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A parallel reactor setup in combination with a spatially resolving Fourier transform infrared focal plane array detector (FTIR-FPA) system in rapid scan mode has been developed which is capable of analyzing simultaneously the specific surface area of 15 copper catalysts. The system allows the reliable determination of copper surface areas with an error of about +/-1 m(2)/g. Problems are encountered with very fluffy catalyst powders, since this leads to excessive pressure drop over the catalyst bed. The error brought about by this effect can be eliminated by taking into account the flow deviations between channels in such cases.

The first paper attempting direct calculation of the Yang-Mills vacuum wave functional was published by Greensite in 1979. I review some recent results of the determination of the vacuum wave functional in Monte Carlo simulations of SU(2) lattice gauge theory., 17 pages, 17 figures; based on talks presented at the DISCRETE 2014 Symposium, King's College, London, UK, Dec. 2-6, 2014, and at the 4th Winter Workshop on Non-Perturbative Quantum Field Theory, INLN, Sophia Antipolis, France, Feb. 2-5, 2015

Modified SBA-15 materials were studied as catalysts in the vapor-phase Beckmann rearrangement of cyclohexanone oxime to e -caprolactam. Their combined micropore and mesopore system allows the investigation of the influence of pore dimensions, acid site concentration and strength, and location on the catalytic activity. A treatment utilizing H 2 SO 4 allows to study the contribution of silanol groups as potential catalytically active sites in mesopores and micropores independent of one another. Applying 29 Si solid-state NMR and DRIFTS experiments using a probe molecule, surface and in-wall silanol groups can be discriminated and quantified, making analysis correlating location, acidity, and catalytic activity possible. Combining all results leads to conclusions concerning the location of the catalytic reaction, the nature of the catalytic active sites, and their properties, which provides a basis for a rational optimization of catalysts.

We review the confinement scenario in Coulomb gauge. We show that when thin center vortex configurations are gauge transformed to Coulomb gauge, they lie on the common boundary of the fundamental modular region and the Gribov region. This unifies elements of the Gribov confinement scenario in Coulomb gauge and the center-vortex confinement scenario. We report on recent numerical studies which support both of these scenarios., Comment: Talk given at QCD Down Under, Adelaide, Australia, March 10-19, 2004. 6 pages. 6 figures

Ratios of the true Yang-Mills vacuum wavefunctional, evaluated on any two field configurations out of a finite set of configurations, can be obtained from lattice Monte Carlo simulations. The method was applied some years ago to test various proposals for the vacuum wavefunctional in 2+1 dimensions. In this article we use the same method to test our own proposal for the Yang-Mills ground state in 3+1 dimensions. This state has the property of "dimensional reduction" at large scales, meaning that the (squared) vacuum state, evaluated on long-wavelength, large scale fluctuations, has the form of the Boltzmann weight for Yang-Mills theory in D=3 Euclidean dimensions. Our numerical results support this conjectured behavior. We also investigate the form of the ground state evaluated on shorter wavelength configurations.

Magnetic activated carbons were obtained by in situ formation of coated superparamagnetic iron nanoparticles in the pores of carbons initially impregnated with ferric salt solution.

We find, in close analogy to Abelian dominance in the maximal Abelian gauge, the phenomenon of center dominance in the maximal center gauge for SU(2) lattice gauge theory. The maximal center gauge is a gauge-fixing condition that preserves a residual ${Z}_{2}$ gauge symmetry; ``center projection'' is the projection of SU(2) link variables onto ${Z}_{2}$ center elements, and ``center dominance'' is the fact that the center-projected link elements carry most of the information about the string tension of the full theory. We present numerical evidence that the thin ${Z}_{2}$ vortices of the projected configurations are associated with ``thick'' ${Z}_{2}$ vortices in the unprojected configurations. The evidence also suggests that the thick ${Z}_{2}$ vortices may play a significant role in the confinement process.

