Magnetic Dirac-harmonic maps

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.

References in corpus (4)

• Dirac-harmonic maps from index theory
• Liouville Theorems for Dirac-Harmonic Maps
• Bundle Gerbes and Surface Holonomy
• Regularity at the free boundary for Dirac-harmonic maps from surfaces

Cited by in corpus (11)

• Some aspects of Dirac-harmonic maps with curvature term
• Dirac-harmonic maps with torsion
• Energy estimates for the supersymmetric nonlinear sigma model and applications
• The heat flow for the full bosonic string
• On the evolution of regularized Dirac-harmonic Maps from closed surfaces
• A vanishing result for the supersymmetric nonlinear sigma model in higher dimensions
• On conservation laws for the supersymmetric sigma model
• Energy methods for Dirac-type equations in two-dimensional Minkowski space
• A global weak solution to the full bosonic string heat flow
• Nonlinear Dirac equations, Monotonicity Formulas and Liouville Theorems
• Dirac-harmonic maps with potential