$\mathcal{N}=2$ $\,\textrm{CFT}_{3}\textrm{'s}\,$ from $\,\mathcal{N} = 4\,$ gauged supergravity

We use holography and four-dimensional $\,\mathcal{N}=4\,$ gauged supergravity to collect evidence for a large class of interconnected three-dimensional $\,\mathcal{N}=2\,$ conformal field theories. On the gravity side, we construct a one-parameter family of $\,{\textrm{ISO}(3) \times \textrm{ISO}(3)}$ gaugings of half-maximal supergravity containing a rich structure of $\,\mathcal{N}=2\,$ AdS$_{4}$ solutions at fixed radius. By looking at excitations around these AdS$_{4}$ solutions, the spectrum of low lying operators in the dual $\,\mathcal{N}=2\,$ CFT$_{3}$'s is computed and further arranged into $\,\mathfrak{osp}(2|4)$ supermultiplets. Upon suitable removal of gauge redundancies, we identify the Zamolodchikov metric on the conformal manifold dual to the AdS$_{4}$ moduli space, and recover previous results in the S-fold literature. Two special points of $\,\mathcal{N}=4\,$ supersymmetry enhancement occur. While one describes an S-fold CFT$_{3}$ dual to a non-geometric type IIB twisted compactification, the string-theoretic realisation of the other, if any, is still lacking.