symmetry. We also find a severe breakdown of the monopole dominance approximation, as well as positivity, in this charge-2 case. These results imply that the abelian-projected lattice is not adequately represented by a monopole Coulomb gas; the data is, however, consistent with a center vortex structure. Further evidence is provided, in lattice Monte Carlo simulations, for collimation of confining color-magnetic flux into vortices.