Three-dimensional flux vacua from IIB on co-calibrated G2 orientifolds

We derive the 3D N = 1 superpotential for the closed string sector of type IIB supergravity on toroidal O5 orientifolds with co-calibrated G2 structure and RR background flux. We find that such compactifications can provide full closed string moduli stabilization on supersymmetric $$\hbox {AdS}_3$$ AdS 3 vacua, and once we include brane-supersymmetry-breaking we also find indication for the existence of classical 3D de Sitter solutions. The latter however are rather difficult to reconcile with the “shape” moduli stabilization and flux quantization. We also discuss the possibility of achieving scale separation in $$\hbox {AdS}_3$$ AdS 3 and $$\hbox {dS}_3$$ dS 3 vacua, but such effects seem to be hindered by the geometric flux quantization.

Dirac Operator on a 7-Manifold with Deformed G2 Structure

In this work, we consider the deforming of a G2 structure by a vector field on a 7-manifold. To obtain the metric corresponding to deformed G2 structure, a new map is defined. By using this new map, the co- variant derivatives on associated spinor bundles are compared. Then, the relation between Dirac operators on spinor bundles are investigated under some restrictions.