Volker Branding

Some aspects of Dirac-harmonic maps with curvature term

We study several geometric and analytic aspects of Dirac-harmonic maps with curvature term from closed Riemannian surfaces.

Dirac-harmonic maps with torsion

We study Dirac-harmonic maps from surfaces to manifolds with torsion, which is motivated from the superstring action considered in theoretical physics. We discuss analytic and geometric properties of such maps and outline an existence result for uncoupled solutions.

Magnetic Dirac-harmonic maps

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.

BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time

In this paper we present a family of supersymmetric Wilson loops of

Energy Estimates for the Supersymmetric Nonlinear Sigma Model and Applications

\mathcal{N}=4

The evolution equations for regularized Dirac-geodesics

supersymmetric Yang-Mills theory in Minkowski space. Our examples focus on curves restricted to hyperbolic submanifolds,

The heat flow for the full bosonic string

{\mathbb{H}}_{3}

An estimate on the nodal set of eigenspinors on closed surfaces

and

Energy methods for Dirac-type equations in two-dimensional Minkowski space

{\mathbb{H}}_{2}

On Conservation Laws for the Supersymmetric Sigma Model

, of space-time. Generically they preserve two supercharges, but in special cases more, including a case which has not been discussed before, of the hyperbolic line, conformal to the straight line and circle, which is