Why are fractional charges of orientifolds compatible with Dirac quantization?

Understand

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 $GL(2,\mathbb{Z})$.