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Five vortex equations

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Manton, NS 

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.

Description

Keywords

U(1) vortices, Baptista metric, conical singularities, Liouville equation

Journal Title

Journal of Physics A: Mathematical and Theoretical

Conference Name

Journal ISSN

1751-8113
1751-8121

Volume Title

50

Publisher

IOP Publishing
Sponsorship
Science and Technology Facilities Council (ST/L000385/1)
Science and Technology Facilities Council (ST/P000681/1)