Branes and Fluxes in Orientifolds and K-theory

TL;DR

This paper compares K-theory and cohomology classifications of RR fluxes in string backgrounds with orientifold planes, revealing new relations between branes and obstructions, and establishing conditions to prevent gauge anomalies.

Contribution

It introduces a comparison between K-theory and cohomology classifications of fluxes in orientifold backgrounds, uncovering new correlations and topological conditions for anomaly avoidance.

Findings

New correlations between branes on orientifold planes and obstructions.

A topological condition to prevent global gauge anomalies.

Comparison of K-theory and cohomology classifications via spectral sequence.

Abstract

RR fields in string backgrounds including orientifold planes and branes on top of them are classified by K-theory. Following the idea introduced in hep-th/0103183, we also classify such fluxes by cohomology. Both of them are compared through the Atiyah-Hirzebruch Spectral Sequence. Some new correlations between branes on orientifold planes $Op^\pm$ and obstructions to the existence of some branes are found. Finally, we find a topological condition that avoid the presence of global gauge anomalies in lower dimensional systems.