$\mathcal{N}=2$ ${\text{CFT}}_3\text{’s}$ from $\mathcal{N}=4$ gauged supergravity

Abstract

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 $\text{ISO}(3)\times \text{ISO}(3)$ 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.

35 pages, 1 figure. v2: clarifications added, published version

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