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arXiv · 2604.05676

Vortex Harmonic Spinors on the Nappi-Witten Space

Calum Ross·Raúl Sánchez Galán
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Abstract

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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Calum Ross, Raúl Sánchez Galán. 2026-04-07. Vortex Harmonic Spinors on the Nappi-Witten Space. https://doi.org/10.1016/j.geomphys.2026.105917

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