Regularity of Dirac-harmonic maps with lambda -curvature term in higher dimensions

Abstract

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 (phi ,psi ) from a smooth bounded open domain Omega subset {mathbb {R}}^m with mge 2 to a compact Riemannian manifold N, if psi in W^{1,p}(Omega ) for some p>frac{2m}{3}, we prove that (phi , 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,ldots , m-1, then (phi ,psi ) is smooth.