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Qun Chen, Jürgen Jost, Jiayu Li and Guofang Wang
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.