| Summary: | Abstract We use holography and four-dimensional N $$ \mathcal{N} $$ = 4 gauged supergravity to collect evidence for a large class of interconnected three-dimensional N $$ \mathcal{N} $$ = 2 conformal field theories. On the gravity side, we construct a one-parameter family of ISO(3) × ISO(3) gaugings of half-maximal supergravity containing a rich structure of N $$ \mathcal{N} $$ = 2 AdS4 solutions at fixed radius. By looking at excitations around these AdS4 solutions, the spectrum of low lying operators in the dual N $$ \mathcal{N} $$ = 2 CFT3’s is computed and further arranged into 𝔬𝔰(2|4) supermultiplets. Upon suitable removal of gauge redundancies, we identify the Zamolodchikov metric on the conformal manifold dual to the AdS4 moduli space, and recover previous results in the S-fold literature. Two special points of N $$ \mathcal{N} $$ = 4 supersymmetry enhancement occur. While one describes an S-fold CFT3 dual to a non-geometric type IIB twisted compactification, the string-theoretic realisation of the other, if any, is still lacking.
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