Non-abelian Tensor-multiplet Anomalies

We use the anomaly cancellation of the M-theory fivebrane to derive the R-symmetry anomalies of the $A_{N}$ $(0,2)$ tensor-multiplet theories. This result leads to a simple derivation of black hole entropy in $d=4, \mathcal{N}=2$ compactifications of $M$-theory. We also show how the formalism of normal bundle anomaly cancellation clarifies the Kaluza-Klein origin of Chern-Simons terms in gauged supergravity theories. The results imply the existence of interesting 1/N corrections in the AdS/CFT correspondence.