Five vortex equations
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Authors
Publication Date
2017-02-24Journal Title
Journal of Physics A: Mathematical and Theoretical
ISSN
1751-8113
Publisher
IOP Publishing
Volume
50
Number
125403
Language
English
Type
Article
This Version
AM
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Manton, N. (2017). Five vortex equations. Journal of Physics A: Mathematical and Theoretical, 50 (125403)https://doi.org/10.1088/1751-8121/aa5f19
Abstract
The Taubes equation for Abelian Higgs vortices is generalised to five distinct U(1) vortex equations. These include the Popov and Jackiw–Pi vortex equations, and two further equations. The Baptista metric, a conformal rescaling of the background metric by the squared Higgs field, gives insight into these vortices, and shows that vortices can be interpreted as conical singularities superposed on the background geometry. When the background has a constant curvature adapted to the vortex type, then the vortex equation is integrable by a reduction to Liouville's equation, and the Baptista metric has a constant curvature too, apart from its conical singularities. The conical geometry is fairly easy to visualise in some cases.
Sponsorship
STFC (ST/L000385/1)
STFC (ST/P000681/1)
Identifiers
External DOI: https://doi.org/10.1088/1751-8121/aa5f19
This record's URL: https://www.repository.cam.ac.uk/handle/1810/263897
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