Intersecting D-branes, Chern-kernels and the inflow mechanism

We analyse a system of arbitrarily intersecting D-branes in ten-dimensional supergravity. Chiral anomalies are supported on the intersection branes, called I-branes. For non-transversal intersections anomaly cancellation has been realized until now only cohomologically but not locally, due to short-distance singularities. In this paper we present a consistent local cancellation mechanism, writing the delta-like brane currents as differentials of the recently introduced Chern--kernels, J=dK. In particular, for the first time we achieve anomaly cancellation for dual pairs of D-branes. The Chern-kernel approach allows to construct an effective action for the RR-fields which is free from singularities and cancels the quantum anomalies on all D-branes and I-branes.