Anomalies, Branes, and Currents

TL;DR

The paper extends the anomaly inflow framework to D-branes wrapping curved cycles with twisted normal bundles, showing that formerly non-factorizable anomalies become cancelable once topological data, encoded in Euler classes, are incorporated. It introduces a symmetric Ramond-Ramond action and carefully treats brane currents to derive consistent equations of motion and inflow cancellations, including nontransversal intersections. The authors also compute how normal-bundle twisting modifies induced Ramond-Ramond charges across representative Type II compactifications, linking anomaly cancellation to RR-charge induction in string dualities. Overall, the work provides a robust topological mechanism for ensuring brane configuration consistency in curved backgrounds and connects anomaly inflow to observable RR-charge shifts.

Abstract

When a D-brane wraps around a cycle of a curved manifold, the twisting of its normal bundle can induce chiral asymmetry in its worldvolume theory. We obtain the general form of the resulting anomalies for D-branes and their intersections. They are not cancelled among themselves, and the standard inflow mechanism does not apply at first sight because of their apparent lack of factorizability and the apparent vanishing of the corresponding inflow. We show however after taking into consideration the effects of the nontrivial topology of the normal bundles, the anomalies can be transformed into factorized forms and precisely cancelled by finite inflow from the Chern-Simons actions for the D-branes as long as the latter are well defined. We then consider examples in type II compactifications where the twisting of the normal bundles occurs and calculate the changes in the induced Ramond-Ramond charges on the D-branes.