A method of measuring relative probabilities of various gauge-field configurations in the Yang-Mills vacuum was proposed long ago [Phys. Lett. B 223 (1989) 207]. We applied this method to compute the square of the YM vacuum wave functional (VWF) in numerical simulations of SU(2) lattice gauge theory in D=3+1 dimensions for sets of abelian plane waves. The results were compared to predictions based on some VWF proposals in the literature. None of them describes the data satisfactorily at large plane-wave momenta. The phenomenological best fit to data, containing three free parameters, appears to reduce in the continuum limit to the approximate form proposed in [Phys. Rev. D 77 (2008) 065003]., Comment: 7 pages, 4 figures (8 EPS files), uses PoS.cls; presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

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., 3 pages, 2 EPS figures, Lattice2001(confinement)

The gauge-independent phenomenon of color confinement in Yang-Mills theory manifests itself differently in different gauges. Therefore, the gauge dependence of quantities related to the infrared structure of the theory becomes important for understanding the confinement mechanism. Particularly useful are classes of gauges that are controlled by a single gauge parameter. We present results on propagators and the color-Coulomb potential for the so-called lambda-gauges, which interpolate between the (minimal) Landau gauge and the (minimal complete) Coulomb gauge. Results are reported for the SU(2) lattice gauge theory in three and four space-time dimensions. We investigate especially intermediate and low momenta. We find a continuous evolution of all quantities with the gauge parameter, except at zero four-momentum.

We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in 2+1 dimensions to sets of abelian plane wave configurations of varying amplitude and wavelength, and sets of non-abelian constant configurations. The results are compared to the predictions of several proposed versions of the Yang-Mills vacuum wavefunctional that have appeared in the literature. These include (i) a suggestion in temporal gauge due to Greensite and Olejnik; (ii) the "new variables" wavefunction put forward by Karabali, Kim, and Nair; (iii) a hybrid proposal combining features of the temporal gauge and new variables wavefunctionals; and (iv) Coulomb gauge wavefunctionals developed by Reinhardt and co-workers, and by Szczepaniak and co-workers. We find that wavefunctionals which simplify to a "dimensional reduction" form at large scales, i.e. which have the form of a probability distribution for two-dimensional lattice gauge theory, when evaluated on long-wavelength configurations, have the optimal agreement with the data., Comment: 19 pages, 11 figures

We report results on the Coulomb-gauge ghost propagator and the color-Coulomb potential computed in two lattice gauge-field ensembles: (1) configurations derived from our recently proposed Yang-Mills vacuum wave functional in 2+1 dimensions, and (2) lattices generated by Monte Carlo simulations of the three-dimensional Euclidean SU(2) lattice gauge theory with the Wilson action. We observe remarkable agreement between the ghost propagators in both ensembles, but some differences in the potentials. Those originate from rare configurations with very small values of the lowest eigenvalue of the Coulomb-gauge Faddeev-Popov operator. If the same cuts on such exceptional configurations are applied in both ensembles, then the color-Coulomb potentials are also in reasonably good agreement., 7 pages, 4 figures (7 EPS files). Presented at the XXVIII International Symposium on Lattice Field Theory (Vacuum Structure and Confinement), June 14-19, 2010, Villasimius, Sardinia, Italy

The flux tube between a quark and an antiquark in Coulomb gauge is imagined in the gluon-chain model as a sequence of constituent gluons bound together by Coulombic nearest-neighbor interactions. We diagonalize the transfer matrix in SU(2) lattice gauge theory in a finite basis of states containing a static quark-antiquark pair together with zero, one, and two gluons in Coulomb gauge. We show that while the string tension of the color-Coulomb potential (obtained from the zero-gluon to zero-gluon element of the transfer matrix) overshoots the true asymptotic string tension by a factor of about three, the inclusion of a few states with constituent gluons reduces the discrepancy considerably. The minimal energy eigenstate of the transfer matrix in the zero-, one-, and two-gluon basis exhibits a linearly rising potential with the string tension only about 1.4 times larger than the asymptotic one., 8 pages, 5 figures. Presented at the XXVII International Symposium on Lattice Field Theory (Vacuum Structure and Confinement), July 26-31, Beijing, China

