D-brane anomaly inflow revisited

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Axial and gravitational anomaly of field theories, when embedded in string theory, must be accompanied by canceling inflow. We give a self-contained overview for various world-volume theories, and clarify the role of smeared magnetic sources in I-brane/D-brane cases. The proper anomaly descent of the source, as demanded by regularity of RR field strengths H's, turns out to be an essential ingredient. We show how this allows correct inflow to be generated for all such theories, including self-dual cases, and also that the mechanism is now insensitive to the choice between the two related but inequivalent forms of D-brane Chern-Simons couplings. In particular, SO(6)ᵣ axial anomaly of d=4 maximal SYM is canceled by the inflow onto D3-branes via the standard minimal coupling to C₄. We also propose how, for the anomaly cancelation, the four types of Orientifold planes should be coupled to the spacetime curvatures, of which conflicting claims existed previously.