A Torsion Correction to the RR 4-Form Fieldstrength

TL;DR

This paper proposes a torsion correction to the RR 4-form field strength in type IIA string theory, derived from D2-brane anomaly cancellation, aligning with known O4-plane tensions and K-theory classifications.

Contribution

It introduces a torsion correction to the RR 4-form field strength in type IIA, addressing previous inconsistencies and connecting fluxes to K-theory.

Findings

Consistent shifted quantization condition for G_4 in IIA.

Torsion correction aligns with O4-plane tensions.

RR fluxes lift to K-theory classes.

Abstract

The shifted quantization condition of the M-theory 4-form G_4 is well-known. The most naive generalization to type IIA string theory fails, an orientifold counterexample was found by Hori in hep-th/9805141. In this note we use D2-brane anomaly cancellation to find the corresponding shifted quantization condition in IIA. Our analysis is consistent with the known O4-plane tensions if we include a torsion correction to the usual construction of G_4 from C_3, B and G_2. The resulting Bianchi identities enforce that RR fluxes lift to K-theory classes.