Anomalies, Branes, and Currents

TL;DR

This paper investigates how topological twisting of normal bundles in D-branes wrapping curved cycles induces anomalies, and demonstrates their cancellation via inflow mechanisms considering the topology, with applications to type II compactifications.

Contribution

It derives the general anomaly form for twisted D-branes, shows how to factorize and cancel these anomalies using inflow, and applies the results to specific string theory compactification examples.

Findings

Anomalies from twisted normal bundles can be factorized and canceled.

The inflow mechanism applies when considering the topology of normal bundles.

Changes in Ramond-Ramond charges are computed in specific compactification scenarios.

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.