Dirac-harmonic maps from index theory
  We prove existence results for Dirac-harmonic maps using index theoretical tools. They are mainly interesting if the source manifold has dimension 1 or 2 modulo 8. Our solutions are uncoupled in the sense that the underlying map between the source and target manifolds is a harmonic map. 
Bernd Ammann and Nicolas Ginoux
math.DG math.AP