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

TL;DR

This paper investigates RR charge cancellation in string compactifications using D-brane probes, revealing that uncancelled charges cause gauge anomalies and establishing a probe-based criterion for consistency, especially in complex geometries.

Contribution

It introduces a probe-based method to analyze RR charge cancellation, extending consistency checks beyond vacuum states to include topological sectors and K-theory charges.

Findings

Uncancelled RR charges lead to gauge anomalies on D-brane probes.

Tadpole cancellation ensures consistency across all topological sectors.

Models with canceled RR charge but nontrivial K-theory charge are inconsistent due to anomalies.

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.