Cartan Connections and Integrable Vortex Equations
arXiv:2112.08328 · doi:10.1016/j.geomphys.2022.104613
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.
20 pages, 1 figure