The Coulomb-gauge ghost propagator, and the color-Coulomb potential, are computed in an ensemble of configurations derived from our recently proposed Yang-Mills vacuum wavefunctional in 2+1 dimensions. The results are compared to the corresponding values obtained by standard Monte Carlo simulations in three Euclidean dimensions. The agreement is quite striking for the Coulomb-gauge ghost propagator. The color-Coulomb potential rises linearly at large distances, but its determination suffers from rather large statistical fluctuations, due to configurations with very low values of $\mu_0$, the lowest eigenvalue of the Coulomb-gauge Faddeev-Popov operator. However, if one imposes cuts on the data, effectively leaving out configurations with very low $\mu_0$, the agreement of the potential in both sets of configurations is again satisfactory, although the errorbars grow systematically as the cutoff is eliminated., Comment: 8 pages, 5 figures (10 EPS files), RevTeX4.1. V2: original figs. 4 and 5 compressed into a new fig. 5; a new fig. 4; sec. IV.B slightly modified to reflect the changes. Version to appear in Phys. Rev. D. V3: a reference corrected.

We review properties and lattice evidence in support of the recently proposed temporal-gauge Yang-Mills vacuum wave functional in 2+1 dimensions., Comment: 3 pages, 3 EPS figures, uses aipproc.cls; talk presented by S. Olejnik at the conference "Quark Confinement and the Hadron Spectrum IX", Madrid, Spain, Aug. 30-Sep. 3, 2010; submitted to AIP Conference Proceedings; after publication, it will be found at http://link.aip.org/link/?apc

Potentials between static quarks and antiquarks from a few lowest representations were evaluated in numerical simulations of 4-dimensional pure G$_2$ lattice gauge theory at various couplings. The obtained potentials are linearly rising at intermediate distances and their string tensions exhibit (approximate) Casimir scaling. This result is in accordance with a model of the vacuum of non-Abelian gauge theories with a domain structure, in which the (color) magnetic flux randomly fluctuates within a domain, but the total flux in each domain is quantized in units of the gauge group center., Contribution presented at the conference "Quark Confinement and the Hadron Spectrum VIII", Mainz, Germany, Sept. 1-6, 2008; 5 pages, 2 figures (5 EPS files), uses pos.cls

We computed potentials between static color sources from the six lowest representations of G(2) lattice gauge theory, in numerical simulations with the Wilson action on asymmetric lattices with nonperturbatively estimated values of the bare anisotropy. We present evidence for (approximate) Casimir scaling of the obtained intermediate string tensions. The agreement with the Casimir-scaling prediction improves by increasing the coupling beta in the weak-coupling region above the crossover observed in G(2) gauge theory. The result naturally fits into confinement models with magnetic disorder and vacuum domain structure, but may represent a challenge for other approaches., Comment: 14 pages, 12 figures (24 EPS files), RevTeX4. In v2: typos corrected, discussion of systematic errors and of smearing expanded, references added. Version to appear in Phys. Rev. D

We study correlations between center vortices and the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. In particular we address a puzzle raised some years ago by Gattnar et al. [Nucl. Phys. B 716, 105 (2005)], who noted that the low-lying Dirac eigenmodes required for chiral symmetry breaking do not appear to be present in center-projected configurations. We show that the low-lying modes are in fact present in the staggered (asqtad) formulation, but not in the overlap and ``chirally improved'' formulations, and suggest a reason for this difference. We also confirm and extend the results of Kovalenko et al. [Phys. Lett. B 648, 383 (2007)], showing that there is a correlation between center vortex locations, and the scalar density of low-lying Dirac eigenmodes derived from unprojected configurations. This correlation is strongest at points which are associated, in the vortex picture, with non-vanishing topological charge density, such as vortex intersection and ``writhing'' points. We present supporting evidence that the lowest Dirac eigenmodes, in both asqtad and overlap formulations, have their largest concentrations in point-like regions, rather than on submanifolds of higher dimensionality., Comment: some high temperature results and references added

