Type IIB S-folds: flat deformations, holography and stability

We review recent progress in the study of S-folds in light of the gauge/gravity duality and the AdS swampland conjecture. S-folds correspond to non-geometric backgrounds of type IIB supergravity of the form $\,\textrm{AdS}_4 \, \times \, \textrm{S}^1 \, \times \, \mathcal{M}\,$ that involve a non-trivial $\,\textrm{SL}(2,\,\mathbb{Z})\,$ (S-duality) monodromy for the type IIB fields when moving around the $\,\textrm{S}^1$. We present four such solutions with $\,\mathcal{M}=\textrm{S}^{5}\,$ that preserve $\,\mathcal{N}=4,2,1,0\,$ supersymmetries. Via the AdS/CFT correspondence, these solutions are conjectured to describe new strongly coupled three-dimensional CFT's on a localised interface of SYM. We discuss the existence of flat deformations in the gravity side dual to marginal deformations of the conjectured S-fold CFT's. From a geometrical perspective, the flat deformations induce a monodromy $\,h\,$ on $\,\mathcal{M}\,$ and replace $\,\textrm{S}^1 \,\times\, \mathcal{M}\,$ by the so-called mapping torus $\,T(\mathcal{M})_h$. Interestingly, the flat deformations provide a controlled mechanism of supersymmetry breaking for $\,\mathcal{N} \ge 2\,$ S-folds. We present a class of such non-supersymmetric S-folds obtained by flat-deforming the $\,\mathcal{N}=4\,$ S-fold and discuss their (non-)perturbative stability.