D6-branes and torsion

Abstract

The D6-brane spectrum of type IIA vacua based on twisted tori T̃6 and RR background fluxes is analyzed. In particular, we compute the torsion factors of Hn(T̃6,ℤ) and describe the effect that they have on D6-brane physics. For instance, the fact that H3(T̃6,ℤ) contains ℤN 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.