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Vortex Harmonic Spinors on the Nappi–Witten Space
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We establish a correspondence between vortex equations on flat Riemann surfaces and harmonic spinors on the Nappi–Witten space, the group manifold of a central extension of the Euclidean group SE(2). Vortex configurations lift naturally to this setting, producing explicit solutions of a twisted Dirac equation. Using the conformal flatness of the Nappi–Witten metric, these solutions induce harmonic spinors on four-dimensional Minkowski space. This yields a geometric construction of Abelian magnetic zero-modes on flat Minkowski spacetime from vortex data.
Title: Vortex Harmonic Spinors on the Nappi–Witten Space
Description:
We establish a correspondence between vortex equations on flat Riemann surfaces and harmonic spinors on the Nappi–Witten space, the group manifold of a central extension of the Euclidean group SE(2).
Vortex configurations lift naturally to this setting, producing explicit solutions of a twisted Dirac equation.
Using the conformal flatness of the Nappi–Witten metric, these solutions induce harmonic spinors on four-dimensional Minkowski space.
This yields a geometric construction of Abelian magnetic zero-modes on flat Minkowski spacetime from vortex data.
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