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Center Vortex
Center vortices are line-like topological defects that exist in the vacuum of Yang–Mills theory and QCD. There is evidence in lattice simulations that they play an important role in the confinement of quarks. Topological description Center vortices carry a gauge charge under the center elements of the universal cover of the gauge group ''G''. Equivalently, their topological charge is an element of the fundamental group of this universal cover quotiented by its center. On a 2-dimensional space ''M'' a center vortex at a point ''x'' may be constructed as follows. Begin with a trivial ''G'' bundle over ''M''. Cut along a circle linking ''x''. Glue the total space back together with a transition function which is a map from the cut circle to a representation of ''G''. The new total space is the gauge bundle of a center vortex. Now the vortex at ''x'' is constructed. Its topological charge can be computed as follows. Lifting this map up to the universal cover of ''G'', ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Topological Defect
In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in a physical system that are stable against perturbations. Solitons do not decay, dissipate, disperse or evaporate in the way that ordinary waves (or solutions or structures) might. The stability arises from an obstruction to the decay, which is explained by having the soliton belong to a different topological homotopy class or cohomology class than the base physical system. More simply: it is not possible to continuously transform the system with a soliton in it, to one without it. The mathematics behind topological stability is both deep and broad, and a vast variety of systems possessing topological stability have been described. This makes categorization somewhat difficult. Overview The original soliton was observed in the 19th century, as a solitary water wave in a barge canal. It was eventually explained by noting that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Wilson Loop
In quantum field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops. They encode all gauge information of the theory, allowing for the construction of loop representations which fully describe gauge theories in terms of these loops. In pure gauge theory they play the role of order operators for confinement, where they satisfy what is known as the area law. Originally formulated by Kenneth G. Wilson in 1974, they were used to construct links and plaquettes which are the fundamental parameters in lattice gauge theory. Wilson loops fall into the broader class of loop operators, with some other notable examples being 't Hooft loops, which are magnetic duals to Wilson loops, and Polyakov loops, which are the thermal version of Wilson loops. Definition To properly define Wilson loops in gauge theory requires considering the fiber bundle formulation of gauge theories. Here for each point in the d-dim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
't Hooft Loop
In quantum field theory, the 't Hooft loop is a magnetic analogue of the Wilson loop whose spatial loop operator give rise to thin loops of magnetic flux associated with magnetic vortices. They play the role of a disorder parameter for the Higgs phase in pure gauge theory. Consistency conditions between electric and magnetic charges limit the possible 't Hooft loops that can be used, similarly to the way that the Dirac quantization condition limits the set of allowed magnetic monopoles. They were first introduced by Gerard 't Hooft in 1978 in the context of possible phases that gauge theories admit. Definition There are a number of ways to define 't Hooft lines and loops. For timelike curves C they are equivalent to the gauge configuration arising from the worldline traced out by a magnetic monopole. These are singular gauge field configurations on the line such that their spatial slice have a magnetic field whose form approaches that of a magnetic monopole : B^i \xright ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
