D6-branes and torsion

TL;DR

This paper investigates the impact of torsion in (co)homology groups on D6-brane physics in type IIA flux compactifications, revealing effects on tadpole conditions, moduli stabilization, and anomalies.

Contribution

It provides a detailed analysis of torsion factors in (co)homology, explaining their influence on D6-brane properties and flux vacua construction in type IIA string theory.

Findings

Torsion in (co)homology affects RR tadpole conditions.

Torsional (co)homology lifts some D6-brane moduli.

Geometrical understanding of Freed-Witten anomaly in this setup.

Abstract

The D6-brane spectrum of type IIA vacua based on twisted tori and RR background fluxes is analyzed. In particular, we compute the torsion factors of the (co)homology groups H_n and describe the effect that they have on D6-brane physics. For instance, the fact that H_3 contains Z_N subgroups explains why RR tadpole conditions are affected by geometric fluxes. In addition, the presence of torsional (co)homology shows why some D6-brane moduli are lifted, and it suggests how the D-brane discretum appears in type IIA flux compactifications. Finally, we give a clear, geometrical understanding of the Freed-Witten anomaly in the present type IIA setup, and discuss its consequences for the construction of semi-realistic flux vacua.