Vortex Harmonic Spinors on the Nappi-Witten Space

TL;DR

This paper establishes a geometric link between vortex equations on flat surfaces and harmonic spinors on the Nappi-Witten space, leading to explicit solutions and magnetic zero-modes on Minkowski space.

Contribution

It introduces a novel correspondence between vortex configurations and harmonic spinors on a specific group manifold, enabling explicit solution construction.

Findings

Explicit solutions of twisted Dirac equations from vortex data

Harmonic spinors on Minkowski space derived from Nappi-Witten space

Construction of Abelian magnetic zero-modes on flat spacetime

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.