We study the string tension σ and chromoelectric flux tube configurations on the lattice at zero and finite T, using a cooling technique along which the short-range quantum fluctuations are reduced while semiclassical configurations are left metastable. We find that σ survives many cooling steps showing a clear plateau and then disappears. The value of σ at the plateau, vs. T, and the value of the deconfinement temperature are the same as found without cooling, suggesting that confinement is produced by semiclassical configurations. We find a clear evidence of chromoelectric flux tube configurations between a static q q pair, which survive as many cooling steps as the string tension, with a transverse size of order 0.5 fm at T = 0, and get broader and broader until they disappear at the deconfinement phase transition. We discuss also some tests of 't Hooft's abelian projection for the flux formation.

The $t$-expansion method for calculating ground-state energies of Hamiltonian systems is generalized to excited states. We introduce quantities ${M}_{n}(t)$ and ${D}_{n}(t)$ which for $t\ensuremath{\rightarrow}\ensuremath{\infty}$ converge to ${\ensuremath{\Sigma}}_{n}={E}_{0}+{E}_{1}+\dots{}+{E}_{n}$ and ${\ensuremath{\Delta}}_{n}={E}_{n+1}\ensuremath{-}{E}_{n}$, respectively. Like in the standard $t$-expansion, the $t$-series for ${M}_{n}(t)$ and ${D}_{n}(t)$ are constructed from moments of the Hamiltonian. The values of ${\ensuremath{\Sigma}}_{n}$ and ${\ensuremath{\Delta}}_{n}$ can then be estimated using (e.g.) a generalization of the connected-moment expansion of Cioslowski.

We study the origin of the Coulomb part of the quark-antiquark potential by lattice calculations. A cooling technique which reduces quantum noise in lattice configurations is applied. We demonstrate that the Coulomb part of the potential vanishes with cooling and is thus due to quantum fluctuations, while the string tension persists many cooling steps. Further, we give an estimate of the energy contained in quantum fluctuations.

We argue that screening of higher-representation color charges by gluons implies a domain structure in the vacuum state of non-abelian gauge theories, with the color magnetic flux in each domain quantized in units corresponding to the gauge group center. Casimir scaling of string tensions at intermediate distances results from random spatial variations in the color magnetic flux within each domain. The exceptional G(2) gauge group is an example rather than an exception to this picture, although for G(2) there is only one type of vacuum domain, corresponding to the single element of the gauge group center. We present some numerical results for G(2) intermediate string tensions and Polyakov lines, as well as results for certain gauge-dependent projected quantities. In this context, we discuss critically the idea of projecting link variables to a subgroup of the gauge group. It is argued that such projections are useful only when the representation-dependence of the string tension, at some distance scale, is given by the representation of the subgroup., Comment: 24 pages, 14 figures; v2: references added; v3: published version containing some additional introductory discussion

G_2 Yang--Mills theory is an interesting laboratory to investigate non-perturbative effects. On one hand, no conventional quark confinement via a linearly rising potential is present. On the other hand, its thermodynamic properties are similar to ordinary SU(N) Yang--Mills theory. Finally, it has been conjectured that gluons are removed from the physical spectrum in the same way as in SU(N) Yang--Mills theory. The last claim will be explored by determining the Landau-gauge ghost and gluon propagators, as well as the Faddeev--Popov operator eigenspectrum, in G_2 lattice gauge theory in two and three dimensions. The results are found to agree qualitatively with the SU(2) and SU(3) case. Therefore, the conjecture that Yang--Mills theories with different gauge groups are qualitatively similar on the level of their Landau gauge Green's functions is supported., Comment: 22 pages, 4 figures, 2 tables; in v2: One figure added, added statistics, extended discussion on some topics, various minor changes

