We construct infinite new classes of $AdS_4\times S^1\times S^5$ solutions of type IIB string theory which have non-trivial $SL(2,\mathbb{ Z})$ monodromy along the $S^1$ direction. The solutions are supersymmetric and holographically dual, generically, to $\mathcal{ N}=1$ SCFTs in $d=3$. The solutions are first constructed as $AdS_4\times \mathbb{ R}$ solutions in $D=5$ $SO(6)$ gauged supergravity and then uplifted to $D=10$. Unlike the known $AdS_4\times \mathbb{ R}$ S-fold solutions, there is no continuous symmetry associated with the $\mathbb{ R}$ direction. The solutions all arise as limiting cases of Janus solutions of $d=4$, $\mathcal{ N}=4$ SYM theory which are supported both by a different value of the coupling constant on either side of the interface, as well as by fermion and boson mass deformations. As special cases, the construction recovers three known S-fold constructions, preserving $\mathcal{ N}=1,2$ and 4 supersymmetry, as well as a recently constructed $\mathcal{ N}=1$ $AdS_4\times S^1\times S^5$ solution (not S-folded). We also present some novel "one-sided Janus" solutions that are non-singular.
Categories: hep-th