@article{BrandingDrukker2009,
  author    = {Branding, Volker and Drukker, Nadav},
  title     = {BPS Wilson loops in N=4 supersymmetric Yang-Mills theory : examples on hyperbolic submanifolds of space-time},
  issn      = {1550-7998},
  doi       = {10.1103/Physrevd.79.106006},
  year      = {2009},
  abstract  = {In this paper we present a family of supersymmetric Wilson loops of N=4 supersymmetric Yang-Mills theory in Minkowski space. Our examples focus on curves restricted to hyperbolic submanifolds, H-3 and H-2, 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 1/2 BPS. We discuss some general properties of these Wilson loops and their string duals and study special examples in more detail. Generically the string duals propagate on a complexification of AdS(5)xS(5) and in some specific examples the compact sphere is effectively replaced by a de Sitter space.},
  language  = {en}
}
@phdthesis{Branding2012,
  author    = {Branding, Volker},
  title     = {The evolution equations for Dirac-harmonic Maps},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64204},
  school      = {Universit{\"a}t Potsdam},
  year      = {2012},
  abstract  = {This thesis investigates the gradient flow of Dirac-harmonic maps. Dirac-harmonic maps are critical points of an energy functional that is motivated from supersymmetric field theories. The critical points of this energy functional couple the equation for harmonic maps with spinor fields. At present, many analytical properties of Dirac-harmonic maps are known, but a general existence result is still missing. In this thesis the existence question is studied using the evolution equations for a regularized version of Dirac-harmonic maps. Since the energy functional for Dirac-harmonic maps is unbounded from below the method of the gradient flow cannot be applied directly. Thus, we first of all consider a regularization prescription for Dirac-harmonic maps and then study the gradient flow. Chapter 1 gives some background material on harmonic maps/harmonic spinors and summarizes the current known results about Dirac-harmonic maps. Chapter 2 introduces the notion of Dirac-harmonic maps in detail and presents a regularization prescription for Dirac-harmonic maps. In Chapter 3 the evolution equations for regularized Dirac-harmonic maps are introduced. In addition, the evolution of certain energies is discussed. Moreover, the existence of a short-time solution to the evolution equations is established. Chapter 4 analyzes the evolution equations in the case that the domain manifold is a closed curve. Here, the existence of a smooth long-time solution is proven. Moreover, for the regularization being large enough, it is shown that the evolution equations converge to a regularized Dirac-harmonic map. Finally, it is discussed in which sense the regularization can be removed. In Chapter 5 the evolution equations are studied when the domain manifold is a closed Riemmannian spin surface. For the regularization being large enough, the existence of a global weak solution, which is smooth away from finitely many singularities is proven. It is shown that the evolution equations converge weakly to a regularized Dirac-harmonic map. In addition, it is discussed if the regularization can be removed in this case.},
  language  = {en}
}