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 –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.