Five vortex equations
Accepted version
Peer-reviewed
Repository URI
Repository DOI
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
1751-8121
Volume Title
50
Publisher
IOP Publishing
Publisher DOI
Sponsorship
Science and Technology Facilities Council (ST/L000385/1)
Science and Technology Facilities Council (ST/P000681/1)
Science and Technology Facilities Council (ST/P000681/1)