We further investigate center vortex percolation and Coulomb gauge remnant symmetry breaking in the SU(2) gauge-Higgs model. We show that string breaking is visible in Polyakov line correlators on the center projected lattice, that our usual numerical tests successfully relate P-vortices to center vortices, and that vortex removal removes the linear potential, as in the pure gauge theory. This data suggests that global center symmetry is not essential to the vortex confinement mechanism. But we also find that the line of vortex percolation-depercolation transitions, and the line of remnant symmetry breaking transitions, do not coincide in the SU(2)-Higgs phase diagram. This non-uniqueness of transition lines associated with non-local order parameters favors a straightforward interpretation of the Fradkin-Shenker theorem, namely: there is no unambiguous distinction, in the SU(2) gauge-Higgs models, between a "confining" phase and a Higgs phase., Comment: 8 pages, 11 figures

We study the spectrum of low-lying eigenmodes of the kinetic operator for scalar particles, in the color adjoint representation of Yang-Mills theory. The kinetic operator is the covariant Laplacian, plus a constant which serves to renormalize mass. In the pure gauge theory, our data indicates that the interval between the lowest eigenvalue and the mobility edge tends to infinity in the continuum limit. On these grounds, it is suggested that the perturbative expression for the scalar propagator may be misleading even at distance scales that are small compared to the confinement scale. We also measure the density of low-lying eigenmodes, and find a possible connection to multi-critical matrix models of order m=1., Comment: 9 pages, 14 figures

The study of lowest eigenmodes of the covariant Laplacian in fundamental representation of the gauge group revealed their specific localization properties. These may bear information on confinement of fundamental scalar particles in SU(2) Yang-Mills vacuum. It was expected that scalar particle eigenmodes in other representations would be localized in different physical volumes. However simulations show strikingly different results for the adjoint and higher (J=3/2) representations. Apart from much higher extent of localization, we find evidence of different scaling behavior of localized eigenmodes., Comment: Talk given at 23rd International Symposium on Lattice Field Field: Lattice 2005, Trinity College, Dublin, Ireland, 25-30 Jul 2005; 6 pages, 9 figures

As a probe of the Yang-Mills vacuum, we study numerically the eigenmode spectrum of the covariant lattice Laplacian operator. We find that the eigenmodes at the low and high ends of the spectrum are localized in finite regions whose volume is insensitive to the lattice volume. We also find that the vacuum is seen very differently by localized modes of the covariant Laplacian in different representations of the gauge group. In the fundamental representation, the data suggests that the localization volume is finite in physical units set by the string tension, and localization disappears when center vortices are removed. In the adjoint and j=3/2 representations the low and high-lying modes are far more localized, and the localization volume appears to scale to zero, in physical units, in the continuum limit. The adjoint Laplacian is insensitive to vortex removal, but we find that exponential localization is absent for adjoint eigenmodes in the Higgs phase of a gauge-Higgs theory. Localization is also absent in the spectrum of the Coulomb gauge Faddeev-Popov operator, as required in Coulomb gauge confinement scenarios., Comment: 11 pages, 24 figures, reference added

The infinite color-Coulomb energy of color-charged states is related to enhanced density of near-zero modes of the Faddeev-Popov operator in Coulomb gauge. We confirm the enhancement in numerical simulations and show that it is tied to the presence of percolating center vortex configurations., Comment: Poster presented at Lattice2005 (Topology and Confinement), Dublin, July 25-30, 2005; 6 pages, 4 figures, uses PoS.cls; to appear in Proceedings of Science

