Abstract
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 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 and hbox {dS}_3 vacua, but such effects seem to be hindered by the geometric flux quantization.
Highlights
String flux compactifications down to dimensions different than four are a valuable resource for our understanding of the swampland
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 AdS3 vacua, and once we include brane-supersymmetrybreaking we find indication for the existence of classical 3D de Sitter solutions
For the reasons outlined above, in this work we continue the study of Type II string flux compactifications with threedimensional external space and minimal supersymmetry, that was initiated in [14,15]
Summary
In this subsection we discuss the basic features of the seven dimensional internal space X to be used in our compactifications. Previous works [14,15] studied the case where ∇ = 0 and all torsions were simultaneously set to zero, the internal space was Ricci flat and the G2 structure group was equivalent to the G2 holonomy of the manifold. Which is the case of co-calibrated G2-structures due to the closure of This happens because the eliminated torsion classes, which were one- and two-forms, were not invariant under the orbifold action. The Betti numbers, which depend on the presence of Wi , coincide with those of the G2 holonomy case b1(X ) = 0, b2(X ) = 0, b3(X ) = 7 This means that the torsion class W27 can be expanded in the fundamental basis i , which will be important for our calculations later. Which gives an exact expression for the W1 torsion class in terms of the moduli si and the geometric fluxes
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