Anomaly free effective action for the elementary M5-brane

We construct an effective action describing an elementary M5-brane interacting with dynamical eleven-dimensional supergravity, which is free from gravitational anomalies. The current associated to the elementary brane is taken as a distribution valued δ-function on the support of the 5-brane itself. Crucial ingredients of the construction are the consistent inclusion of the dynamics of the chiral two-form on the 5-brane, and the use of an invariant Chern-kernel allowing to introduce a D=11 three-form potential which is well-defined on the worldvolume of the 5-brane.