On topological properties of vacuum defects in lattice Yang–Mills theories

Kovalenko, A.V.; Morozov, S. M.; Polikarpov, M.I.; Захаров, В. И.

doi:10.1016/j.physletb.2007.03.036

Cited by 25 publications

(33 citation statements)

References 29 publications

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“…Our results support the view that center vortices alone can induce both confinement and chiral symmetry breaking. 1 In section 3 we report on other correlations between center vortex location, and the density distribution of low-lying Dirac eigenmodes, following the earlier work by Kovalenko et al [10]. These correlations are consistent with the picture advocated by Engelhardt and Reinhardt [11], in which topological charge is concentrated at points where vortices either intersect, or twist about themselves ("writhe") in a certain way.…”

Section: Introductionsupporting

confidence: 77%

Center vortex influence on the Dirac spectrum

Heller¹

2009

Proceedings of the XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)

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We study the influence of center vortices on the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. For center-projected configurations, one finds that the low-lying near-zero modes are present in the staggered (asqtad) formulation, but not in the overlap and "chirally-improved" formulations. We argue that this is due to the absence of a fieldindependent chiral symmetry in the latter formulations, when the Dirac operator is evaluated on the very rough configurations generated by center projection. We also confirm and extend the results of Kovalenko et al. [Phys. Lett. B 648, 383 (2007)], finding strong correlations between center vortex locations, and the scalar density of low-lying Dirac eigenmodes on unprojected lattices, in both asqtad and overlap formulations. It is found that the low-lying eigenmodes have their largest concentrations in point-like regions, rather than on submanifolds of higher dimensionality.

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Section: Introductionsupporting

confidence: 77%

Center vortex influence on the Dirac spectrum

Heller¹

2009

Proceedings of the XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)

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“…Results of measurements can be found in the original paper [55]. Here we just briefly summarize the finding.…”

Section: Lattice Datamentioning

confidence: 78%

“…Near the phase transition p ≈ 1/7 and ρ tot mon ≈ a −3 /7 . Note that it is the density of short clusters that dominates the v.e.v. (55). The percolating cluster is fine tuned, or very dilute near the point of phase transition.…”

Section: B Constraints On Particlesmentioning

confidence: 99%

From confining fields on the lattice to higher dimensions in the continuum

Захаров¹

2007

Braz. J. Phys.

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We discuss the relation between lattice phenomenology of confining fields in the vacuum state of Yang-Mills theories (mostly SU(2) case) and continuum theories. In the continuum, understanding of the confinement is most straightforward in the dual formulation which involves higher dimensions. We try to bridge these two approaches to the confinement, let it be on a rudimentary level. We review lattice data on low-dimensional vacuum defects, like monopoles, center vortices. There is certain resemblance to dual strings, domain walls considered in the continuum version of Yang-Mills theories.

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“…These findings have been complemented by further recent investigations focusing on correlations between center vortices and low-lying overlap Dirac operator eigenmodes [21][22][23], which, on the other hand, can be tied to the topological charge density. Of related interest are studies of the connection between center vortices and other topological charge carriers arising in Yang-Mills theory; a detailed analysis of the vortex content of calorons was presented recently in [32].…”

mentioning

confidence: 76%

“…Two main lines of investigation have contributed to these developments. On the one hand, sparked by the inception of practicable algorithms for the detection of vortices in lattice Yang-Mills configurations [15][16][17], lattice studies of the vortex content of Yang-Mills theory and the effects it induces were carried out [15][16][17][18][19][20][21][22][23]. On the other hand, an infrared effective model based directly on center vortex degrees of freedom with a simplified effective dynamics was introduced to complement the lattice studies and expand on the range of vortex physics that could be accessed quantitatively [24][25][26][27][28][29][30][31].…”

mentioning

confidence: 99%

Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility

Engelhardt

2011

Phys. Rev. D

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The topological susceptibility of the SU (3) random vortex world-surface ensemble, an effective model of infrared Yang-Mills dynamics, is investigated. The model is implemented by composing vortex world-surfaces of elementary squares on a hypercubic lattice, supplemented by an appropriate specification of vortex color structure on the world-surfaces. Topological charge is generated in this picture by writhe and self-intersection of the vortex world-surfaces. Systematic uncertainties in the evaluation of the topological charge, engendered by the hypercubic construction, are discussed. Results for the topological susceptibility are reported as a function of temperature and compared to corresponding measurements in SU (3) lattice Yang-Mills theory. In the confined phase, the topological susceptibility of the random vortex world-surface ensemble appears quantitatively consistent with Yang-Mills theory. As the temperature is raised into the deconfined regime, the topological susceptibility falls off rapidly, but significantly less so than in SU (3) lattice Yang-Mills theory. Possible causes of this deviation, ranging from artefacts of the hypercubic description to more physical sources, such as the adopted vortex dynamics, are discussed.

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On topological properties of vacuum defects in lattice Yang–Mills theories

Cited by 25 publications

References 29 publications

Center vortex influence on the Dirac spectrum

Center vortex influence on the Dirac spectrum

From confining fields on the lattice to higher dimensions in the continuum

Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility

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