Orientifolds, RR Torsion, and K-theory

TL;DR

This paper explores how K-theory provides a more accurate framework than cohomology for understanding RR fluxes and charges in orientifold backgrounds, revealing new physical insights and equivalences.

Contribution

It demonstrates that K-theory naturally explains fractional RR charge shifts and clarifies the classification of orientifold backgrounds compared to cohomology.

Findings

Fractional RR charge shifts are explained by K-theory.

Some orientifold backgrounds are equivalent in K-theory but distinct in cohomology.

Certain backgrounds become unphysical in the K-theory framework.

Abstract

We analyze the role of RR fluxes in orientifold backgrounds from the point of view of K-theory, and demonstrate some physical implications of describing these fluxes in K-theory rather than cohomology. In particular, we show that certain fractional shifts in RR charge quantization due to discrete RR fluxes are naturally explained in K-theory. We also show that some orientifold backgrounds, which are considered distinct in the cohomology classification, become equivalent in the K-theory description, while others become unphysical.