Freed-Witten anomaly in general flux compactification

Turning on a NS-NS three-form flux in a compact space drives some D-branes to be either Freed-Witten anomalous or unstable to decay into fluxes by the appearance of instantonic branes. By applying T-duality on a toroidal compactification, the NS-flux is transformed into metric fluxes. We propose a T-dual version of the Atiyah-Hirzebruch Spectral Sequence upon which we describe the Freed-Witten anomaly and the brane-flux transition driven by NS and metric fluxes in a twisted torus. The required conditions to cancel the anomaly and the appearance of new instantonic branes are also described. In addition, we give an example in which all D6-branes wrapping Freed-Witten anomaly-free three-cycles in the twisted torus T^6/Z(2)XZ(2) are nevertheless unstable to be transformed into fluxes. Evenmore we find a topological transformation between RR, NS-NS and metric fluxes driven by a chain of instantonic branes.