The Local Structure of Anomaly Inflow
  Anomaly cancellation for M-theory fivebranes requires the introduction of a "bump-form" which smoothes out the five-brane source. We discuss the physical origin of this bump-form in the simpler case of axion strings in 3+1 dimensions and construct it in terms of the radial profile of the fermion zero modes. Our treatment allows for a clearer understanding of the role played by covariant rather than consistent anomalies when anomalies are canceled by inflow from the bulk. We briefly discuss the generalization of these results to fivebrane anomalies in M theory. 
Jeffrey A. Harvey and Oleg Ruchayskiy