On vortices and rings in extended Abelian models

Doudoulakis, C.G.

doi:10.1016/j.physd.2007.06.019

Cited by 2 publications

(2 citation statements)

References 25 publications

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“…One can therefore wonder whether such solutions exist. This question has actually a long history, being first addressed by de Vega [49] and by Huang and Tipton [93] over 30 years ago, and being then repeatedly reconsidered by different authors [109], [130], [74], [174], [95], [57], [55], [56].…”

Section: J Searching For Gauged Knotsmentioning

confidence: 99%

“…Trying to find the answer, all the authors were minimizing the energy given by the sum of E[Φ, A k ] and of a potential term that can be either of the form contained in (2.34) or a more general one. A theory with two vector fields with a local U(1)×U(1) invariance -Witten's model of superconducting strings [177] -has also been considered in this context [57], [55], [56]. The energy was minimized within classes of fields with a given topological charge N and having profiles of a loop of radius R. The resulting minimal value of energy was always found to be a monotonously growing function of R, thus always showing the tendency of the loop to shrink thereby reducing its energy.…”

Section: J Searching For Gauged Knotsmentioning

confidence: 99%

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Stationary ring solitons in field theory — Knots and vortons

2008

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We review the current status of the problem of constructing classical field theory solutions describing stationary vortex rings in Minkowski space in 3 + 1 dimensions. We describe the known up to date solutions of this type, such as the static knot solitons stabilized by the topological Hopf charge, the attempts to gauge them, the anomalous solitons stabilized by the Chern-Simons number, as well as the non-Abelian monopole and sphaleron rings. Passing to the rotating solutions, we first discuss the conditions insuring that they do not radiate, and then describe the spinning Q-balls, their twisted and gauged generalizations reported here for the first time, spinning skyrmions, and rotating monopole-antimonopole pairs. We then present the first explicit construction of global vortons as solutions of the elliptic boundary value problem, which demonstrates their non-radiating character. Finally, we describe the analogs of vortons in the Bose-Einstein condensates, analogs of spinning Q-balls in the non-linear optics, and also moving vortex rings in superfluid helium and in ferromagnetics.

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Section: J Searching For Gauged Knotsmentioning

confidence: 99%

Section: J Searching For Gauged Knotsmentioning

confidence: 99%

Stationary ring solitons in field theory — Knots and vortons

2008

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Vortices and superfields on a graph

2009

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We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the 'theory space'. We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U (1) gauge symmetry.We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multi-vector, multi-Higgs models. In our model, [U (1)] p (where p is the number of vertices) is broken to a single U (1). Therefore for specific graphs, we get vortex-like classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.

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On vortices and rings in extended Abelian models

Cited by 2 publications

References 25 publications

Stationary ring solitons in field theory — Knots and vortons

Stationary ring solitons in field theory — Knots and vortons

Vortices and superfields on a graph

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