The Holographic Conformal Manifold of 3d $\mathcal{N}=2$ $S$-fold SCFTs

We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS$_4$ J-fold solutions preserving $\mathcal{N}=2$ supersymmetry. All solutions preserve $\mathfrak{u}(1)\times\mathfrak{u}(1)$ global symmetry and in special limits we recover the previously known $\mathfrak{su}(2)\times\mathfrak{u}(1)$ invariant $\mathcal{N}=2$ and $\mathfrak{su}(2)\times\mathfrak{su}(2)$ invariant $\mathcal{N}=4$ J-fold solutions. This family of AdS$_4$ backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional $S$-fold SCFTs obtained from the $\mathcal{N}=4$ $T[\text{U}(N)]$ theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS$_4$ solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.