Vortex structure vs. monopole dominance in Abelian-projected gauge theory

Ambjørn, J.; Giedt, Joel; Greensite, Jeff

doi:10.1088/1126-6708/2000/02/033

Cited by 101 publications

(128 citation statements)

References 22 publications

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“…In the two-point correlation functions, the exponential decay has been observed for the parallel propagator 80) and for the perpendicular propagator…”

Section: Color Direction Fieldmentioning

confidence: 95%

“…80 80 The RDE in the reformulated Yang-Mills theory has the same form as that considered in BOT [161], but its reasoning behind the RDE is quite different from the previous one, as can be seen from its derivation in Appendix of [19].…”

Section: Reduction Conditionmentioning

confidence: 96%

“…If this is the case, then the 4π monopole flux is not distributed symmetrically on the Abelian-projected lattice, in contrast to the situation one might expect in a Coulomb gas. Rather, it is collimated in units of ±2π along the vortex line [48,78,80]. If this picture is correct, then a vortex sheet on V 2 , a vortex line on S 1 = ∂V 2 , and the magnetic monopoles on C 0 = ∂S 1 = ∂∂V 2 have the mutual positional relation as shown in Fig.…”

Section: = 3 Vortexmentioning

confidence: 98%

“…This paper does not discuss the center vortex picture for confinement. See e.g., [48] for the review on maximal center gauge and also [78,79,80] for the relationship between the center vortex and magnetic monopole.…”

Section: 3)mentioning

confidence: 99%

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Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

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The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the YangMills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator.Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole.We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark confinement. The Wilson loop average is calculated according to the new reformulation written in terms of new field variables obtained from the original Yang-Mills field based on change of variables. The Maximally Abelian gauge in the original Yang-Mills theory is also reproduced by taking a specific gauge fixing in the reformulated Yang-Mills theory. This observation justifies the preceding results obtained in the maximal Abelian gauge at least for gaugeinvariant quantities for SU(2) gauge group, which eliminates the criticism of gauge artifact raised for the Abelian projection. The claim has been confirmed based on the numerical simulations.However, for SU(N) (N ≥ 3), such a gauge-invariant reformulation is not unique, although the extension along the line proposed by Cho, Faddeev and Niemi is possible. In fact, we have found that there are a number of possible options of the reformulations, which are discriminated by the maximal stability 1 groupH of G, while there is a unique option ofH = U(1) for G = SU(2). The maximal stability group depends...

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“…In the two-point correlation functions, the exponential decay has been observed for the parallel propagator 80) and for the perpendicular propagator…”

Section: Color Direction Fieldmentioning

confidence: 95%

Section: Reduction Conditionmentioning

confidence: 96%

Section: = 3 Vortexmentioning

confidence: 98%

Section: 3)mentioning

confidence: 99%

See 2 more Smart Citations

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

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“…On the other hand numerical evidence has emerged [14][15][16][17][18][19][20][21][22][23][24][25][26][27] in favor of the so called center vortex picture where the vacuum consists of a coherent condensate of magnetic flux tubes. Also this theoretical proposal has been advanced long time ago [28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Abelian monopole and vortex condensation in lattice gauge theories

Cea

Cosmai

2001

J. High Energy Phys.

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We study Abelian monopole and vortex condensation in lattice pure gauge theories. Condensation is detected by means of a disorder parameter defined in terms of a gauge-invariant effective action introduced using the lattice Schrödinger functional. Dirac monopoles condense in the confined phase of U(1) lattice gauge theory. Abelian monopoles and Abelian vortices condense in the confined phase of SU(2) and SU(3) lattice gauge theories.

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