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S. Olejnik

Publications and source records attributed to S. Olejnik.

At least 37 records · Page 2Linked to original sources
arXiv2006

Vortices, Symmetry Breaking, and Temporary Confinement in SU(2) Gauge-Higgs Theory

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.

hep-lat↗
arXiv2005

Eigenmodes of covariant Laplacian in SU(2) Yang-Mills vacuum: higher representations

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.

hep-lat↗
arXiv2005

Localized eigenmodes of the covariant lattice Laplacian

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.

hep-lat↗
arXiv2005

Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum

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.

hep-lat↗
arXiv2004

Infrared Divergent Coulomb Self-Energy in Yang-Mills Theory

It is shown numerically that the Coulomb self-energy of an isolated, color non-singlet source diverges in an infinite volume. This is in accord with the Gribov Horizon scenario of confinement advocated by Gribov and Zwanziger. It is also shown that this divergence can be attributed to the presence of center vortices in thermalized lattice configurations.

hep-lat↗
arXiv2003

Adventures in Coulomb Gauge

We study the phase structure of SU(2) gauge theories at zero and high temperature, with and without scalar matter fields, in terms of the symmetric/broken realization of the remnant gauge symmetry which exists after fixing to Coulomb gauge. The symmetric realization is associated with a linearly rising color Coulomb potential (which we compute numerically), and is a necessary but not sufficient condition for confinement.

hep-lat↗
arXiv2003

Coulomb Energy, Vortices, and Confinement

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.

hep-lat↗
arXiv2002

Center Vortices at N > 4 Colors

We discuss two issues related to the physics of center vortices in pure SU(N) lattice gauge theory at large N: (1) Center vortices are stable classical solutions of the Wilson action, as well as of a wide class of improved lattice actions, for any N > 4. (2) The natural scaling of k-string tensions at large N, in the vortex picture of confinement, is σ(k)=k σ(1). This is the common large N limit of Casimir and Sine Law scaling. The crucial feature for explaining this behavior is the existence of center monopoles.

hep-lat↗
arXiv2002

k-String Tensions and Center Vortices at Large N

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.

hep-lat↗
arXiv2002

Status of center dominance in various center gauges

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.

hep-lat↗
arXiv2001

Center Dominance Recovered: Direct Laplacian Center Gauge

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.

hep-lat↗
arXiv2001

Direct Laplacian Center Gauge

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.

hep-lat↗
arXiv2001

Remarks on the Gribov Problem in Direct Maximal Center Gauge

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.

hep-lat↗
arXiv2000

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.

hep-lat↗
arXiv2000

P-Vortices, Gauge Copies, and Lattice Size

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.

hep-lat↗
arXiv2000

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.

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