Why are fractional charges of orientifolds compatible with Dirac quantization?

TL;DR

This paper resolves the apparent inconsistency of fractional orientifold charges with Dirac quantization by analyzing worldvolume fermion anomalies using eta invariants, linking to topological phases and duality groups.

Contribution

It provides a detailed explanation of how anomaly considerations reconcile fractional orientifold charges with Dirac quantization, connecting string theory and topological phases.

Findings

Fractional D-brane charges are consistent with Dirac quantization when anomalies are properly accounted for.

The anomaly analysis involves eta invariants of worldvolume fermions.

The duality group of type IIB is identified as the pin+ version of the double cover of GL(2,Z).

Abstract

Orientifold $p$-planes with $p\le4$ have fractional D$p$-charges, and therefore appear inconsistent with Dirac quantization with respect to D$(6-p)$-branes. We explain in detail how this issue is resolved by taking into account the anomaly of the worldvolume fermions using the $\eta$ invariants. We also point out relationships to the classification of interacting fermionic symmetry protected topological phases. In an appendix, we point out that the duality group of type IIB string theory is the pin+ version of the double cover of $GL(2,\mathbb{Z})$.