Center projection vortices in continuum Yang–Mills theory

Engelhardt, Michael; Reinhardt, Hugo

doi:10.1016/s0550-3213(99)00727-0

Cited by 168 publications

(341 citation statements)

References 59 publications

(82 reference statements)

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“…In fact, Reinhardt and Tok [171] have investigated the relationship among Abelian magnetic monopoles and center vortices in various Yang-Mills back ground fields: one meron, one instanton, instanton-antiinstanton pair, using both the LA gauge and the Laplacian center gauge (LC gauge, LCG). It has been pointed out that an Abelian magnetic monopole and a meron pair are mediated by sheets of center vortices [113]. In fact, Montero and Negele [172] have obtained an Abelian magnetic monopole loop and center vortices for two merons (a meron pair) by using numerical simulations on a lattice, see also [169] for related works.…”

Section: Brief History Before Our Workmentioning

confidence: 99%

“…Hence, the differential reduction condition can also be expressed in terms of V µ and X µ in the vector form: 113) or in the Lie algebra form: 115) and the number of conditions for…”

Section: Reduction Condition In the Maximal Optionmentioning

confidence: 99%

“…20. This may be related to the fact that each self-intersection point of a vortex surface contributes ±k/N (k = 1, · · · , N − 1) to the Pontryagin index [113].…”

Section: = 4 Vortexmentioning

confidence: 99%

“…See also [164,165,166,167,168] for relationships among various topological objects. In the course of studying the relationship between Abelian magnetic monopoles and center vortices [48], merons [174] are recognized as an important object [113,114,170]. Merons [174,175,178] are solutions of the Yang-Mills field equation and are characterized by one half topological charge, i.e., having half-integer Pontryagin index.…”

Section: Brief History Before Our Workmentioning

confidence: 99%

“…This leads to the trace: using the cyclicity of the trace and the unitarity 113) while using the traceless property tr(F µν ) = 0,…”

Section: Chromoelectric Field and Flux Tube Formationmentioning

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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Section: Brief History Before Our Workmentioning

confidence: 99%

“…Hence, the differential reduction condition can also be expressed in terms of V µ and X µ in the vector form: 113) or in the Lie algebra form: 115) and the number of conditions for…”

Section: Reduction Condition In the Maximal Optionmentioning

confidence: 99%

“…20. This may be related to the fact that each self-intersection point of a vortex surface contributes ±k/N (k = 1, · · · , N − 1) to the Pontryagin index [113].…”

Section: = 4 Vortexmentioning

confidence: 99%