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arXiv · 2112.08328

Cartan Connections and Integrable Vortex Equations

Calum Ross
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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.

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Calum Ross. 2021-12-15. Cartan Connections and Integrable Vortex Equations. https://doi.org/10.1016/j.geomphys.2022.104613

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