Magnetic monopoles, center vortices, confinement and topology of gauge fields

Reinhardt, Hugo; Engelhardt, Michael; Langfeld, Kurt; Quandt, Markus; Schäfke, A.

doi:10.1063/1.1303019

Cited by 3 publications

(7 citation statements)

References 18 publications

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“…To ground that the area law is satisfied for Wilson loops U C,Z2 , (2.32), in that theory (at N = 2), it is necessary [6,8] to consider a large area A in a certain plane containing a loop of a much smaller area A W .…”

Section: Topological Specific Of So(3) Group Spacementioning

confidence: 99%

“…Herewith the given number N 1 of intersection points of (thick) vortices with the area A with those with A W is distributed randomly [8].…”

Section: Topological Specific Of So(3) Group Spacementioning

confidence: 99%

“…For this random distribution of intersection points, the probability to find n intersection points in A W is given by [6,8]…”

Section: Topological Specific Of So(3) Group Spacementioning

confidence: 99%

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Fermions with spin 1/2 as global SO(3) vortices

Lantsman

2007

Preprint

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Section: Topological Specific Of So(3) Group Spacementioning

confidence: 99%

“…Herewith the given number N 1 of intersection points of (thick) vortices with the area A with those with A W is distributed randomly [8].…”

Section: Topological Specific Of So(3) Group Spacementioning

confidence: 99%

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Fermions with spin 1/2 as global SO(3) vortices

Lantsman

2007

Preprint

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“…In relativistic quantum fields nexus is the monopole, in which N vortices of the group Z N meet at a center (nexus) provided the total flux of vortices adds to zero (mod N ) [2,3]. In a chiral superfluid with the order parameter of the 3 He-A type, the analog of the nexus is the hedgehog in thel field, in which 4 vortices meet, each with the circulation quantum number N = 1/2. The total topological charge of the four vortices is N = 2 which is equivalent to N = 0 because the homotopy group, which describes the 3 He-A vortices, is π 1 = Z 4 [4], and thus N = 0 (mod 2).…”

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confidence: 99%

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confidence: 99%

Monopole, half-quantum vortex, and nexus in chiral superfluids and superconductors

Volovik

1999

Jetp Lett.

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Two exotic objects are still not identified experimentally in chiral superfluids and superconductors. These are the half-quantum vortex, which plays the part of the Alice string in relativistic theories [1], and the hedgehog in thel field, which is the counterpart of the Dirac magnetic monopole. These two objects of different dimensionality are topologically connected. They form the combined object which is called nexus in relativistic theories [2]. Such combination will allow us to observe half-quantum vortices and monopoles in several realistic geometries.

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Monopoles and fractional vortices in chiral superconductors

Volovik

2000

Proc. Natl. Acad. Sci. U.S.A.

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I discuss two exotic objects that must be experimentally identified in chiral superfluids and superconductors. These are (i) the vortex with a fractional quantum number (N ‫؍‬ 1͞2 in chiral superfluids, and N ‫؍‬ 1͞2 and N ‫؍‬ 1͞4 in chiral superconductors), which plays the part of the Alice string in relativistic theories and (ii) the hedgehog in theˆl field, which is the counterpart of the Dirac magnetic monopole. These objects of different dimensions are topologically connected. They form the combined object that is called a nexus in relativistic theories. In chiral superconductors, the nexus has magnetic charge emanating radially from the hedgehog, whereas the half-quantum vortices play the part of the Dirac string. Each half-quantum vortex supplies the fractional magnetic flux to the hedgehog, representing 1͞4 of the ''conventional'' Dirac string. I discuss the topological interaction of the superconductor's nexus with the 't Hooft-Polyakov magnetic monopole, which can exist in Grand Unified Theories. The monopole and the hedgehog with the same magnetic charge are topologically confined by a piece of the Abrikosov vortex. Such confinement makes the nexus a natural trap for the magnetic monopole. Other properties of half-quantum vortices and monopoles are discussed as well, including fermion zero modes. Magnetic monopoles do not exist in classical electromagnetism. Maxwell equations show that the magnetic field is divergenceless, ٌ⅐B ϭ 0, which implies that the magnetic flux through any closed surface is zero: ͛ S dS⅐B ϭ 0. If one tries to construct the monopole solution B ϭ gr͞r 3 , the condition that magnetic field is nondivergent requires that magnetic flux ⌽ ϭ 4g from the monopole must be accompanied by an equal singular flux supplied to the monopole by an attached Dirac string. Quantum electrodynamics, however, can be successfully modified to include magnetic monopoles. In 1931, Dirac (1) showed that the string emanating from a magnetic monopole becomes invisible for electrons if the magnetic flux of the monopole is quantized in terms of the elementary magnetic fluxwhere e is the charge of the electron. In 1974, it was shown by 't Hooft (2) and Polyakov (3) that a magnetic monopole with quantization of the magnetic charge, according to Eq. 1, can really occur as a physical object if the U(1) group of electromagnetism is a part of the higher symmetry group. The magnetic flux of a monopole in terms of the elementary magnetic flux coincides with the topological charge of the monopole: this quantity remains constant under any smooth deformation of the quantum fields. Such monopoles can appear only in Grand Unified Theories, where all interactions are united by, say, the SU(5) group.In the Standard Model of electroweak interactions, such monopoles do not exist, but the combined objects monopole ϩ string can be constructed without violating of the condition ٌ⅐B ϭ 0. Further, following the terminology of ref. 4, I shall call such a combined object a nexus. In a nexus, the magnetic monopole looks like a Dirac m...

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Magnetic monopoles, center vortices, confinement and topology of gauge fields

Cited by 3 publications

References 18 publications

Fermions with spin 1/2 as global SO(3) vortices

Fermions with spin 1/2 as global SO(3) vortices

Monopole, half-quantum vortex, and nexus in chiral superfluids and superconductors

Monopoles and fractional vortices in chiral superconductors

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