Gauge invariant Z(2) vortex vacuum textures and the SU(2) gluon condensate

Schäfke

2000

Physics Letters B

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The c-vortex ensembles are constructed by means of the recently proposed cooling method which gradually removes the SU (2)/Z 2 coset fields from the SU (2) lattice configurations and which thus reveals the Z 2 vortex vacuum texture. Using Teper's blocking method, the screening masses of the 0 + and the 2 + glueball is calculated from these vortex ensembles and compared with the masses obtained from full configurations. The masses of either case agree within the achieved numerical accuracy of 10%. As a byproduct, we find that the overlaps of the Teper operators with the glueball wavefunctions are significantly larger in the case of the c-vortex ensembles. * Supported in part by Graduiertenkolleg Hadronen und Kerne.PACS: 11.15.Ha 12.38.Aw keywords: confinement, vortex dominance, glueball mass, SU(2) lattice gauge theory. 1Introduction. The idea that the center part of the SU(N) gauge configurations are important for the confinement of quarks dates back to the late seventies [1]. Indeed, the proposal that the vortex free energy serves as an order parameter for quark (de-)confinement was recently confirmed in the case of a SU(2) gauge group by a large scale lattice simulation [2]. Subsequently, Mach and collaborators explicitly constructed a vortex signature of the Yang-Mills vacuum from gauge invariant variables [3]. It was observed at that time that random fluctuations of the vortex structure disorders the Wilson loop and, hence, provides quark confinement. With the increase of the computer performance in the mid eighties, many research efforts were devoted to substantiate this idea on a quantitative level [4,5]. One finds that projecting the full lattice configurations onto its vortex content reproduces the string tension of the static quark anti-quark potential. Recently, it was pointed out that not only the asymptotic behavior of the potential but also the short range part which is due to gluon exchange is reproduced if the plaquette is used for a definition of the vortex ensemble [6]. Moreover, the properties of the vortices arising from the plaquette projection technique strongly depend on the size of the lattice spacing thus rendering a continuum interpretation of the latter vortices cumbersome [6].

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confidence: 79%

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confidence: 99%

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confidence: 99%

“…For removing gluonic (coset) degrees of freedom from SU(2) configurations, the gluonic action density per link is defined by [13] …”

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confidence: 99%

See 2 more Smart Citations

Vortex dominance of the 0+ and 2+ glueball mass in SU(2) lattice gauge theory

Schäfke

2000

Physics Letters B

Self Cite

“…In practice, this subtraction uses the result of a high order calculation in lattice perturbation theory [2]. Alternatively, the gluon contribution can be removed by a cooling procedure which reduces the action of the coset (gluon) fields A µ (x) [1]. The latter approach suggests that the gluon condensate G gets contributions from the energy density stored in the underlying Z 2 fields, which are revealed by the coset cooling mechanism.…”

Section: The Finite Temperature Gluon Condensatementioning

confidence: 99%

Gauge potential singularities and the gluon condensate at finite temperatures

Nuclear Physics B - Proceedings Supplements

Ilgenfritz

Reinhardt

et al. 2002

The continuum limit of SU (2) lattice gauge theory is carefully investigated at zero and at finite temperatures. It is found that the continuum gauge field has singularities originating from center degrees of freedom being discovered in Landau gauge. Our numerical results show that the density of these singularities properly extrapolates to a non-vanishing continuum limit. The action density of the non-trivial Z2 links is tentatively identified with the gluon condensate. We find for temperatures larger than the deconfinement temperature that the thermal fluctuations of the embedded Z2 gauge theory result in an increase of the gluon condensate with increasing temperature.

Singular gauge potentials and the gluon condensate at zero temperature

Nuclear Physics B - Proceedings Supplements

Ilgenfritz

Reinhardt

et al. 2002

We consider a new cooling procedure which separates gluon degrees of freedom from singular center vortices in SU (2) LGT in a gauge invariant way. Restricted by a cooling scale κ 4 /σ 2 fixing the residual SO(3) gluonic action relative to the string tension, the procedure is RG invariant. In the limit κ → 0 a pure Z(2) vortex texture is left. This minimal vortex content does not contribute to the string tension. It reproduces, however, the lowest glueball states. With an action density scaling like a 4 with β, it defines a finite contribution to the action density at T = 0 in the continuum limit. We propose to interpret this a mass dimension 4 condensate related to the gluon condensate. Similarly, this vortex texture is revealed in the Landau gauge.