We study numerically the eigenmode spectrum of the covariant lattice Laplacian, in the fundamental SU(2) color group representation. It is found that eigenmodes at the lower and upper ends of the spectrum are localized, and that the localization volume scales. In contrast, the eigenmodes of the lattice Faddeev-Popov operator are all extended rather than localized (as required for confinement) despite the similarity of the kinetic and Faddeev-Popov operators., Comment: Talk presented by J. Greensite at Lattice2005 (Topology and Confinement), Dublin, July 25-30, 2005; 6 pages, 4 figures, uses PoS.cls; to appear in Proceedings of Science

We review numerical evidence on connections between the center-vortex and Gribov-horizon confinement scenarios., Comment: Plenary talk presented by S. Olejnik at "Quark Confinement and the Hadron Spectrum VI", Villasimius, Sardinia, Italy, Sep. 21-25, 2004; 10 pages, 11 EPS figures, uses AIP Proceedings style files

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., 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 JHEP

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., 18 pages, 19 figures, revtex4

We report on connections between the confining color Coulomb potential, center vortices, and the unbroken realization of remnant gauge symmetry in Coulomb gauge., Comment: 6 pages. Invited talk at "QCD Down Under," Adelaide, Australia, March 2004

We estimate the Coulomb energy of static quarks from a Monte Carlo calculation of the correlator of timelike link variables in Coulomb gauge. We find, in agreement with Cucchieri and Zwanziger, that this energy grows linearly with distance at large quark separations. The corresponding string tension, however, is several times greater than the accepted asymptotic string tension, indicating that a state containing only static sources, with no constituent gluons, is not the lowest energy flux tube state. The Coulomb energy is also measured on thermalized lattices with center vortices removed by the de Forcrand-D'Elia procedure. We find that when vortices are removed, the Coulomb string tension vanishes., 8 pages, 4 EPS figures, RevTeX4; reference added

We study the SU(2) gauge-Higgs system in D=4 dimensions, and analyze the influence of the fundamental-representation Higgs field on the vortex content of the gauge field. It is shown that center projected Polyakov lines, at low temperature, are finite in the infinite volume limit, which means that the center vortex distribution is consistent with color screening. In addition we confirm and further investigate the presence of a "Kertesz-line" in the strong-coupling region of the phase diagram, which we relate to the percolation properties of center vortices. It is shown that this Kertesz-line separates the gauge-Higgs phase diagram into two regions: a confinement-like region, in which center vortices percolate, and a Higgs region, in which they do not. The free energy of the gauge-Higgs system, however, is analytic across the Kertesz line., Comment: 7 pages, 10 figures

We point out that there is a natural explanation, in terms of the center vortex confinement mechanism, for the expected Casimir/Sine Law scaling of k-string tensions in the large N limit. The crucial ingredient is the existence of Z(N) center monopoles, which go over to U(1) monopoles in this limit. Vortex densities leading to Casimir/Sine Law scaling at large-N are constructed; these densities have no obvious pathologies and in particular do not grow with N. We also note that center vortices are stable classical solutions of the Wilson action, for all SU(N) gauge theories with N>4, and extend this old result to a broad class of lattice actions motivated by the improved action program and the renormalization group., 23 pages, 2 figures

We review lattice evidence showing that center-vortex condensation is a serious candidate for the mechanism of colour confinement in quantum chromodynamics.

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.

