S-folds and $Ad{S}_3$ flows from the D3-brane

We investigate supersymmetric flows in type IIB supergravity that preserve an $SO(2,2)$ space-time symmetry and asymptote to $Ad{S}_5\times S^5$ at both endpoints. The flows are constructed as Janus-type $\mathbb{R}\times Ad{S}_3$ BPS domain-walls in the effective four-dimensional $[SO(1,1)\times SO(6)]⋉{\mathbb{R}}^{12}$ gauged maximal supergravity describing the massless sector of type IIB supergravity compactified on $S^1\times S^5$. The compactification includes an S-duality hyperbolic twist along the $S^1$ which, when combined with an appropriate choice of boundary conditions for the running scalars, generates special flows that develop an S-fold regime at their core, thus enhancing the space-time symmetry there to $SO(2,3)$. Via the AdS/CFT correspondence, the flows constructed here are conjectured to describe conformal interfaces in a circle compactification of $\mathcal{N}=4$ ${\text{SYM}}_4$.