Abstract
We construct a gravitational-anomaly-free effective action for the coupled system of type-IIA $D=10$ dynamical supergravity interacting with a NS5-brane. The NS5-brane is considered as elementary in that the associated current is a $\ensuremath{\delta}$ function supported on its world volume. Our approach is based on a Chern kernel which encodes the singularities of the three-form field strength near the brane in an SO(4)-invariant way and provides a solution for its Bianchi identity in terms of a two-form potential. A dimensional reduction of the recently constructed anomaly-free effective action for an elementary M5-brane in $D=11$ is seen to reproduce our ten-dimensional action. The Chern-kernel approach provides in particular a concrete realization of the anomaly cancellation mechanism envisaged by Witten.
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