Stefan Olejnik

Detection of center vortices in the lattice Yang-Mills vacuum

We discuss the implementation of the {open_quotes}direct{close_quotes} maximal center gauge (a gauge which maximizes the lattice average of the squared-modulus of the trace of link variables), and its use in identifying Z{sub 2} center vortices in Yang-Mills vacuum configurations generated by lattice Monte Carlo calculations. We find that center vortices identified in the vacuum state account for the full asymptotic string tension. Scaling of vortex densities with lattice coupling, change in vortex size with cooling, and sensitivity to Gribov copies are discussed. Preliminary evidence is presented, on small lattices, for center dominance in SU(3) lattice gauge theory. {copyright} {ital 1998} {ital The American Physical Society}

Casimir scaling from center vortices: Towards an understanding of the adjoint string tension

We argue that the approximate {open_quotes}Casimir scaling{close_quotes} of the string tensions of higher-representation Wilson loops is an effect due to the finite thickness of center vortex configurations. It is shown, in the context of a simple model of the Z{sub 2} vortex core, how vortex condensation in Yang-Mills theory can account for both Casimir scaling in intermediate size loops and color-screening in larger loops. An implication of our model is that the deviations from exact Casimir scaling, which tend to grow with loop size, become much more pronounced as the dimensionality of the group representation increases. {copyright} {ital 1998} {ital The American Physical Society}

Coulomb energy, remnant symmetry, and the phases of non-Abelian gauge theories

We show that the confining property of the one-gluon propagator, in the 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\char22{}surprisingly\char22{}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 region 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.

Color screening, Casimir scaling, and domain structure in G(2) and SU(N) gauge theories

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.

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.

Evidence for flux tubes from cooled QCD configurations

Abstract We analyze field configurations between a static qq in SU(2) lattice gauge theory using a cooling technique, which reduces quantum fluctuations while preserving the string tension and the topological charge. We find clear evidence of chromoelectric flux tube configurations, of transverse size which scales properly and in physical units is of the order of about 0.4 fm.

Center vortices and the Dirac spectrum

Institute of Physics, Slovak Academy of Sciences, SK–845 11 Bratislava, Slovakia(Dated: June 20, 2008)We study correlations between center vortices and the low-lying eigenmodes of the Dirac operator, in boththe 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-lyingDirac eigenmodes required for chiral symmetrybreaking do not appear to be present in center-projected configurations. We show that the low-lying modes are infact 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 e xtend the results of Kovalenko et al. [Phys.Lett. B 648, 383 (2007)], showing that there is a correlation between center vortex locations, and the scalardensity of low-lying Dirac eigenmodes derived from unprojected configurations. This correlation is strongestat points which are associated, in the vortex picture, with non-vanishing topological charge density, such asvortex intersection and “writhing” points. We present supp orting evidence that the lowest Dirac eigenmodes,in both asqtad and overlap formulations, have their largest concentrations in point-like regions, rather than onsubmanifolds of higher dimensionality.I. INTRODUCTION

Dimensional reduction and the Yang-Mills vacuum state in 2+1 dimensions

We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills Schrodinger equation in both the free-field limit, and in a strong-field zero mode limit. Our proposal contains a single parameter with dimensions of mass/ confinement via dimensional reduction is obtained if this parameter is non-zero, and a non-zero value appears to be energetically preferred. A method for numerical simulation of this vacuum state is developed. It is shown that if the mass parameter is fixed from the known string tension in 2+1 dimensions, the resulting mass gap deduced from the vacuum state agrees, to within a few percent, with known results for the mass gap obtained by standard lattice Monte Carlo methods.

Casimir scaling in G{sub 2} lattice gauge theory

We computed potentials between static color sources from the six lowest representations of G{sub 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{sub 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.

A first look at Landau-gauge propagators in G2 Yang-Mills theory

G2 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 G2 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 Greens functions is supported.