D-brane probes, RR tadpole cancellation and K-theory charge

TL;DR

The paper develops a probe-based framework to study RR tadpole cancellation in string vacua with open strings, showing that uncancelled RR charges appear as chiral world-volume anomalies on suitable D-brane probes. This links tadpole cancellation to the full consistency of the compactified theory across topological sectors and clarifies why tadpole constraints are stronger than vacuum anomaly cancellation. By applying probes to curved K3 orientifolds and to torsion (K-theory) charges, Uranga demonstrates how global anomalies on probes signal inconsistencies and derive K-theory consistency conditions. The approach provides practical tools for verifying consistency in complex vacua and highlights the role of K-theory in D-brane charge cancellation.

Abstract

We study RR charge cancellation consistency conditions in string compactifications with open string sectors, by introducing D-brane probes in the configuration. We show that uncancelled charges manifest as chiral gauge anomalies in the world-volume of suitable probes. RR tadpole cancellation can therefore be described as the consistency of the effective compactified theory not just in the vacuum, but also in all topological sectors (presence of D-brane probes). The result explains why tadpole cancellation is usually much stronger than anomaly cancellation of the compactified theory (in the vacuum sector). We use the probe criterion to construct consistent six-dimensional orientifolds of curved K3 spaces, where usual CFT techniques to compute tadpoles are not valid. As a last application, we consider compactifications where standard RR charge cancels but full K-theory charge does not. We show the inconsistency of such models manifests as a global gauge anomaly on the world-volume of suitable probes.