Preface. Chiral zero-mode for abelian BPS dipoles P. van Baal. Dual superconductivity, effective string theory, and Regge trajectories M. Baker, R. Steinke. Confinement-deconfinement order parameters V.A. Belavin, et al. Analytical study of low temperature phase of 3D LGT in the plaqette formulation O. Borisenko, et al. Monopoles from instantons F. Bruckmann. Color superconductivity in two- and three-flavor systems at moderate densities M. Buballa, M. Oertel. Lattice monopoles in hot SU(2) gluodynamics as blocked continuum defects M.N. Chernodub, et al. Color confinement and dual superconductivity: An update A. Di Giacomo. An effective theory for the SU(2) mass gap? L. Dittmann, et al. Matrix models on the fuzzy sphere B.P. Dolan, et al. Dynamical mass generation in quantum field theory: Some methods with application to the Gross-Neveu model and Yang-Mills theory D. Dudal, et al. Center vortex model for nonperturbative strong interaction physics M. Engelhardt. Status of center dominance in various center gauges M. Faber, et al. Solitons and spontaneous symmetry breaking in 2 and 4 dimensions M. Faber, et al. SO(3) versus SU(2) lattice gauge theory Ph. de Forcrand, O. Jahn. SU(2) Abelian projected action for renormalisation group flows F. Freire. Center vortices, magnetic condensate and confinement in a simple gauge system F. Gliozzi, et al. Lattice chiral gauge theories through gauge fixing M. Golterman, Y. Shamir. Spectra of lattice Dirac operators in non-trivial topology backgrounds A. Gonzalez-Arroyo. The gluon chain model revisited J. Greensite. Connections between thin, thick and projection vortices in SU(2) lattice gauge theory R.W. Haymaker, A.Alexandru. Charges, monopoles and gauge invariance R. Horan, et al. Low-lying Dirac eigenmodes, topological charge fluctuations and the Instanton Liquid Model I. Horvath, et al. Anisotropic QCD superfluids J. Hosek. Towards the topological susceptibility with overlap fermions T.G. Kovacs. Vortex waistlines T.G. Kovacs, E.T. Tomboulis. Vortex induced confinement and the Kugo-Ojima confinement criterion K. Langfeld. Monopoles and Lyapunov exponents in U(1) lattice gauge theory H. Markum, et al. Massive light front QED(1+1) in the Weyl gauge L'. Martinovic. Topology of center vortices H. Reinhardt. Electric flux sectors and confinement L. von Smekal, Ph. de Forcrand. Confinement in SU(3): Simple and generalized maximal abelian gauge J.D. Stack, et al. Supersymmetric Yang-Mills quantum mechanics J. Wosiek. Scalar-particle projection of gluodynamics: Fine Tuning V.I. Zakharov. List of Participants.

We present a variety of numerical data supporting the Center Vortex theory of confinement. A method is introduced for identifying the location of center vortices, in thermalized gauge-field configurations generated by lattice Monte Carlo. Fluctuations in the number of such vortices, linked to fundamental representation Wilson loops, appear to be responsible for the asymptotic string tension extracted from those loops., Comment: Invited talk by J. Greensite at the Nato Workshop "New Developments in Quantum Field Theory," Zakopane, Poland (June 1997). 19 pages, including 21 figures, Latex2e. Uses plenum.sty

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., Comment: 24 pages, 11 figures, latex2e

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., Comment: 14 pages, 6 figures

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., Lattice 2000 (Topology and Vacuum), 4 pages

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., 17 pages, 5 figures, latex2e

In SU(2) lattice gauge theory in maximal center gauge, we investigate the dependence of center-projected Creutz ratios and the vortex density on lattice size and the number of gauge copies. The dependence on the number of copies is rather strong on small lattices, but almost disappears on lattices sufficiently large compared to the expected average vortex thickness. The center-projected string tension, evaluated on sufficiently large lattices, is in good agreement with the full asymptotic string tension, and the vortex density scales according to the second-order asymptotic-freedom formula., Comment: Lattice 2000 (Topology and Vacuum), 4 pages, 4 EPS-figures

The center-vortex model of color confinement was proposed more than 20 years ago by ‘t Hooft [1] and other authors [2]. It was quite popular for a while, but then fell in oblivion, before being subjected to thorough tests in simulations of quantum chromodynamics on a lattice. One of the exceptions was the work of Tomboulis and collaborators [3]. In recent years the interest in this picture has been renewed due to our discovery of center dominance in SU(2) lattice gauge theory in maximal center gauge [4]. Substantial lattice evidence has then been accumulated on the role played by center vortices in color confinement [5, 6, 7].

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., Comment: LATTICE99 - 3 pages, 6 figures