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Magnetic Dirac-harmonic maps

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Abstract

We study a functional, whose critical points couple Dirac-harmonic maps from surfaces with a two form. The critical points can be interpreted as coupling the prescribed mean curvature equation to spinor fields. On the other hand, this functional also arises as part of the supersymmetric sigma model in theoretical physics. In two dimensions it is conformally invariant. We call critical points of this functional magnetic Dirac-harmonic maps. We study geometric and analytic properties of magnetic Dirac-harmonic maps including their regularity and the removal of isolated singularities.

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  1. Institut für Diskrete Mathematik und Geometrie, TU Wien Wiedner Hauptstraße 8–10, 1040 , Wien, Austria

    Volker Branding

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  1. Volker Branding
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Correspondence to Volker Branding.

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Branding, V. Magnetic Dirac-harmonic maps. Anal.Math.Phys. 5, 23–37 (2015). https://doi.org/10.1007/s13324-014-0081-1

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  • DOI: https://doi.org/10.1007/s13324-014-0081-1

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