Brane resolution and gravitational Chern-Simons terms

We show that gravitational Chern-Simons corrections, associated with the (sigma)-model anomaly on the M5-brane worldvolume, can resolve the M2-brane solution with Ricci-flat, special holonomy transverse space. We explicitly find smooth solutions in the cases when the transverse space is a manifold of Spin(7) holonomy and SU(4) holonomy. We comment on the consequences of these results for the holographically related three-dimensional theories living on the worldvolume of a stack of such resolved M2 branes.