Type IIB flux compactifications with $h^{1,1}=0$

We revisit flux compactifications of type IIB string theory on `spaces' dual to rigid Calabi-Yau manifolds. This rather unexplored part of the string landscapes harbors many interesting four-dimensional solutions, namely supersymmetric $\mathcal{N}=1$ Minkowski vacua without flat direction and infinite families of AdS vacua, some potentially with unrestricted rank for the gauge group. We also comment on the existence of metastable dS solutions in this setup. We discuss how these solutions fit into the web of swampland conjectures.

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