Extended abelian monopoles and confinement in the SU(2) lattice gauge theory

Ivanenko, T.L.; Pochinsky, Andrew; Polikarpov, M. I.

doi:10.1016/0370-2693(90)90497-t

Cited by 95 publications

(89 citation statements)

References 14 publications

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“…The constant N is defined by the normalization condition (5). The asymptotics of our solutions (18),…”

Section: B Zero-mode Solutionsmentioning

confidence: 95%

“…Namely, chiral condensate must be non-zero in the presence of the large monopole cluster, i.e., in the confinement phase. In the high temperature, deconfinement phase, the large monopole cluster is absent [18], and, as a result, the chiral symmetry breaking ceases to exist. Naively, one may suggest that the chiral condensate is proportional to the density of the largest monopole cluster, ρ IR , at least, at zero temperatures,…”

Section: Phenomenological Applications Conclusionmentioning

confidence: 99%

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Fermionic signature of the lattice monopoles

Chernodub

Захаров

2002

Phys. Rev. D

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We consider fermions in the field of static monopole-like configurations in the Euclidean spacetime. In all the cases considered there exists an infinite number of zero modes, labeled by frequency iω. The existence of such modes is a manifestation of instability of the vacuum in the presence of the monopoles and massless fermions. In the Minkowski space the corresponding phenomenon is well known and is a cornerstone of the theory of the magnetic catalysis. Moreover, the well known zero mode of Jackiw and Rebbi corresponds to the limiting case, ω = 0. We provide arguments why the chiral condensate could be linked to the density of the monopoles in the infrared cluster. A mechanism which can naturally explain the equivalence of the critical temperatures for the deconfinement and chiral transitions, is proposed. We discuss possible implications for the phenomenology of the lattice monopoles.

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“…The constant N is defined by the normalization condition (5). The asymptotics of our solutions (18),…”

Section: B Zero-mode Solutionsmentioning

confidence: 95%

Section: Phenomenological Applications Conclusionmentioning

confidence: 99%

Fermionic signature of the lattice monopoles

Chernodub

Захаров

2002

Phys. Rev. D

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“…Another special feature of the monopole action at finite temperature comes from the finite size in the time direction. We define a blockspin transformation of monopole currents [31] as …”

Section: Monopole Action At Finite Temperaturementioning

confidence: 99%

Effective Monopole Action at Finite Temperature in SU(2) Gluodynamics

Ishiguro¹,

Suzuki²,

Yazawa³

2002

J. High Energy Phys.

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Effective monopole action at finite temperature in SU(2) gluodynamics is studied on anisotropic lattices. Using an inverse Monte-Carlo method and the blockspin transformation for space directions, we determine 4-dimensional effective monopole action at finite temperature. We get an almost perfect action in the continuum limit under the assumption that the action is composed of two-point interactions alone. It depends on a physical scale b s and the temperature T . The temperature-dependence appears with respect to the spacelike monopole couplings in the deconfinement phase, whereas the timelike monopole couplings do not show any appreciable temperature-dependence. The dimensional reduction of the 4-dimensional SU(2) gluodynamics ((SU(2)) 4D ) at high temperature is the 3-dimensional Georgi-Glashow model ((GG) 3D ). The latter is studied at the parameter region obtained from the dimensional reduction. We compare the effective instanton action of (GG) 3D with the timelike monopole action obtained from (SU(2)) 4D . We find that both agree very well for T ≥ 2.4T c at large b region. The dimensional reduction works well also for the effective action.

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“…M. Polikarpov started to create his own scientific group in 1990. The first paper published by this group [8] was written in collaboration with his graduate students T. L. Ivanenko and A. V. Pochinsky. In this paper it was numerically demonstrated in SU (2) lattice gauge theory in maximal Abelian gauge that the density of Abelian monopoles which occupy several lattice cells (extended monopoles) is strongly correlated with the string tension.…”

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confidence: 99%