Ross, Calum;
(2022)
Cartan connections and integrable vortex equations.
Journal of Geometry and Physics
, 179
, Article 104613. 10.1016/j.geomphys.2022.104613.
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Abstract
We demonstrate that integrable abelian vortex equations on constant curvature Riemann surfaces can be reinterpreted as flat non-abelian Cartan connections. By lifting to three dimensional group manifolds we find higher dimensional analogues of vortices. These vortex configurations are also encoded in a Cartan connection. We give examples of different types of vortex that can be interpreted this way, and compare and contrast this Cartan representation of a vortex with the symmetric instanton representation.
| Type: | Article |
|---|---|
| Title: | Cartan connections and integrable vortex equations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.geomphys.2022.104613 |
| Publisher version: | https://doi.org/10.1016/j.geomphys.2022.104613 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Integrable vortex equations, Cartan geometry, Dirac Operator |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10152305 |
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