MiS Preprint Repository

In this paper, we will study the partial regularity for stationary Dirac-harmonic maps with $\lambda -$curvature term. For a weakly stationary Dirac-harmonic map with $\lambda -$curvature term $(\varphi ,\psi )$ from a smooth bounded open domain $\mathrm{\Omega }\subset {\mathbb{R}}^m$ with $m\ge 2$ to a compact Riemannian manifold $N$, if $\psi \in W^{1,p}(\mathrm{\Omega })$ for some $p>\frac{2m}{3}$, we prove that $(\varphi ,\psi )$ is smooth outside a closed singular set whose $(m-2)$-dimensional Hausdorff measure is zero. Furthermore, if the target manifold $N$ does not admit any harmonic sphere $S^l$, $l=2,...,m-1$, then $(\varphi ,\psi )$ is smooth.