Stable knot-like structures in classical field theory

Faddeev, L. D.; Niemi, Antti J.

doi:10.1038/387058a0

Cited by 618 publications

(679 citation statements)

References 11 publications

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“…It has been proposed as a low energy limit of Yang-Mills theory. The higher derivative terms makes three dimensional topological soliton solutions possible [2]. Properties as a topological charge and a lower bound to the mass is associated to the solitons.…”

Section: Introductionmentioning

confidence: 99%

The supersymmetric extension of the Faddeev model

Freyhult

2004

Nuclear Physics B

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We study the supersymmetric extension of the Faddeev model in four dimensions. The Faddeev model contains three dimensional soliton solutions and we are interested in how these solitons are affected by supersymmetry. We consider both the N = 1 and N = 2 extensions and find that in neither case it is possible to supersymmetrize the model without adding additional bosonic terms. There are essentially two ways of constructing the supersymmetric theory, one that will lead to a model which allows for solitons and another that gives a model where solitons are excluded.The N = 2 model is studied since extending supersymmetry is the natural way of including topological charges in the algebra. A lower bound to the mass is obtained by computing the central charge. The result is that it is possible to have a non-trivial lower bound on the mass, this in principle allows for massive solitons.

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Section: Introductionmentioning

confidence: 99%

The supersymmetric extension of the Faddeev model

Freyhult

2004

Nuclear Physics B

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“…For this we can use the analytic expression [25] of the SU (2) Polyakov loop along the z-axis. The location of the spurious defect, z 1 = (0, 0, z), is found by solving 3πµ 2 …”

Section: Spurious Defectsmentioning

confidence: 99%

“…The hope was that the static knotted solutions constructed numerically [2] in the model originally introduced by Faddeev [3], were possibly related to glueballs [4]. A difficulty is that one would not expect dynamics for a quantity that is associated with the colour direction, due to gauge invariance.…”

Section: Introductionmentioning

confidence: 99%

Reflections on topology - viewpoints on abelian projections

Baal

2002

Nuclear Physics B - Proceedings Supplements

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This talk discusses two topological features in non-abelian gauge theories, related by the notion of abelian projection and the Hopf invariant. Minimising the energy of the non-linear sigma model with a Skyrme-like term (the Faddeev-Niemi model), can be identified with a non-linear maximal abelian gauge fixing of the SU (2) gauge vacua with a winding number equal to the Hopf invariant. In the context of abelian projection the Hopf invariant can also be associated to a monopole world line, through the Taubes winding, measuring its contribution to topological charge. Calorons with non-trivial holonomy provide an explicit realisation. We discuss the identification of its constituent monopoles through degenerate eigenvalues of the Polyakov loop (the singularities or defects of the abelian projection). It allows us to study the correlation between the defect locations and the explicit constituent monopole structure, through a specific SU (3) example.

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“…In this Letter we address some simple results that involve rewriting the Faddeev-Niemi model [1]. This model has stable static solutions that represent knots.…”

Section: Introductionmentioning

confidence: 99%

Classical gauge vacua as knots

Baal

Wipf

2001

Physics Letters B

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The four dimensional O(3) non-linear sigma model introduced by Faddeev and Niemi, with a Skyrme-like higher order term to stabilise static knot solutions classified by the Hopf invariant, can be rewritten in terms of the complex two-component CP 1 variables. A further rewriting of these variables in terms of SU(2) curvature free gauge fields is performed. This leads us to interpret SU(2) pure gauge vacuum configurations, in a particular maximal abelian gauge, in terms of knots with the Hopf invariant equal to the winding number of the gauge configuration.

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Stable knot-like structures in classical field theory

Cited by 618 publications

References 11 publications

The supersymmetric extension of the Faddeev model

The supersymmetric extension of the Faddeev model

Reflections on topology - viewpoints on abelian projections

Classical gauge vacua as knots

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