  We introduce a functional that couples the nonlinear sigma model with a
spinor field:
  $L=\int_M[|d\phi|^2+(\psi,\D\psi)]$. In two dimensions, it is conformally
invariant. The critical points of this functional are called Dirac-harmonic
maps. We study some geometric and analytic aspects of such maps, in particular
a removable singularity theorem.
