Gauge-fixing ambiguity and monopole number

Hioki, S.; Kitahara, Shun-ichi; Matsubara, Yoshimi; Miyamura, O.; Ohno, Satoshi; Suzuki, Tsuneo

doi:10.1016/0370-2693(91)91300-k

Cited by 36 publications

(35 citation statements)

References 10 publications

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“…This is actually consistent with lattice results. In [28,26,27] it was observed that the number of monopoles decreases the better the MAG is fixed, i.e. the closer one approaches the absolute maximum of the lattice MAG functional.…”

Section: Discussionmentioning

confidence: 99%

“…The nontrivial task is to find normalizable zero modes of FP given by (2.22) which is a complicated partial differential operator. We are, however, encouraged by lattice calculations, in which such copies have been detected numerically, for the first time in [28] and with refined techniques in [26,27]. One should keep in mind, though, that some (if not all) of these copies can be lattice artifacts which do not survive in the continuum limit.…”

Section: )mentioning

confidence: 98%

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Instantons and Gribov copies in the maximally Abelian gauge

et al. 2000

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We calculate the Faddeev-Popov operator corresponding to the maximally Abelian gauge for gauge group SU (N ). Specializing to SU (2) we look for explicit zero modes of this operator. Within an illuminating toy model (Yang-Mills mechanics) the problem can be completely solved and understood. In the field theory case we are able to find an analytic expression for a normalizable zero mode in the background of a single 't Hooft instanton. Accordingly, such an instanton corresponds to a horizon configuration in the maximally Abelian gauge. Possible physical implications are discussed.

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Section: Discussionmentioning

confidence: 99%

Section: )mentioning

confidence: 98%

Instantons and Gribov copies in the maximally Abelian gauge

et al. 2000

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“…These correspond to the (lattice) Gribov copies. Gauge dependent quantities appear to vary by O(10%) depending upon the Gribov copy chosen; this is true not only of local quantities such as the magnetic current density [19] but also of supposedly long range, physical numbers such as the Abelian and monopole string tensions [7,18]. Some criterion must be employed for the selection of the maxima of R, and in the absence of a clear understanding of which maximum, if any, is the most 'physical', one maximum was selected at random in [1].…”

Section: This Calculationmentioning

confidence: 99%

Monopole clusters,Z(2)vortices, and confinement in SU(2)

Hart

Teper

1999

Phys. Rev. D

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Abstract.We extend our previous study of magnetic monopole currents in the maximally Abelian gauge [1] to larger lattices at small lattice spacings (20 4 at β = 2.5 and 32 4 at β = 2.5115). We confirm that at these weak couplings there continues to be one monopole cluster that is very much longer than the rest and that the string tension, K, is entirely due to it. The remaining clusters are compact objects whose population as a function of radius follows a power law that deviates from the scale invariant form, but much too weakly to suggest a link with the analytically calculable size distribution of small instantons. We also search for traces of Z(2) vortices in the Abelian projected fields; either as closed loops of 'magnetic' flux or through appropriate correlations amongst the monopoles. We find, by direct calculation, that there is no confining condensate of such flux loops. We also find, through the calculation of doubly charged Wilson loops within the monopole fields, that there is no suppression of the q = 2 effective string tension out to at distances of at least r ≃ 1.6/ √ K, suggesting that if there are any vortices they are not encoded in the monopole fields.

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“…Unambiguous computation of the gauge fixed configuration is impossible, and certain quantities such as the monopole density are fairly sensitive to this ambiguity [ 7,8]. One would like to have a smooth gauge without lattice Gribov problem.…”

Section: Introductionmentioning

confidence: 99%