Cartan Connections and Integrable Vortex Equations

DOI10.1016/J.GEOMPHYS.2022.104613arXiv2112.08328WikidataQ114173370 ScholiaQ114173370MaRDI QIDQ6385791

Publication date: 15 December 2021

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.

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of global analysis to the sciences (58Z05) Applications of differential geometry to physics (53Z05) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

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