Magnetic Dirac-harmonic maps

TL;DR

This paper introduces magnetic Dirac-harmonic maps, a new class of critical points coupling Dirac-harmonic maps with a two-form, with applications in geometry and theoretical physics, focusing on their properties and singularity behavior.

Contribution

It defines magnetic Dirac-harmonic maps, explores their geometric and analytic properties, and investigates regularity and singularity removal, linking geometry with supersymmetric sigma models.

Findings

Establishment of regularity results for magnetic Dirac-harmonic maps

Analysis of singularity removal for these maps

Connection to supersymmetric sigma models in physics

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.