Laplacian abelian projection

Sijs, A.J. van der

doi:10.1016/s0920-5632(96)00710-4

Cited by 35 publications

(52 citation statements)

References 10 publications

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“…That the lowest adjoint Laplacian eigenmode on an instanton background has a zero of second order at the instanton location has been shown in the continuum in [34]. Zeroes in this mode underly the construction of Abelian projected monopoles in the Laplacian Abelian gauge [36]. Thus, for calorons these monopoles coincide with the (gauge independent) constituent monopoles.…”

Section: Adjoint Representationmentioning

confidence: 85%

Laplacian modes probing gauge fields

Bruckmann

Ilgenfritz

2005

Phys. Rev. D

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We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU (2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison.In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.

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Section: Adjoint Representationmentioning

confidence: 85%

Laplacian modes probing gauge fields

Bruckmann

Ilgenfritz

2005

Phys. Rev. D

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“…However, they are confirmed only in specific gauges, i.e., Abelian gauges, such as the MA gauge, Laplacian Abelian gauge [42,43] and maximal center gauge [48]. All these gauge fixing break color symmetry explicitly.…”

Section: 3)mentioning

confidence: 99%

“…We adopt the Euclidean formulation. The following functional F MAG of the off-diagonal gluon field A a µ (x) is minimized, i.e., min ω F MAG [A ω ] with respect to the gauge transformation ω: 43) where (·, ·) is the L 2 inner product.…”

Section: Maximally Abelian Gaugementioning

confidence: 99%

“…Subsequently, Bruckmann, Heinzl, Vekua and Wipf (BHVW) [162] have performed a systematic and analytical treatment to this problem within the Laplacian Abelian gauge (LA gauge, LAG) [43], 169 which has succeeded to shed new light on the relationship between an Abelian magnetic monopole and an instanton from a different angle. In the LA gauge, zeros of an auxiliary Higgs field φ(x) induce topological defects in the gauge potential, upon diagonalization.…”

Section: Brief History Before Our Workmentioning

confidence: 99%

“…(5.136) 43 The derivation of this identity was given in Appendix B of [24], which is presented later in this chapter.…”

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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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Monopoles From Instantons

Bruckmann

2002

Confinement, Topology, and Other Non-Perturbative Aspects of QCD

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The relation between defects of Abelian gauges and instantons is discussed for explicit examples in the Laplacian Abelian gauge. The defect coming from an instanton is pointlike and becomes a monopole loop with twist upon perturbation. The interplay between magnetic charge, twist and instanton number -encoded as a Hopf invariantis investigated with the help of a new method, an auxiliary Abelian fibre bundle.

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Laplacian abelian projection

Cited by 35 publications

References 10 publications

Laplacian modes probing gauge fields

Laplacian modes probing gauge fields

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

Monopoles From Instantons

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