Vortices, Confinement and Higgs fields

We review lattice evidence for the vortex mechanism of quark confinement and study the influence of charged matter fields on the vortex distribution.Comment: 10 pages, 6 eps figures, talk presented by M.F. at the 5th International Conference "Quark Confinement and the Hadron Spectrum", Gargnano, Italy, September 10-14, 200

The Structure of Projected Center Vortices at Zero and Finite Temperature

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 figure

Susceptibility of Monte-Carlo Generated Projected Vortices

We determine the topological susceptibility from center projected vortices and demonstrate that the topological properties of the SU(2) Yang-Mills vacuum can be extracted from the vortex content. We eliminate spurious ultraviolet fluctuations by two different smoothing procedures. The extracted susceptibility is comparable to that obtained from full field configurations.Comment: 3 pages, 4 figures; Lattice2001(confinement

Remnant Symmetry and the Confinement Phase in Coulomb Gauge

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 200

Vortices in the SU(2)-Higgs model -- Vortices and the covariant adjoint Laplacian

Vortices in the SU(2)--Higgs model: The presence of a fundamental Higgs in the SU(N)-Higgs model yields color screening at some finite distance. Whereas the transition to the Higgs "phase" is accompanied by a suppression of projected center vortices, there is nearly no influence of color screening on the vortex properties in the confined "phase". Hence the behavior of the Wilson loop can be described in both phases within the vortex picture of confinement. Vortices and the covariant adjoint Laplacian: Laplacian center gauge is a method to localize center vortices in SU(N) gauge theory. We show that the eigenvectors of the covariant adjoint Laplacian identify vortices for a special class of gauge field configurations. However, for Monte Carlo generated configurations, modified approaches are required.Comment: 3 pages, 4 figures; Lattice2001(confinement

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

Center vortex model for the infrared sector of Yang-Mills theory

A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic vortices represented by (closed) random surfaces, is presented. The model quantitatively describes both confinement (including the finite-temperature transition to a deconfined phase) and the topological susceptibility of the Yang-Mills ensemble. A first (quenched) study of the spectrum of the Dirac operator furthermore yields a behavior for the chiral condensate which is compatible with results obtained in lattice gauge theory.Comment: Lattice2001(confinement) proceedings, 3 pages, 3 ps figure

Stress-energy tensor correlators from the world-sheet

The large $N$ limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an $\mathfrak{sl}(2,\mathbb{R})$ WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective.Comment: 16+9 page

Center vortex model for the infrared sector of Yang-Mills theory - Quenched Dirac spectrum and chiral condensate

The Dirac operator describing the coupling of continuum quark fields to SU(2) center vortex world-surfaces composed of elementary squares on a hypercubic lattice is constructed. It is used to evaluate the quenched Dirac spectral density in the random vortex world-surface model, which previously has been shown to quantitatively reproduce both the confinement properties and the topological susceptibility of SU(2) Yang-Mills theory. Under certain conditions on the modeling of the vortex gauge field, a behavior of the quenched chiral condensate as a function of temperature is obtained which is consistent with measurements in SU(2) lattice Yang-Mills theory.Comment: 36 LaTeX pages, 13 ps figures included via epsf; minor reformulations and added cross-referencing for the purpose of clarit

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.Comment: 3 pages, 2 EPS figures, Lattice2001(confinement